In this paper we examine the calendar anomalies in the stock market index of Athens. Specifically we examine the day of the week and the month of the year effects, where we expect negative or lower returns on Monday and the highest average returns on Friday for the day of the week effect and the higher average returns in January, concerning the January effect. For the period we examine we found insignificant returns on Monday, but significant positive and higher average returns on Friday. Also our results are consistent with the literature for the month of the year effect, where we find the highest average returns in January. Furthermore we estimate with ordinary least squares (OLS) and symmetric and asymmetric Generalized Autoregressive Conditional Heteroskedasticity (GARCH) rolling regressions and we conclude that the week day returns are not constant through the time period we examine but are changed. Specifically, while in the first half-period of the rolling regression there are negative returns on Mondays so we observe the day of the week effecting, in the last half-period of the rolling regression Friday presents the highest returns, but the lowest returns are reported on Tuesday and not on Monday, indicating a change shift in the pattern of the day of the week effect. Full programming routines of rolling regressions in EVIEWS and MATLAB software are described.
Table of Contents
1. Introduction
2. Methodology
2.1 The estimated model
2.2 Symmetric and Asymmetric Generalized Autoregressive Conditional Heteroskedasticity-GARCH
3. Data
4. Results
Research Objectives and Themes
This paper investigates calendar anomalies within the Athens Stock Market, specifically focusing on the day-of-the-week and month-of-the-year effects, while utilizing rolling regression techniques to analyze the temporal stability of these patterns through both OLS and various GARCH models.
- Examination of day-of-the-week effects and return volatility patterns.
- Analysis of the month-of-the-year effect (January effect).
- Implementation of rolling regressions to assess time-varying coefficients.
- Application and programming of OLS, GARCH, EGARCH, and GJR-GARCH models.
- Evaluation of stock market efficiency in the Athens Exchange.
Excerpt from the Book
2.2 Symmetric and Asymmetric Generalized Autoregressive Conditional Heteroskedasticity-GARCH
Because the data we use in order to examine the day of the week effect are daily we expect that OLS method will present ARCH effects and autocorrelation. These problems can be eliminated by applying Generalized Autoregressive Conditional Heteroskedasticity-GARCH models. The first model we estimate is the symmetric GARCH(1,1) model proposed by Bollerslev (1987) and is defined as:
ε_t | φ_(t-1) ~ N(0, σ_t^2) (3)
σ_t^2 = ω + αε_(t-1)^2 + βσ_(t-1)^2 (4)
, where ε_t is the disturbance term or residuals of equation (1) and follows the distribution in (3). GARCH (1,1) equation is presented in relation (4), where ω denotes the constant of variance equation GARCH and coefficients α and β express the ARCH and GARCH effects respectively. The problem with symmetric GARCH is that only squared residuals with lags enter the conditional variance equation, and then shocks have no effect on conditional volatility. With the symmetric GARCH we can’t estimate the leverage effects. Leverage effects refer to the fact that “bad news” or negative shocks tend to have a larger impact on volatility than “good news” or positive shocks have. The first asymmetric GARCH we estimate is Exponential Generalized Autoregressive Conditional Heteroskedasticity EGARCH (1,1) which was proposed by Nelson (1991) and is defined as:
log(σ_t^2) = ω + log β(σ_(t-1)^2) + α [|u_(t-1)|/√(σ_(t-1)^2) - √(2/π)] (5)
, where coefficient γ indicates the leverage effects. The second asymmetric GARCH is Glosten-Jagannathan-Runkle Generalized Autoregressive Conditional Heteroskedasticity- GJR-GARCH (1,1) model proposed by Glosten et al. (1993). The variance equation is presented in (6).
Summary of Chapters
1. Introduction: This chapter provides an overview of existing research on calendar anomalies and sets the stage for the study's focus on the Athens stock market.
2. Methodology: This chapter introduces the econometric models, including OLS and various GARCH specifications, used to analyze day-of-the-week and month-of-the-year effects.
3. Data: This chapter details the dataset used, including the frequency of data and the specific time period covered for the Athens Stock Market index.
4. Results: This chapter presents the empirical findings from the OLS and GARCH estimations and discusses the observed patterns and structural shifts in calendar effects.
Keywords
Calendar Anomalies, Athens Stock Market, Day of the Week Effect, Month of the Year Effect, January Effect, Rolling Regressions, OLS, GARCH, EGARCH, GJR-GARCH, Volatility, Market Efficiency, Econometrics, Financial Time Series, Programming Routines
Frequently Asked Questions
What is the primary focus of this research paper?
The paper examines calendar anomalies, specifically the day-of-the-week and month-of-the-year effects, in the Athens Stock Market index.
What are the central thematic areas covered?
The research centers on market efficiency, volatility modeling, and the temporal stability of seasonal anomalies in financial returns.
What is the primary research objective?
The objective is to determine if seasonal effects exist in the Athens stock market and to demonstrate how these effects change over time using rolling regression analysis.
Which econometric methods are employed?
The author uses OLS regression for baseline analysis and advanced volatility models including symmetric GARCH(1,1), EGARCH(1,1), and GJR-GARCH(1,1).
What is addressed in the main part of the study?
The main part covers the theoretical model derivation, data sources, empirical estimation results, and the implementation of rolling window techniques in EVIEWS and MATLAB.
Which keywords best characterize this work?
Key terms include Calendar Anomalies, Rolling Regressions, GARCH models, Volatility, and Market Efficiency.
How does the author define the "January effect"?
The author investigates the January effect as a monthly calendar anomaly where higher average returns are expected, specifically identifying a potential shift in this pattern over time.
Why are rolling regressions used in this study?
Rolling regressions are used to investigate whether the calendar effects are constant or if they fluctuate significantly over the examined time period.
What is the significance of the GJR-GARCH model here?
The GJR-GARCH model is employed to account for asymmetric volatility, specifically capturing "leverage effects" where bad news impacts volatility differently than good news.
- Quote paper
- Eleftherios Giovanis (Author), 2008, The Day of the Week and the Month of the Year Effects: Applications of Rolling Regressions in EVIEWS and MATLAB, Munich, GRIN Verlag, https://www.grin.com/document/146637
