An Analysis of Price Volatility, Trading Volume and Market Depth of Stock Futures Market in India

TABLE OF CONTENTS

Chapter - I

Introduction and Research Design

Chapter - II

Review of Literature

Chapter - III

Theoretical Overview of Futures and Option Market

Chapter - IV
4.1 Introduction
4.2 Econometric Methodology
4.2.1 Unit Root Test
4.2.1.1 Augmented Dickey Fuller Test
4.2.1.2 Phillips-Peron (PP) test
4.2.2 GARCH Model
4.2.3 Augmented GARCH Model
4.2.3.1 Expected Components of Trading Volume Open Interest
4.2.3.2 Unexpected Components of Trading Volume Open Interest
4.3 Results and Discussion
4.4 Conclusion

Chapter - V
5.1 Introduction
5.2 Econometric Methodology - Linear and Non- Linear Models
5.3 Results Discussion
5.4 Forecast Evaluation
5.5 Summary and Conclusion

Chapter - VI
Summary, Conclusion and Policy Implications

Bibliography

CHAPTER - I

INTRODUCTION AND RESEARCH DESIGN

Every modern economy is based on a sound financial system and acts as a monetary channel for productive purpose with effecting economic growth. It encourages saving habit by throwing open and plethora of instrument avenues suiting to the individuals requirements, mobilizing savings from households and other segments and allocating savings into productive usage such as trade, commerce, manufacture etc. Thus a financial system can also be understood as institutional arrangements, through which financial surpluses are mobilized from the units generating surplus income and transferring them to the others in need of them. In nutshell, financial market, financial assets, financial services and financial institutions constitute the financial system. The activities include exchange and holding of financial assets or instruments of different kinds of financial institutions, banks and other intermediaries of the market. Broadly speaking, the organizational structure of financial system includes the following three components; they are

- Financial Markets.
- Financial Institutions and Intermediaries.
- Financial Products.

Financial markets provide channels for allocation of savings to investment and provide variety of assets to savers in various forms in which the investors can park their funds. At the same time, financial market is one that integral part of the financial system which makes significant contribution to the countries’ economic development. It establishes a link between the demand and supply of long-term capital funds. The economic strength of a country depends squarely on the state of financial market, apart from the productive potential of the country. The efficient allocation of fund by the capital market depends on the state of capital market. All the countries therefore focus more on the functioning of the capital market. Indian financial market has faced many challenges in the process of effecting more efficient allocation and mobilization of capital. It has attained a remarkable degree of growth in the last decade and in continuing to achieve the same in current decade also. Opening up of the economy and adoption of the liberalized economic policies have driven our economy more towards the free market. Over the last few years, financial markets, more specifically the security market were experiencing a lot of structural and regulatory changes. The major constituents of financial market are money market and the capital market catering to the type of capital requirements.

The capital market is a market for financial investments that are direct or indirect claims to capital (Gart, 1988)^[1]. It is wider than the securities market and embraces all forms of lending and borrowing, whether or not evidenced by the creation of a negotiable financial instrument (Drake, 1980)^[2]. The capital market comprises the complex of institutions and mechanisms through which intermediate term funds and long term funds are pooled and made available to business, government and individuals. The capital market also encompasses the process by which securities already outstanding are transferred (Dougall, 1986)^[3].

Money Market: The money market refers to the market where borrowers and lenders exchange short-term funds to solve their liquidity needs. Money market instruments are generally financial claims that have low default risk, maturities under one year and high marketability.

Capital Market: It is a wide term used to comprise all operations in the new issues and stock market. New issues made by the companies constitute the primary market, while trading in the existing securities relate to the secondary market. It is to be noted that we can only buy in the primary market and not sell, but we can buy and sell securities in the secondary market. All long-term borrowings and lending constitute the capital market.

The securities market, however, refers to the market for those financial instruments that are commonly and readily transferable by sale. The securities market has two inter-dependent and inseparable segments they are, new issues (primary) market and the stock (secondary) market. The primary market provides the channel for sale of new securities, while the secondary market deals in securities previously issued. The issuer of securities sells the securities in the primary market to raise funds for investment and to discharge some obligation. The secondary market enables those who hold securities to adjust their holdings in response to changes in their assessment and risk and return. They also sell securities for cash to meet their liquidity needs. The price signals, which subsume all information about the issuer and his business including, associated risk generated in the secondary market, help the primary market in allocation of funds. This secondary market has further two components.

1. The spot market where securities are traded for immediate delivery and payment, the other is futures market where the securities are traded for future delivery and payment.

2. Another variant is the options market where securities are traded for conditional future delivery. Generally, two types of options are traded in the options market. A put option permits the owner to sell a security to the writer of the option at a pre-determined price before a certain date, while a call option permits the buyer to purchase a security from the writer of the option at a particular price before a certain date.

The market for derivatives has grown rapidly during the past decade owing to the broad range of applications for these derivative products and their wide acceptance by financial and non-financial firms. Financial derivatives are contracts that derive their value from an underlying asset or index. They are broadly grouped into currency derivatives, equity derivatives, commodity derivatives and interest derivatives. Nowadays, all firms are facing numerous kinds of risk in their normal course of business activities. Along with this, the development of economic globalization has led the society to what is called as a ‘risky environment’ by unfavorable external and internal disequilibrium. Due to the increased effects of globalization, economies are invariably exposed to global market factors and are volatile and sensitive to rising level of complexity of risks and changing conditions. Hence risk has become universal. However, to word of the ill effect of wide fluctuation and risk various financial innovations have taken place at all times. Derivatives are the most important among them, off late the uses of derivatives have become very predominant because of increased globalization and financial integration causing unpredictable variables and fluctuations. To mitigate the effects of these fundamental risks, firms are using financial derivatives. Employing the right strategy is only half the battle won; companies need to constantly monitor and assess the effectiveness of the hedging tools employed and ensure from time to time that they are in synchronized with the exposed risk.

With continuous innovation of financial instruments, rapid expansion of financial assets, terrorist attacks, corporate and risk management failures, risk management is a forefront topic in management today. Cutting across all functional areas, they occupy the top of the priority list of the management. The recent financial crises has proved this fact, and proved that the deterioration in the financial system has the potential to plunge the overall economy into a crisis despite the solid macroeconomic base of an economy. Financial risk is negligible and create excessive financial losses that are either endogenous which is under management’s control or exogenous over which there is little or no control. The financial risk management deals with financial risks arising from either macro-economic factors like a catastrophe or terrorist attack etc., or from micro economic factors like exchange rate, interest rate, stock prices, commodity prices etc. Though derivative instruments provide benefits they come with certain risks as well. The specific risks arising out of usage of a particular derivative transaction largely depends on the terms of the transaction, financial condition, time frame of the contract, adversities in the macro and micro environment, and circumstances of the parties involved in the transaction.

Need of the Study

Derivative market as a counterpart of security market has been accepted worldwide. Even the developing countries have realized the importance of derivatives market. Despite the growing importance of derivative market over the past decades in depth study in derivative market are very few which can throw light on various relationship and on its inherent characteristics etc. Though studies are plenty in stock market, very few studies have been done on derivatives at national and international level. Even within the available researchers at the international level also the studies are mostly confined to U.S and Australia, and there is very little evidence of the existing literature in South Asia. Those few studies also do not throw much light on the in depth understanding of the derivative market characteristics as the results of consensus.

The impact of derivative market on the spot market in terms of market volatility, price changes etc also need careful and consorted analysis. Financial sector reforms, impact of technology, liberalization policy of the government, trend of globalization, etc., are the contributors to the development of derivative markets. Derivatives markets have been outstandingly successful due to reduction of funding costs by borrowers, enhancing the yield on assets, modifying the payment structure of assets. However, the policymakers, practitioners and regulators in these markets are concerned about the impact of derivatives market. One of the reasons for this concern is the belief that derivative trading may attract speculators who then destabilize spot prices. In the flipside, the presence of derivative market helps the speculators to take advantage of booking profit by entering in both the markets and their active presence may also bring a destabilizing effect in the stock market. It is believed that the speculators take advantage of earning profit when the volatility of share increases and as the volatility decreases the investors start investing in the stock market to make profit. The above diversified theoretical arguments create phenomenon of stock return and trading volume an important field for study.

The structural changes on the capital market more specifically stock market kindled by the financial reforms has brought the derivative market to a comparable global standard. The introduction of derivative market also was another step in furthering the capital market’s development at par with developed market. In the present scenario, there is a need for in depth study of derivatives market and its link with the underlying security market and the price discovery process and forecasting the market volatility. The relationship between the settlement prices, trading volume, open interest and volatility etc, modeling and forecasting volatility for stock futures contract still remains the muddy water in the context of changing scenario and the behaviour of market players etc.

Statement of Problem

The fluctuations in futures markets has its root with the underlying spot market volatility, trading activity etc which are not only explained by publicly available information but also by non-information like trade due to certain events, short selling and insider trading etc. These factors are considered to be the important information which influences both future prices and price fluctuations in futures market. Price movements, trading volumes and open interest can be jointly considered as aggregate market information and the volatility measures derived from high-frequency data may prove to be more information, and may help in better forecast. Since, most existing studies have focused on the relationship between market returns and trading activity variables, and only limited studies are available in the U.S and Australian futures markets in terms of examining open interest, this study tries to bring all the three variables together to study the inherent character of derivative market in India.

To understand market dynamics an accurate forecast is important to both practitioners and academicians. Modelling and forecasting volatility in stock futures contracts is one of the important areas in the finance literature. But existing literature reveals that most studies have focused on stock index futures and petroleum futures in the U.S markets. In India, no attempt has been made towards forecasting the volatility and its dynamics for stock futures contracts. Against this backdrop, it is worthwhile to study the relationship between the multivariate series and to identify the suitable model to forecast volatility for select stock futures contracts in India. The complexities of relationship between the variables, and difficulty in forecasting the volatility are still grey in derivatives market study. Hence the research has been made by the researcher to make an in-depth study.

Objectives of the Study

1. To study the conceptual framework of derivatives and development of derivatives market in India.
2. To assess the dynamic relationship between price volatility, trading volume and market depth for select stock futures contracts in India.
3. To identify the suitable model to forecast volatility for stock futures contracts in India.
4. Finally, to summarize the findings and provide suggestions for the policy makers, academicians and research community.

Hypothesis

In an attempt to study the price volatility, trading volume and market depth in Indian futures market and to identify a suitable model for forecasting volatility the following hypothesis are set;

1. Information arrival is simultaneous for all investors.
2. There is a positive contemporaneous relationship between futures returns and trading volume.
3. Volatility of stock futures contracts can be forecasted by linear models.
4. A nonlinear forecasting model can better forecast the volatility.

Research Gap of the Study

The study has been developed on the background of earlier studies attempted in this area. In empirical finance literature, there are many empirical papers that provide indirect evidence on the relationship between trading volume and stock returns. Clark (1973) examined Mixture of Distributions Hypothesis which plays a prominent role in the empirical finance arena. As suggested by Morgan (1976) volume is regarded as a major risk factor contributing to the volatility of returns, particularly in less liquid and thin markets including emerging markets. In the mixture model of Epps and Epps (1976), trading volume is used to measure disagreement among traders, as investors revise their reservation prices based on the arrival of new information to the market. Similarly, positive contemporaneous relationship between variance of price change and trading volume was linked by Ragalski (1978), Figlewski and Cornell (1981) who studied the basic relationship between the variables. Tauchen and Pitts (1983), and Lastrapes and Lamoureux (1990) alleges that the conditional heteroskedasticity in stock returns can be explained by a serially correlated mixing variable that measures the rate at which information is transmitted to the market. These authors have shown that the information arrivals stemming from the existence of exogenous variables which can be identified by the mixture of distributions, and these variables exhibit time-varying ARCH effect.

There is quite a strong body of literature advocating the use of the GARCH family of models to test the relationship between these variables. Lamoureux and Lastrapes (1990) examined the presence of ARCH/GARCH based on the hypothesis that daily returns are generated by a mixture of distributions, using trading volume as a proxy for the rate of daily information arrival. They found that volatility persistence vanishes under the presence of trading volume series in the conditional variance equation. Brailsford (1996) found that the direction in price change was significant across three measures of daily trading volume for the aggregate market and was significant for individual stocks. An overwhelming number of studies have examined both theoretical and empirical relationship between future return, trading volume and open interest. Bessembinder and Seguin (1993) investigated the relations between volume, volatility, and market depth in eight physical and financial futures markets and suggested that unexpected volume shocks have a larger effect on volatility, the role of open interest provides information to mitigate volatility and he suggested that the volatility-volume relation in financial markets depends on the type of trader. A large number of studies have been conducted at international level to test the relationship between futures return, trading volume and open interest contacts, whereas in India the empirical works are quite limited. Pati Kumar (2006) tested the maturity, volume effects and volatility dynamics for Indian futures market and suggested that time-to-maturity is not a strong determinant for futures price volatility, but rate of information arrival proxies by volume and open interest are the important sources of volatility. Finally, they concluded that Samuelson Hypothesis does not provide support for Indian futures market so the investors should not base their investment decision on time-to-maturity. Hence, the current study attempts to shed light on the existing literature and to examine the relationship between future return, trading volume and market depth for stock futures contracts in India.

As far as modelling and forecasting is concerned, there exist a strand of literature focusing on the modelling and forecasting of equity markets by Akgiray (1989), Dimson and Marsh (1990), Pagan and Schwert (1990), Bollerslev et.al (1992), Francis and Van Dijk (1996), Brailsford and Faff (1996), McMillan, Speight and Gwilym (2000) and Brooks and Persand (2002). The observations of these studies are; First, large changes tend to be followed by large changes and small changes tend to be followed by small changes, which mean that volatility clustering is observed in financial returns data. Secondly, financial time series data often exhibit leptokurtosis, which indicate that the return distribution is fat-tailed as observed by Mandelbrot (1963), Fama (1965), Laurent and Peters (2002). Finally, changes in stock prices tend to be negatively related to changes in stock volatility which is identified to be “leverage effect” Black (1976), Christie (1982), Nelson (1991), Koutmas and Saidi (1995).

In light of the importance of volatility in financial markets, a seminal contribution to the study of stock market volatility was of Schwert (1989). He sought to establish which economic variables are highly correlated with volatility in returns, and found little evidence that volatility in economic fundamentals had a discernible influence on stock market returns. He conjectured that, in general, GARCH effects in earlier studies were really measuring the persistence in the arrival of new information. To capture the above uniqueness, ARCH class of models were introduced by Engle (1982) and GARCH (Generalized Autoregressive Conditional Heteroskedasticity) by Bollerslev (1986) and Taylor (1986). Financial economists have long known that the daily range of the log price series contains extra information about the course of volatility over the day. Despite the elegant theory and the support of simulation results, the price range as a proxy of volatility has performed poorly in empirical studies. Therefore, the GARCH type of models are the most-adopted ones for modeling the time-varying conditional volatility, as they considers time varying variance as a function of lagged squared residuals and lagged conditional variance.

There exists quite a number of research work done on modelling and forecasting volatility at international level, however only a limited attempt has been made the Indian stock market in this direction. Varma (1999) examined the volatility estimation models comparing GARCH and EWMA models in the risk management setting. Pandey (2002) analyzed the extreme value estimators and found the performance with Parkinson estimator for forecasting volatility over these horizons. Karmakar (2005) has estimated that the movement in stock returns volatility is not explained by the fundamental economic factors, but reported the presence of ‘fade’ due to the actions of noise traders, liberalizing policies and procedures of the government. Kumar (2006) examined the comparative performance of volatility forecasting models in Indian markets and the results were found contrary to Brailsford and Faff (1996). Still, further research is needed to forecast the volatility of futures market for an in-depth understanding about the behavioural characteristics of Indian capital markets, and to fill the gap in the existing literature.

Data and Model Specification adopted for the Study

The study is purely based on the secondary data drawn from the website of NSE, India. The sample of data used in this exercise, spanned over the period from January 2003 to December 2008. During the sample period, the futures securities trade from 9:55 A.M to 3:30 P.M. All the required information for the stock futures contracts trade on the National Stock Exchange (NSE) and contract specifications and trading details were retrieved from their website (www.nseindia.com). Usually three types of contracts are traded simultaneously in the futures markets (i.e.) near month, middle month and far month futures contracts. Near month futures contracts are considered for the analysis, because most trading activities take place in the near month contracts than on the other two types of contracts. The data were analyzed by using the econometric software package Eviews 7. The purpose of the study is broken into two major sections;

1. First, to measure the dynamic relationship between price volatility, trading volume and market depth. For such measurement and analysis daily settlement prices, trading volume and open interest series were used by adopting the base model by Bessembinder and Seguin (1993) with modification of Mahmood and Salleh (2006). An adjusted continuously compounded return was calculated as Rt = ln(Pt/Pt-1) where Pt and Pt-1 are natural logarithms of adjusted return on day t and t-1 respectively. The logarithm of the price relative was used to calculate the price change. It is understood that the use of logarithmic price changes prevents non-stationarity of the price level of the data being affected by the future price variability.

2. Second, modeling and forecasting stock futures market volatility was attempted by using various statistical and econometrical models, for this methodology developed by Najand (2002) and Sadorsky (2006) was adopted in the futures market return series. The daily volatility of stock futures returns were estimated by the model developed by Schwert (1990) and Schwert and Seguin (1990).

Sampling Design of the Study

To examine the dynamic relationship between price changes, trading volume and market depth process and to attempt modeling and forecasting volatility of stock futures returns, 237 stock futures contract was process till 31st December 2008. Out of 237 stock futures, 25 stock futures contracts were selected. The dataset drawn over the period from January 2003 to December 2008 were considered for analysis. In this process, the study Sequential sampling method and in the process following companies become the representative sample for detailed analysis.

Company Name Symbols

1. Associated Cement Co. Limited ACC
2. Bharat Electronics Limited BEL
3. Bharat Heavy Electricals Limited BHEL
4. Bharat Petroleum Corporation Limited BPCL
5. Cipla Limited CIPLA
6. Dr. Reddy's Laboratoires Limited DRREDDY
7. Grasim Industries Limited GRASIM
8. HCL Technologies Limited HCLTECH
9. Housing Development Finance Corporation Ltd. HDFC
10. Hero Honda Motors Limited HEROHONDA
11. Hindustan Petroleum Corporation Limited HINDPETRO
12. ICICI Bank Limited ICICIBANK
13. Infosys Technologies Limited INFOSYSTCH
14. ITC Limited ITC
15. Mahindra Mahindra Limited MM
16. Mahanagar Telephone Nigam Limited MTNL
17. National Aluminium Co. Ltd NATIONALUM
18. Oil Natural Gas Corp. Limited ONGC
19. Polaris Software Lab Limited POLARIS
20. Ranbaxy Laboratoires RANBAXY
21. Reliance Industries Limited RELIANCE
22. State Bank of India SBIN
23. Tata Power Co. Limited TATAPOWER
24. Tata Tea Limited TATATEA
25. Wipro Limited WIPRO

Limitation of the Study

Since this study is based upon the secondary data, all the limitations inherent to the secondary data are applicable to this study. In this research work, our special focus was to examine the relationship, modelling and forecasting volatility for select stock futures contracts in India. The overall structural patterns, volatility behaviour and persistence of information for stock futures contracts are alone considered for the period. The other key determining factors like Inflation Rates, Industrial Production Index (IIP), Gross Domestic Product (GDP), Exchange Rate etc. were not taken into account. The micro structure aspects of stock futures contracts returns have not been attempted. The thesis work is limited to the period from January 2003 to December 2008 and is based on daily data. In spite of these limitations, it is hoped that the findings will be instrumental to identify the state and representation of the derivative market in India.

Organization of Study

The study is divided into six chapters. Chapter - 1 presents the chronicle introduction of derivative markets, importance of study, Data and Methodology of the study, Need for the study, Statement of the problem, and Limitation to the study. Brief review of antecedent literature is presented in Chapter - 2. Chapter - 3 discusses the conceptual framework of derivatives and the development of derivatives market. Mechanisms of futures trading include its structure, types of products, functions, memberships, economic and social roles of futures markets and most fundamental factors that influence stock indexes. Chapter - 4 incorporates the dynamic relationship between price volatility, trading volume and market depth. Chapter - 5 examines strength of modelling and forecasting volatility for stock futures contracts through Linear and Non-linear models. Finally, summary, concluding remarks and recommendations for future studies are presented in Chapter - 6.

CHAPTER – II

REVIEW OF LITERATURE

Out of many liberalization policies and structural changes implemented by the government of India one of the most noteworthy was introduction of derivatives in Indian securities markets. Derivatives are believed to be very important to the stock market as well as for the economy of a country in terms of its risk management capability. The arrival of this new financial product in the securities markets has treated renewed interest in the academicians, researchers and practitioners to learn more about derivatives and derivatives markets, its operations and implications. Thus the empirical works on derivatives market has grown manifold in recent years at national and international level.

This empirical research work adds to the growing literature on existing research by examining the relationship between price volatility, trading volume and market depth for futures markets, and forecasting the symmetric and asymmetric behaviour of futures market. As a prelude the literatures that considered the characteristics of return and volume relationship without specific reference to the open interest as proxy variables for calculating market depth are reviewed. While the reference of open interest is often mentioned briefly in most futures textbooks, relatively little research has considered this specific relationship between price volatility, trading volume and market depth for futures markets. The present research focused on relationship and modeling volatility is expected to be helpful to test the market efficiency, market setting, anomalies in investor behavior and its applicability for the futures markets. An exhaustive literature review has been carried to identify the gap. For the sake of clarity and simplicity all the studies reviewed have been categorized the relationship studies and forecasting and modeling studies.

1. Relationship between Futures Return, Trading Volume Market Depth Variables:

Thomas Epps and Mary Lee Epps (1976) have investigated the financial markets based upon two-parameter portfolio model to identify the stochastic dependence between transaction volume and changes in security price from one transaction to next. The change price can be viewed as mixture of distributions with transaction volume as the mixing variable. In common stocks, these distributions appear to be pronounced in the excess of frequency near the mean and a deficiency in outliers, relative to the normal. Finally, the findings are consistent with the hypothesis that stock price changes over fixed intervals of time follow mixtures of finite variance distributions.

Richard Rogalski (1978) examined does the security prices and volume are causally related. The existing models that attempt to analyze the interdependence of price and volume in speculative markets are dependent. Significant cross correlations were observed at zero lag using a 5% significance level. The results suggest that the knowledge of behavior of volume may marginally improve conditional price forecasts over price forecasts based on past prices alone. A shortcoming of the methodology is that one cannot distinguish between contemporaneous feedback and unidirectional causality for which there is no lag effect. In other words, sample cross correlations that are non-zero primarily at lag zero are consistent with three types of causality: volume causes price change, price change causes volume, and feedback between price change and volume. All three cases are indicative of dependence as revealed by this study. Finally, the results of this study have not established that speculative markets are operating inefficiently. This would require correlation between current price change and lagged volume. No such dependence has been found in this study. Thus, even if volume series could be predicted from past volume values by an appropriate ARMA model, such predictions would contain no information relevant to the expected value of price change. Such predictions would be useful, however, in forecasting the variance of price change.

Figlewski (1981) has analyzed the impact of futures trading in Government National Mortgage Association (GNMA) on price volatility in the cash market. The objective of this study was to examine price volatility, the standard deviation of day to day price changes. The empirical evidence showed that price volatility in the GNMA cash market was related to several factors like increased volatility, measured by GNMA’s outstanding and proxies for the volume of cash market activity, and lower average prices tended to stabilize the market, while futures market activity increased the volatility of prices. Several possible reasons for this result were discussed; however there were no evidence of insufficient speculative activity in futures relating to hedging, and price manipulation because of the extensive safeguards against it. The futures prices are believed to be determined largely by the actions of inexperienced new class of traders who were likely to have less information than the GNMA securities and set prices in the cash market. When the additional “noise” in futures prices is transmitted to the cash market, price volatility increases. Finally, the effect is expected to diminish as they become more seasoned and broaden the population of GNMA.

Tauchen George and Pitts Mark (1983) studied the relationship between the variability of daily price change and the daily volume of trading on speculative markets for the period from 6th January to 30th June 1979. The work extends the theory of speculative markets in two ways. First, the joint probability distribution of the price change was derived along with trading volume over any interval of time within the trading day. And secondly, the paper tried to determine how joint distribution changes as more traders enter (or exit from) the market. The results of the estimation found reconciling the conflict between the price variability-volume relationship for the market and the relationship obtained by previous investigators for other speculative markets.

Grammatikos and Saunders (1986) examined the contemporaneous and sequential relation between price variability and trading volume in futures markets using disaggregated data and improved measures of price variability. The sample consisted of daily observations for five different foreign currency futures traded on the International Monetary Market (IMM): the German mark, the Swiss franc, the British pound, the Canadian dollar, and the Japanese yen over the period March 1978-March 1983. They employed both classical and Garman-Klass estimators of price volatility, to test whether there exists a positive contemporaneous correlations between trading volume and price volatility. The results appeared to be consistent with the MDH and inferences were drawn as maturity is not a suitable surrogate for the common directing variable. Specifically, while maturity has a strong effect on volume, no such relation is found for price variability. Finally, consistent with previous work with stock market data it was found that, in majority of the cases price variability and trading volume were contemporaneously correlated, there were a significant number of cases in which a sequential relation between price variability and volume appeared to be present.

Karpoff Jonathan (1987) attempted an empirical and theoretical research into the price-volume relation for 18 financial markets including equities, futures, currencies and Treasury Bills. The theoretical justifications for studying price volume relationship, that were put forth are, the returns or trading volume relation provides insight into the structure of financial markets. Second, the return or trading volume relation is important for event studies that use a combination of stock returns and trading volume data to draw inferences. Third, the returns or trading volume relation is critical to the debate over the empirical distribution of speculative prices. The main conclusion has been the positive correlation between price and volumes exists and is mainly conspicuous with larger volumes.

Bessembinder Seguin (1992) have examined whether greater futures trading activity is associated with greater equity market volatility for SP 500 index from January 1978 to September 1989. He evaluated with the help of Pearson Correlation Coefficients, Regression of SP 500 return standard deviation for spot and future trading using dummy variables. Their findings were consistent with the theories predicting that active futures markets enhance the liquidity and depth of equity markets. They provide additional evidence suggesting that active futures markets are associated with decreased rather than increased volatility. However, the evidence reported here, that equity volatility declines with predictable futures-trading activity, is consistent with the reasoning that the low cost of futures trading attracts additional informed traders, and the equity volatility is reduced in future market.

Douglas Foster and Viswanathan (1993) examined the empirical behavior of stock market trading volume, trading costs, and price change for New York Stock Exchange data from 1988, with the help of Ordinary Least Square Method. The Intraday test results indicate that, for actively traded firms trading volume, adverse selection costs, and return volatility are higher in the first half-hour of the day. This evidence is inconsistent with the Admati and Pfleiderer (1988) model which predicts that trading costs are low when volume and return volatility are high. Intraday test results showed that, for actively traded firms, trading volume is low and adverse selection costs are high on Monday, which is consistent with the predictions of the Foster and Viswanathan (1990) model. The result indicates that existing theoretical models based on the adverse selection faced by the market maker are broadly consistent with observed patterns in the volume-volatility relation. That is, intraday trading volume is high when returns are most volatile.

Bessembinder Seguin (1993) has examined the relations between volume, volatility, and market depth in eight physical and financial futures markets, employing econometric methods that accommodate volatility persistence, asymmetries in the volume-volatility relation and interactions of conditional return means and conditional return volatilities over the period from May 1982 to March 1990. The evidences suggest that linking volatility to total volume does not extract all information. When volume is partitioned into expected and unexpected components, the paper finds that unexpected volume shocks have a larger effect on volatility. Further, the relation is asymmetric; the impact of positive unexpected volume shocks on volatility is larger than the impact of negative shocks.

Hiemstra and Jones (1994) examined the dynamic relation between daily Dow Jones stock returns, percentage changes in New York Stock Exchange (NYSE) and trading volume by using both linear and nonlinear Granger causality tests. By applying the tests to check daily Dow Jones stock returns and percentage changes in NYSE trading volume over the period from 1915 to 1946 and 1947 to 1990. The modified Baek and Brock test provides evidence of significant bidirectional nonlinear causality between stock returns and trading volume in both sample periods. It also examined whether the nonlinear causality from volume to stock returns detected by the modified Baek and Brock test could be due to volume serving as a proxy for daily information flow in the stochastic process generating stock return variance. After controlling for simple volatility effects, the modified Baek and Brock test continued to provide evidence of significant nonlinear Granger causality from trading volume to stock returns. However, nonlinear theoretical mechanisms and empirical regularities could have been considered when devising and evaluating models for the joint dynamics of stock prices and trading volume.

Brailsford Timothy (1994) has empirically analyzed the relationship between trading volume and stock return volatility in the Australian market with the period from 24th April 1989 to 31st December 1993. Trading volume was then examined in the context of conditional volatility using a GARCH framework. He tested both the asymmetric model and the mixture of distributions hypothesis in relation to the Australian market. The results indicate strong support for the asymmetric model. Furthermore, the results were also found consistent with Lamoureux and Lastrapes ^[1990] and showed that ARCH effects are diminished and persistence in variance is reduced when trading volume is incorporated as an explanatory variable in the general ARCH model. These results have implications for inferring return behaviour from trading volume data. Hence, there is evidence that if trading volume proxies for the rate of information arrival, then ARCH effects and much of the persistence in variance can be explained.

Andersen (1996) demonstrated the return volatility-trading volume relationship by integrating the market microstructure framework in which informational asymmetries and liquidity needs motivate trade in response to information arrivals. A continuously compounded daily return series, corrected for dividends and stock splits, is constructed from closing prices on IBM common stock over January 1, 1973 to December 31, 1991 with a sample of 4693 observations. The resulting system modified the so-called "Mixture of Distribution Hypothesis" (MDH). The dynamic features were governed by the information flow, modeled as a stochastic volatility process, and generalize standard ARCH specifications. Specification tests support the modified MDH representation and show that it vastly outperforms the standard MDH. Finally, our findings suggest model may be useful for analysis of the economic factors behind the observed volatility clustering in returns.

Ragunathan Peker (1997) investigated the nature of the relationship between volume, price variability and market depth for four futures contracts traded on the Sydney Futures Exchange and is based on the methodology developed by Bessembinder and Seguin (1992, 1993) between January 1992 to December 1994. He tested the asymmetries in volume and open interest shocks by separating volume and open interest into expected and unexpected variables, this study envisaged the asymmetric relationship between volume, open interest and volatility, and tried to investigate whether unexpected volume and open interest had a positive or negative shock. The results lead to the conclusion that positive volume shocks have a greater impact on volatility than negative shocks. The same conclusion is arrived at when open interest shocks are analyzed, that is, a positive open interest shock is more likely to have an impact on volatility than a negative shock. Therefore, it can be concluded that market depth does have an effect on volatility.

Galloway and Miller (1997) explored the relation between index futures trading and volatility in equity market using the SP MidCap 400 stock index and MidCap 400 index futures. Daily return and trading volume data were obtained for 398 stocks from the CRSP database for three separate periods. The first i.e. pre-index period includes 250 trading days before June 5, 1991. This period precedes both the existence of MidCap index and the trading of MidCap futures. The second, or interim, period includes 175 trading days after June 5, 1991 till February 13, 1992. The study documents a significant decrease in return volatility and systematic risk, and a significant increase in trading volume for the MidCap 400 stocks after the introduction of MidCap index. A control sample of medium-capitalization stocks, however, exhibits similar contemporaneous changes in these measures. The MidCap stocks and control stocks also experienced a significant decrease in volatility and an increase in volume after the introduction of MidCap 400 index futures. Consequently, the study confirms that there is no significant relationship between futures trading and volatility in the stock market. Finally, a new puzzle emerged concerning why there are market-wide changes in risk and liquidity. Prior studies document that aggregate stock market volatility varies over time and the variation is related to a variety of economic variables.

Jacobs and Onochie (1998) revealed that there is a positive relationship between trading volume and price volatility, by measuring the price changes in conditional heteroskedasticity in international financial futures markets by applying bivariate GARCH(1,1). The underlying products are interest rate assets representing investments in various international money and bond markets of Sterling, Eurodollar, U.S. Treasury bond, German Government bond (Bund), 3-month European Currency Unit (ECU), and the Euromark. The result suggest that there is a strong evidence of second-order dependence in the joint return and trading volume process for various international financial futures markets and the level of trading volume positively influences the conditional variance of futures price change. It also inferred that the issue of time varying volatility is of importance to option pricing. The implication of these findings that futures price changes and volume are not only jointly distributed, but also influences price volatility, can guide theorists and practitioners alike in rethinking the pricing relationships for financial futures.

Gong-meng Chen, Michael Firth and Oliver Rui (2001) examined the dynamic relationship between returns, volume, and volatility for major nine national stock indexes for the period from 1973 to 2000. They evaluated with the help of quadratic time trend method, Augmented Dickey Fuller test, Regression the daily trading volume on stock returns and absolute returns, Vector Auto regression (VAR) and EGARCH techniques were used to examine the returns, trading volume, conditional volatility relation. The results show a positive correlation between trading volume and absolute value of stock price change. Granger Causality tests demonstrated that for some countries, returns cause volume and volume causes returns. The findings indicate that trading volume contributes some information to the returns process and more can be learned about the stock market through studying the joint dynamics of stock prices and trading volume than by focusing only on the univariate dynamics of stock prices. The results of the study were found robust across all nine major stock markets, implying that there are similar returns, trading volume, and volatility patterns across all markets under study.

Toshiaki Watanabe (2001) examined the relation between price volatility, trading volume and open interest for Nikkei 225 stock index futures traded on the Osaka Securities Exchange (OSE) by employing the method developed by Bessembinder and Seguin (1993) for the sample period extended from 24th August 1990 to 30th December 1997. The reason for investigating the Nikkei 225 futures traded on the OSE was that the OSE changed regulation such as margin requirements, price range and time interval in updating quotation several times. The authors felt interesting to examine whether changes in regulation may influence the effects of volume on volatility. Therefore, the samples prior to and beginning 14 February 1994 were analyzed separately. However, no relation between price volatility, volume and open interest was found for the period prior to 14 February 1994, when the regulation increased gradually. This result provides evidence that the relation between price volatility, volume and open interest may vary with the regulation.

Bhanupant (2001) investigated the dynamic relationship between stock index returns and trading volume using the Augmented Dickey-Fuller (ADF), Linear and Non-Linear Granger Causality hypothesis test on the National Stock Exchange (NSE) data 1 January 1996 to 6 August 2002 with a total of 1649 data points. Linear Granger Causality test was used to investigate the linear relationship while the Non-Linear Granger causality was investigated using modified Baek and Brock test proposed by Hiemstra and Jones (1994) for the daily returns on SP CNX Nifty and the total trading volume at NSE. Bidirectional linear Granger causality between index returns and volume change was observed for the period when rolling settlement was either not introduced or partially introduced. The period, when rolling settlement was introduced, there found no evidence of linear causality in either direction. The shift in linear causal relationship indicates that efficiency at NSE has improved with introduction of rolling settlement mechanism. Nonlinear Granger causality between the returns and volume change was not evident in either direction.

Otavio Medeiros Bernardus Van Doornik (2006) investigated the empirical relationship between stock returns, return volatility and trading volume for Brazilian stock market covering a period 1st March 2000 to 29th December 2005. The empirical methods used include cross-correlation analysis, unit-root tests, bivariate simultaneous equations regression analysis, GARCH modeling, VAR modeling, and Granger causality tests. Their evidence suggests that there was a significant relationship between stock returns and trading volume, which is detected in the cross-correlation analysis. Additionally, by applying Granger-causality, the results showed no signs of causality between trading volume and stock returns. However, a simultaneous equation analysis showed that stock returns depend on trading volume, but it does not apply the other way. This result contributes to the understanding of the microstructure of emerging stock markets.

Pati Kumar (2006) attempted to examine the maturity and volume effects on the volatility dynamics for futures price in Indian Futures Market for the period from January 1, 2002 to December 29, 2005 for near month contract with 1009 sample data points. For empirical analysis they used ARMA-GARCH, ARMA-EGARCH models. The empirical evidence suggests that there is time-varying volatility, volatility clustering and leverage effect in Indian futures market. With respect to volume-volatility relationship, the results suppressed the Mixtures of Distribution Hypothesis. This study concluded that time-to-maturity is not a strong determinant of futures price volatility, but rate of information arrival proxied by volume and open interest are the important sources of volatility. This relationship has important implications for the new futures contracts. This study does not provide support for the Samuelson Hypothesis in Indian futures market, which is found to be informational efficient. The finding of this study had a message for investors, market regulator-market surveillance that risk management practices should be further strengthened to take care of greater market volatility associated with an increased volume of trading. Finally, the result suggests maturity effect does not hold in Indian futures markets, the investors should not base their investment decision on time-to-maturity.

Mahmood Salleh (2006) examined the relationship between return, trading volume and market depth for two futures contracts, namely Stock Index Futures and Crude Oil Futures traded at the Kaula Lumpur Option and Financial Futures and Commodity and Monetary Exchange for the period from 15th December 1995 to 19th January 2001. They tested with the two famous hypothesis one, whether the sequential arrival of new information to the market move both the trading volume as well as price. The second one is about the mixture of distribution hypothesis where information may be considered as mixing variable. They used the diagnostic tests like Unit root Test, Ljung-Box Test and ARIMA (10,1 ,0) and evaluated with the help of GARCH (1,1). The effects of volume as well as open interest, proxy of market depth, on volatility and vice versa were also studied. Since both volume and open interest were found highly serially correlated, these variables were divided into expected and unexpected components. Finally, the results showed a positive expected and unexpected volume and market depth effect on volatility.

Eric Girard Rita Biswas (2007) surveyed the relationship between volatility and volume in 22 developed markets by using 27 emerging markets for the period from January 1985 to June 2005. In this study the empirical analysis were carried out by applying TGARCH model specification for explaining the daily time dependence with the rate of information arrival to the market for all stocks traded in frontier market exchange. Thus, using volume as a proxy for the flow of information, TARCH was found to be an appropriate model to mimic the conditionality of second moments. Compared to developed markets, emerging markets showed a greater response to large information shocks and exhibited greater sensitivity to unexpected volume. Both of these findings evidenced the presence of noise trading and speculative bubbles in emerging markets. Their results suggest that negative relation was found between expected volume and volatility in several emerging markets, which can be attributed to the speculative trading activity which drives bid-ask spreads higher, and diminishes the relative inefficiency in those markets. The findings showed that official price reporting mechanisms and insider trading laws are also relatively weaker in these countries; a change in local policies to design better systems is warranted if foreign investors are to be attracted to these markets.

Christos Floros Dimitrios Vougas (2007) examined the contemporaneous relationship between trading volumes and returns in Greek stock index futures contracts in the Athens Derivatives Exchange (ADEX) for the period September 1999 to August 2001. They utilized the tools like Generalized Method Moments (GMM), Unit root test and GARCH effect. The study suggested that GARCH effects were explained by trading volume under both GARCH and GMM. For FTSE/ASE-20, trading volume contributes significantly in explaining GARCH effects. However, the estimated results of GMM suggested that there is a significant relationship between lagged volume and absolute returns, while a positive contemporaneous relationship does not hold good. Their findings indicate that market participants use volume as indicators of prices, but for FTSE/ASE Mid 40, the empirical results give different conclusions. Both GARCH and GMM methods confirm that there is no evidence of positive relationship between trading volume and returns.

Malabika Srinivasan (2008) analyzed the empirical relationship between stock return, trading volume and volatility for select Asia-Pacific Stock Market by applying preliminary test, Granger Causality test and EGARCH (1,1) model. The data set comprises of seven national stock markets for the period spanning from 1st January 2004 to 31st March 2008. The results evidenced a significant relationship between trading volume and the absolute value of price changes. Granger Causality test was used to explore, whether return causes volume or volume causes return. The results suggested that the returns were influenced by volume and volume also was influenced by returns for most of the markets. Therefore, trading volume contributes some information to the return and volatility for determining contemporaneous and lagged volume effect after incorporation. The empirical results were found robust across the national markets during the study period.

Mahajan and Singh (2008) suggested the pattern of information flow between trading volume and return volatility using daily data for Nifty index during the period from July 2001 to March 2006. The methods used included Correlation analysis, Unit root tests, VAR modeling, Granger causality test, GARCH (1,1) and EGARCH model. The study provided evidence of low but significant positive contemporaneous relationship between volume and return volatility that was indicative of both mixture of distribution and sequential arrival hypothesis. The differential cost of taking long and short positions were examined by applying asymmetric EGARCH (1,1) model to check the relationship between the variables. The study further confirmed a weak unidirectional causality from volume to return volatility, which also indicates the mild support for sequential information flow directed from volume to price change. The study contributes to the enhance understanding of researchers, regulators, speculators, and other participants in market on market efficiency and information processing.

2. Modelling and Forecasting Futures Market Volatility:

Franses and Van Dijk (1996) compared the volatility forecasting performance of GARCH model, Quadratic GARCH model and Threshold GARCH models against Random Walk model using weekly dataset for German, Dutch, Italian, Spanish and Swedish stock index returns over the period from 1986 to 1994. They report that the random walk model performs particularly well when the crash of 1987 was included in the estimated sample, while the QGARCH model can significantly improved the linear GARCH model and found no significant change in forecasting.

McMillan, Speight and Apgwilym (2000) analyzed and compared the volatility forecasting performance by using GARCH models, asymmetric TGARCH and exponential GARCH models for the Financial Times-Stock Exchange (FTSE 100) index and Financial Times Actuaries All Share index at the London Stock Exchange. The dataset are partitioned into in-sample and out-sample estimation periods from 2 January 1984 to 31 July 1996 for the FTSE100 index and 1 January 1969 to 31 July 1996 for the FTA All Share index data, the out-of-sample forecast periods covering the remaining period from 1995 to 1996 for both data sources. A total of ten volatility forecasting models are considered, including the historical mean, moving average, random walk, exponential smoothing, exponentially weighted moving average, simple regression, GARCH, TGARCH, EGARCH, and CGARCH models. The forecasting performed for monthly, weekly and daily data frequencies under symmetric and asymmetric loss functions. The results suggest that the random walk model provides superior monthly volatility forecasts, while random walk, moving average, and recursive smoothing models provide moderately superior weekly volatility forecasts, and GARCH, moving average and exponential smoothing models provide marginally superior daily volatility forecasts. If attention is restricted to one forecasting method for all frequencies, the most consistent forecasting performance is provided by moving average and GARCH models. More generally, their results suggested that GARCH class models provide relatively poor volatility forecasts.

Najand Mohammad (2002) examined the relative ability of various models to forecast daily stock index futures volatility for SP 500 futures index between January 1983 and December 1996 with a continuous sequence of 3561 observations are gathered over fourteen year period. He estimated the models using 3500 and 3380 observations and saving the last 60 and 180 observations for out-of-sample forecasting comparisons between models. The linear and non linear models employed for the study are Random Walk, AR model, MA model, Single Exponential Smoothing models, Double (Holt) Exponential Smoothing models, GARCH - M, EGARCH and ESTAR models. Their findings suggest autoregressive (AR) model is a more appropriate model under RMSE and MAPE criteria. In non linear model, GARCH and ESTAR model fitting were more appropriate than linear models by using RMSE and MAPE error statistics. Finally, EGARCH appeard to be the best model for forecasting stock index futures price volatility.

Yu Jun (2002) explored the volatility forecasting performance for New Zealand Stock Exchange 40 index for the sample period consists of 4741 daily returns over the period from 1 January 1980 to 31 December 1998. The competing modes contain both simple models such as the Random Walk, Historical average, Moving Average, Simple Regression, Exponential smoothing, Exponentially-weighted moving average (EWMA) and complex models such as ARCH, GARCH, SV model. Four different measures were used to evaluate the forecasting accuracy, namely, the root mean square error (RMSE), the mean absolute error (MAE), the Theil-U statistic and the LINEX loss function. The main results are the following: (1) the stochastic volatility model provides the best performance among all the models; (2) ARCH-type models can perform well or badly depending on the dataset chosen for the study. (3) The regression and exponentially weighted moving average models do not perform well according to any assessment measure, in contrast to the results found in various markets. Moreover, all the models examined in this paper belong to the univariate time series family and multivariate models should be kept into consideration to forecast volatility. However, he finds that the added information cannot improve the out-of sample forecasting performance and there are some other variables that are useful to forecast volatility, such as inflation rates or numbers of listed companies.

Pandey Ajay (2002) reported the empirical performance of various unconditional volatility estimators and conditional volatility models by using SP CNX Nifty, India. The dataset on SP CNX Nifty for the period 1st January 1996 to 31st December 2001 were considered by using different class of models. In order to test the ability of models estimated to forecast volatility, he compared the unconditional estimators with the realized volatility measure. For conditional volatility models, the forecasts for the same periods are obtained by estimating models from the time-series prior to the forecast period. The results indicate, that the conditional volatility models provide less biased estimates, extreme-value estimators are more efficient estimators of realized volatility. As far as forecasting ability of models is concerned, conditional volatility models fare extremely poorly in forecasting five-day (weekly) or monthly realized volatility. In contrast, extreme value estimators, other than the Parkinson estimator, perform relatively well in forecasting volatility over these horizons.

Caiado Jorge (2004) investigated the volatility forecast for daily and weekly data for Portuguese Stock Index (PSI-20) by using simple GARCH, GARCH -M, Exponential GARCH and Threshold ARCH models from the period January 2, 1995 to November 23, 2001 for a total of 1708 and 359 observations respectively. The out-of sample forecast error statistics Root Mean Square Prediction Error, Mean Absolute Prediction Error and Mean Absolute Percentage Prediction Error for each model obtained by sequences of both 100 one day ahead and 20 one week ahead forecasts for PSI - 20 indexes. The findings suggested that, there are significant asymmetric shocks to volatility in daily stock returns and declined by 24.42 per cent, but the same was not evidenced in the weekly stock returns, indicating that the Portuguese stock market becomes more nervous when negative shocks take place. Finally, the EGARCH models were found to provide better daily forecasts, while the GARCH model with the variance equation provided superior weekly forecasts. Therefore, he concluded that reduction of the sample period for estimation improves the accuracy of predicting future observations of the PSI-20 index and stock returns.

Sarno Lucio and Valente Giorgio (2005) have investigated the dynamic relationship between spot and futures prices in stock index futures markets using data since 1989 at weekly frequency for three major stock market indices - the SP 500, the Nikkei 225 and the FTSE 100 indices by using a conventional cost of carry model to show that futures and stock prices must be Cointegrated and, therefore, linked by a VECM that can be used both to explain and forecast stock returns. The data set comprises weekly time series on prices of futures contracts written on the SP 500, the Nikkei 225 and the FTSE 100 indices. The sample period examined spans from January 1989 to December 2002. The empirical work was carried out during the period January 1989-December 1998, reserving the last four years of data for out-of-sample forecasting tests. The empirical results provided evidence in favor of the existence of international spillovers across these stock markets and a well-defined long-run equilibrium relationship between spot and futures prices which was consistent with mean reversion in the futures basis. Using the estimated models in an out-of-sample forecasting exercise it was found that both nonlinearity and international spillovers are important in forecasting stock returns. Overall, their empirical evidence suggests that the statistical performance of the linear and nonlinear models examined, differs little in terms of conditional mean, regardless of whether allowance is made for international spillovers across the stock indices. In particular, they focused on the information provided by the futures market for forecasting stock returns.

Karmakar (2005) estimated the conditional volatility models in an effort to capture the stock market volatility in India by employing GARCH (1,1) models by suing three sets of data. The first 2 sets comprised of S P CNX Nifty and BSE Sensex for the period from 2nd January, 1991 to 10th June 2003. The third set comprised of daily closing prices of 50 underlying individual companies from June 1994 to October 2002. To evaluate the models in terms of out-of-sample forecast accuracy by Mean Error, Mean Absolute Error, Mean Absolute Percentage Error and Root Mean Square error are investigated whether there is any leverage effect in Indian companies. It is observed that the GARCH (1,1) model provides reasonably good forecasts of market volatility. The findings suggest, the movement in stock market return volatility is not explained by the fundamental economic factors, but also the presence of ‘fade’ due to the actions of noise traders in the market might be associated with these immeasurable elements of stock price volatility. However, the initial boost up of share prices and the resultant fluctuation were believed to be due to fundamental economic factors of the period which were supplemented by a number of liberalization policies and procedures of the government. Finally, the real cause of excessive movement was attributed to the irrational behaviour of the market speculators and frenzy investors who drove the price away from fundamental level resulting in fads or bubble as the natural outcome of the price formation process.

Gospodinov, Gavala and Jiang (2006) investigated several parametric and nonparametric volatility measures, such as implied, realized and model-based volatility for SP 100 index and the forecasting performance of different volatility models were evaluated among ARFIMA models, Near-integrated AR model, EGARCH, FIEGARCH and Stochastic volatility models. The daily dataset were used for the exercise for the SP 100 index and the implied volatility index VIX for the period June 1, 1988 to May 17, 2002. To obtain measures of realized and historical volatility SP 100 returns were used as proxies of the latent integrated volatility process. The result suggested that implied volatility provides valuable information about future movements of volatility and the information content of option prices were considered as more efficient methods for modeling and forecasting the volatility process. Furthermore, their findings suggest that combined information from different volatility models tends to improve the performance of volatility forecasts, especially at long forecasting horizons. Finally, their paper considered only forecasts from univariate models by using simultaneously information from stock returns and option prices by including the implied volatility in a GARCH-type model or adding exogenous variable that contain some incremental information about volatility such as trade volume, that lead to increased forecast accuracy.

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