The concept of predictive regressions has been studied for over the past 20 years and its application is particularly present in applied economics, finance and econometrics. The basic set-up in the predictive regression framework associates the noisy explained variable with the lagged persistent regressor, which can be characterized as a process close to the unit root process. In my work I describe the relevance and implications of an adoption of the linear predictive regressions in forecasting the volatile stock return using the lagged variable, dividend-price ratio, which is highly persistent. Subsequently, I aim to answer questions whether the excess stock returns are predictable using dividend yields and whether the predictability is stable over time. The analysis I conduct, based on financial data, aim to detect the hypothetical presence of structural breaks in the model. In order to search for the structural instability of coefficients I construct a Wald test for each possible structural break location and investigate the accuracy of the SupWald statistic and its tabulated critical values in the framework described. Having obtained the test statistic for each of the possible break-points, I describe predictive power of explanatory variable and provide economic rationale to support some of the statistical outcomes.
Table of Contents
1. Introduction
2. Linear Predictive Regression Model
3. Econometric Methodology and Hypothesis of Interest
4. Empirical Results
5. Economic Interpretation
6. Conclusions
References
Appendix
Table I, II, III
Table IV, V, VI
Table VII, VIII
Table IX, X
Figure I
Research Objectives and Core Themes
This dissertation examines the predictive power of dividend yields in forecasting future excess stock returns within a linear predictive regression framework, while explicitly addressing the issue of structural instability over time.
- Application of linear predictive regression to financial time series.
- Econometric challenges posed by persistent explanatory variables (endogeneity and near-unit-root processes).
- Detection of structural breaks using the Andrews (SupWald) test.
- Assessment of parameter stability across distinct economic regimes.
- Economic interpretation of findings in relation to historical stock market shocks.
Excerpt from the Book
3 Econometric Methodology and Hypothesis of Interest
Lettau and Nieuwerburgh (2007) in their studies describe the incompatible outcomes of stock predictability shown in the recent literature. There have been various opinions, some supporting the claim that the stock returns may be partially forecastable with financial data, and others declaring the nonexistence of predictability. Certainly, findings were not identical because test measures, assumptions and methodologies presented in these paper were not unified and not all statistical problems were taken into account. For example, Fama and French (1988) report a high predictive ability of dividend-price ratio on the future stock returns, but they relied mainly on asymptotic theory. Hence, due to the inference problem that may appear as a result of structural instability it would be sensible to test the null hypothesis of linearity: H0: α1=α2, β1=β2 (3.1) against the general model presented in equations (2.4). Hence, the intuition is to test the structural stability of both, intercept and slope coefficient, in the linear predictive regression model (parameters α and β from equation (2.1)). The implication of the presence of a break is that it may alter the conditional expected stock return E(yt+1|xt). As a consequence, the predictive power of the lagged explanatory variable can be inappropriately estimated. If the null hypothesis cannot be rejected, this result could justify the methodology previously described in the literature by, exempli gratia, Campbell and Yogo (2006). What is more, in the case where the result suggests the constant mean specification, that is α1=α2=0 and β1=β2=0, the predictive power of the lagged independent variable used in the regression is said to be nonexistent. On the other hand, the evidence of the structural break would support the claim presented by Rapach and Wohar (2006). In order to verify which of the confronting claims may be correct, I proceed to testing for the structural instability of the coefficients.
Summary of Chapters
1. Introduction: Outlines the concept of predictive regressions, identifies statistical challenges like persistence and endogeneity, and states the primary research goal of assessing predictive ability and stability.
2. Linear Predictive Regression Model: Defines the mathematical framework of the regression model and discusses the econometric issues arising from persistent variables and endogenous innovations.
3. Econometric Methodology and Hypothesis of Interest: Details the testing procedure for structural breaks, specifically discussing the Andrews (SupWald) test as a remedy for unknown break dates.
4. Empirical Results: Presents the findings of applying the model to US stock market data (1927-2007), testing for unit roots and evaluating coefficient stability across sub-periods.
5. Economic Interpretation: Provides context for the statistical findings by correlating identified potential break-points with major historical economic events and shifts in stock market dynamics.
6. Conclusions: Summarizes the dissertation's contributions, acknowledging the complexity of predictive regression models and the necessity of testing for structural instability.
Keywords
Predictive regression, Dividend yields, Excess stock returns, Structural break, Andrews test, SupWald statistic, Parameter instability, Financial econometrics, Endogeneity, Persistence, Unit root, Forecasting, Market efficiency, Economic regime, Asset pricing.
Frequently Asked Questions
What is the core focus of this dissertation?
This work explores whether dividend yields can predict excess stock returns and whether this predictive relationship remains stable over time or is subject to structural breaks.
What are the central thematic fields covered?
The research sits at the intersection of financial econometrics and asset pricing, specifically focusing on the statistical validity of predictive models for stock returns.
What is the primary research question?
The study asks if excess stock returns are predictable using dividend yields and if such predictability holds stable across different economic regimes.
Which scientific method is applied?
The author employs a linear predictive regression framework and utilizes the Andrews (SupWald) test to detect potential structural instability in model coefficients.
What is covered in the main section of the work?
The work covers the theoretical formulation of the predictive model, the identification of statistical pitfalls (like endogeneity), the empirical application to long-term financial data, and the economic interpretation of found instabilities.
Which keywords best characterize the work?
Key terms include Predictive regression, Dividend yields, Structural break, SupWald statistic, and Asset pricing.
Why is the Andrews test used instead of a standard Chow test?
The Andrews test is used because the exact timing of potential structural breaks in the financial data is unknown, whereas the Chow test requires an a priori known break-point.
How do economic events influence the statistical findings?
The author notes that statistical break-points, such as those found in 1932 and 1995, often coincide with significant historical market events like the Great Depression and the emergence of new technologies in the 90s.
- Quote paper
- Lukasz Prochownik (Author), 2011, Linear predictive regression framework, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/182493
