Predictive Regression and Robust Hypothesis Testing: Predictability Hidden by Anomalous Observations

2011

This paper investigates, both in finite samples and asymptotically, statistical inference on predictive regressions where time series are generated by present value models of asset prices. We show that regression-based tests, including robust tests such as Jansson and Moreira's conditional test and Campbell and Yogo's Q-test, are inconsistent and thus suffer from lack of power in local-to-unity models for the regressor persistence. The main reason is that the near-integrated regressor from the present value model slows down the convergence rates of the estimates, an effect which is masked in predictive regressions analysis with exogenous constant covariance of innovations. We illustrate these properties in a simulation study and analyze the predictability of several stock returns series. JEL Classification: C12, C22, G1. We are grateful to the Co-Editor and two anonymous referees for helpful comments and suggestions. We also thank Enrique Sentana for helpful suggestions.

Journal of Financial Econometrics, 2013

This paper investigates, both in finite samples and asymptotically, statistical inference on predictive regressions where time series are generated by present value models of stock prices. We show that regression-based tests, including robust tests such as the conditional test and the Q-test, are inconsistent and thus suffer from lack of power in local-to-unity models for the regressor persistence. The main reason is that, despite the near-integrated dividend-price ratio, the convergence rates of the estimates are slowed down because the present value model implies a shrinking innovation variance on the predictor, an effect which is masked in a predictive regression analysis with exogenous constant covariance of innovations. We illustrate these properties in a simulation study.

Journal of Econometrics, 2016

We provide a simple and innovative approach to test for predictability in stock returns. Our approach consists of two methodologies, time change and instrumental variable estimation, which are employed respectively to deal effectively with persistent stochastic volatility in stock returns and endogenous nonstationarity in their predictors. These are prominent characteristics of the data used in predictive regressions, which are known to have a substantial impact on the test of predictability, if not properly taken care of. Our test finds no evidence supporting stock return predictability, at least if we use the common predictive ratios such as dividend-price and earnings-price ratios.

SSRN Electronic Journal

This paper aims to test an important hypothesis in …nancial economics: whether equity returns are predictable over various horizons? The conventional wisdom in the literature is that aggregate dividend yields strongly predict excess returns, and the predictability is stronger at longer horizons (Fama and French (1988), Campbell (1991), and Cochrane (1992)). In contrast, Ang and Bekaert (2007) …nd that dividend yields, together with the short rate, predict excess returns only at short horizons, and do not have any long-horizon predictive power. In this paper, we undertake an analysis of both in-sample and out-of-sample tests of equity return predictability to better understand the empirical evidence on return predictability over di¤erent time horizons. We …rst propose a nonparametric test to examine the predictability of equity returns, which can be interpreted as a signal-to-noise ratio test. Our empirical results show that the short rate, dividend yields and earnings yields have good predictability power for both short and long horizons, which is di¤erent from both the conventional wisdom and Ang and Bekaert (2007). Also, using our nonparametric test, a comprehensive in-sample and out-of-sample analysis documents that the predictor variables (dividend yields, earnings yields, dividend payout ratio, short rate, in ‡ation, book-to-market ratio, investment to capital ratio, corporate issuing activity, and consumption, wealth, and income ratio) have predictability power on equity returns but this cannot be well captured by linear prediction models. In addition, we use the nonparametric test to compare the conventional long-horizon prediction regression models on predictor variables with the historical mean model, where there has exists a debate about which model has better forecasting power for equity returns (Campbell and Thompson (2007) and Goyal and Welch (2007)). We …nd that the prevailing prediction model has a better forecasting power than the historical mean model because the former has a lower neglected signal-to-noise ratio. Finally, our nonparametric predictive models have lower RMSE than the historical mean model at both shorthorizon and long-horizon. Using our nonparametric methods, both combined and individual forecast outperform the historical average.

SSRN Electronic Journal, 2013

Testing procedures for predictive regressions with lagged autoregressive variables imply a suboptimal inference in presence of small violations of ideal assumptions. We propose a novel testing framework resistant to such violations, which is consistent with nearly integrated regressors and applicable to multi-predictor settings, when the data may only approximately follow a predictive regression model. The Monte Carlo evidence demonstrates large improvements of our approach, while the empirical analysis produces a strong robust evidence of market return predictability hidden by anomalous observations, both in-and out-of-sample, using predictive variables such as the dividend yield or the volatility risk premium.

Finance Research Letters, 2019

A bootstrap test is proposed for predictability of asset returns. The bootstrap is conducted with the likelihood ratio test in a restricted VAR form. The test shows no size distortion in small samples with desirable power properties. A wild bootstrap version, valid for financial returns showing unknown forms of conditional heteroskedasticty, is also proposed. As an application, predictive powers of dividend-price ratio and interest rate for U.S stock returns are evaluated.

Journal of Asset Management, 2015

This paper considers stock return predictability and its source using ratios derived from stock prices, dividends, output and consumption. We analyse twenty-nine stock markets (sampled quarterly) and seventeen stock markets (sampled annually). One period ahead predictive regressions provide some support for predictability of returns although there is also evidence supporting dividend and consumption growth predictability. Greater evidence for predictable stock market returns is found when estimating panel regressions and through consideration of long-horizon predictability. Furthermore, examining long-horizons allows us to comment on the source of predictability. Our results suggest that predictability arises from both time-variation in expected returns and cash-flow.

Predictive regressions are linear specifications linking a noisy variable such as stock returns to past values of a very persistent regressor with the aim of assessing the presence of predictability. Key complications that arise are the potential presence of endogeneity and the poor adequacy of asymptotic approximations. In this paper we develop tests for uncovering the presence of predictability in such models when the strength or direction of predictability may alternate across different economically meaningful episodes. An empirical application reconsiders the Dividend Yield based return predictability and documents a strong predictability that is countercyclical, occurring solely during bad economic times.

Quantitative Finance, 2015

This paper examines the return predictability of the US stock market using portfolios sorted by size, book-to-market ratio and industry. We use novel panel variance ratio tests, based on the wild bootstrap proposed in this paper, which exhibit desirable size and power properties in small samples. We have found evidence that stock returns have been highly predictable from 1964 to 1996, except for a period leading to the 1987 crash and its aftermath. After 1997, stock returns have been unpredictable overall. At a disaggregated level, we find evidence that large-cap portfolios have been priced more efficiently than small-or medium-cap portfolios; and that the stock returns from high-tech industries are far less predictable than those from non-high-tech industries.

SSRN Electronic Journal, 2000

A number of recent studies have measured the quantitative effect of excess return predictability on the optimal consumption and portfolio choices of a rational investor, and they have used the utility costs of ignoring predictability as a natural measure of economic significance. We use a general equilibrium model as a laboratory for generating predictable excess returns and for assessing the properties of the estimated consumption/portfolio rules, under both the empirical and the true dynamics of excess returns. We find that conditional rules based on ordinary least squares estimates of excess returns are severely biased, and they have a large variance across multiple simulated histories of the model. In this experiment, we find the estimation issues to be so severe that the simple unconditional consumption and portfolio rules, from Merton (1969), actually outperform (in a utility cost sense) both simple and bias-corrected empirical estimates of conditionally optimal policies.