In this paper the Box- Jenkins forecasting technique should be applied to the stock price of the ThyssenKrupp AG. ThyssenKrupp arose from the merger of the “Thyssen AG”
and the “Friedrich Krupp AG Hoesch-Krupp” in 1999. The main focus of the trust lies on steel, industrial goods and services with its five sections Stainless, Steel, Technologies, Elevator and Services. With 191,350 employees in over 70 countries and a turnover of 51.7 billion Euro p.a., ThyssenKrupp is one of the largest industry and technology groups in the world. At the same time it is Germany’s biggest steel and armaments manufacturer. I chose the stock price of the ThyssenKrupp trust for several reasons. First, it is a blue chip listed on the stock exchange since 1999 allowing me easy access to a sufficient and reliable
amount of data. Second, I have no reason to believe that this trust underlies any influence of seasonality since it has so many different segments that contribute to its economic
performance. Third, since the steel demand and thus prices are steadily increasing in the last years it is not surprising that the stock price of the ThyssenKrupp AG does this too (see
figure 2 further down) giving me a reason to question financial market theories. In particular, financial investors and researches are very often interested to predict future
values of stock prices. On the one hand they do so, to gain profits from investing in stocks from buying at a low price and selling at a higher price and on the other hand to verify if
financial markets work efficiently. For the latter reason, financial research for a long time believed stock prices to follow a random walk and thus that prices of the stock market
cannot be predicted2. This implies that financial markets are at least weak form efficient and excess returns cannot be earned by using investment strategies based on historical shareprices, i.e. time- series analyses can not be used to predict future values of stock prices. In this paper I will try to find out if the stock price of the ThyssenKrupp AG follows a random walk or not using the Box-Jenkins forecasting approach. For my analysis I use the weekly opening stock price starting at 01/01/2003 and ending at 04/21/08 and thus I have 278 observations. To analyze the data I use the software STATA (version 9.1.).
Table of Contents
1. The Box-Jenkins-Approach
2. Modeling A Stationary Time Series For The Stock Price Of The ThyssenKrupp AG Using The Box-Jenkins-Approach
2.1. Test for Stationarity
2.2. Postulate a General Class of Models
2.3. Identification of an Adequate Model
2.4. Estimation and Diagnostic Checking
2.5. Validation and Forecast
3. Conclusion
Research Objectives and Topics
This paper aims to investigate whether the stock price of ThyssenKrupp AG follows a random walk pattern by applying the Box-Jenkins forecasting technique. The study seeks to determine if historical share prices can be used to predict future values, thereby questioning the weak-form efficiency of financial markets for this specific security.
- Application of the Box-Jenkins forecasting approach to stock market data.
- Testing for time series stationarity using Augmented Dickey-Fuller tests.
- Model identification via autocorrelation (ACF) and partial autocorrelation (PACF) functions.
- ARIMA model estimation and diagnostic residual checking.
- Validation of forecasting accuracy using Mean Squared Error (MSE) and Theil's inequality measure.
Excerpt from the Book
2.1. Test for Stationarity
The first thing to do before we really can go on with the Box-Jenkins approach is to check our time series for stationarity. If we interpret a time series as realizations of one random variable out of an infinite universe of random variables we can call this random variable a stochastic process. A time series is stationary if the underlying stochastic process that generated that series is invariant with respect to time, i.e. mean, variance and covariance are constant over all data points of the time series. A stationary series allows us to model its underlying process via an equation with fixed coefficients that can be estimated from the given historical data. Another important issue is that the time series has no seasonality included. Otherwise, we have to deseasonalize the series beforehand and apply the Box-Jenkins approach to the data without seasonality. Having a closer look at the plot of the opening stock price of ThyssenKrupp from 01/01/2003 until 04/21/2008 in figure 2 suggests that there is no seasonality but a trend included in the time series. A trend yields the long term movement of the time series, i.e. the upward or downward tendency of it.
Summary of Chapters
1. The Box-Jenkins-Approach: This chapter introduces the theoretical framework of the Box-Jenkins forecasting method and outlines the three-stage process involved in time series analysis.
2. Modeling A Stationary Time Series For The Stock Price Of The ThyssenKrupp AG Using The Box-Jenkins-Approach: This section applies the methodology to ThyssenKrupp stock data, covering stationarity testing, model postulation, identification, parameter estimation, diagnostic checking, and final validation.
3. Conclusion: This chapter summarizes the findings, confirming that the stock price does not follow a random walk and validating the effectiveness of the ARIMA(2,1,2) model for forecasting.
Keywords
Box-Jenkins-Approach, ThyssenKrupp AG, Time Series Analysis, ARIMA, Stationarity, Augmented Dickey-Fuller Test, Random Walk, Forecasting, Stock Price, Econometrics, ACF, PACF, Residuals, Model Identification, STATA
Frequently Asked Questions
What is the primary focus of this paper?
The paper focuses on applying the Box-Jenkins forecasting technique to the weekly opening stock prices of ThyssenKrupp AG to determine if the series exhibits random walk characteristics.
What are the central thematic fields covered?
The study centers on time series econometrics, financial market efficiency, and predictive modeling for equity markets.
What is the primary research question?
The primary goal is to assess whether historical stock price patterns of ThyssenKrupp AG allow for future price prediction or if they follow an unpredictable random walk.
Which scientific methods are utilized?
The author employs the Box-Jenkins approach, including Augmented Dickey-Fuller tests for stationarity, analysis of ACF and PACF plots, ARIMA model estimation, and diagnostic checks using Portmanteau tests.
What topics are addressed in the main body?
The main body covers the transition from non-stationary data to stationary series, the selection of an ARIMA(2,1,2) model, and the rigorous validation of that model against actual historical data.
Which keywords characterize this work?
Key terms include ARIMA, Box-Jenkins, Stationarity, Random Walk, Stock Price, and Time Series Analysis.
Why was the ARIMA(2,1,2) model chosen?
It was selected through a trial-and-error process because it provided the optimal combination of low MSE, AIC, and BIC values along with statistically significant coefficients.
What does the validation process reveal about the model?
The validation process shows that the model fits the data extremely well, with a very low Theil's U statistic and small root mean-squared errors, suggesting strong predictive potential.
Are there limitations to the findings?
Yes, the author notes that as steel demand evolves, more advanced models like ARCH or GARCH might be better suited, and suggests that heteroskedasticity should be further investigated.
- Citation du texte
- M.A. Peter Schmidt (Auteur), 2008, The Stock Price of the ThyssenKrupp AG - A Time Series Analysis Using the Box Jenkins Approach, Munich, GRIN Verlag, https://www.grin.com/document/121797
