Robust Predictive Regression

SSRN Electronic Journal, 2012

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, using predictive variables such as the dividend yield, the volatility risk premium or, labor income.

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.

2011

This paper focuses on the analytical discussion of a robust t-test for predictability and on the analysis of its …nite-sample properties. Our analysis shows that the procedure proposed exhibits approximately correct size even in fairly small samples. Furthermore, the test is well-behaved under short-run dependence, and can exhibit improved power performance over alternative procedures. These appealing properties, together with the fact that the test can be applied in a simple and direct way in the linear regression context, suggests that the modi…ed t-statistic introduced in this paper is well suited for addressing predictability in empirical applications.

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.

2007

Robust estimation techniques, such as LAD, M and L k and quasi-maximum likelihood techniques based on symmetric probability density functions, such as student's T, Laplace, GED and GT, are often used instead of OLS to obtain more efficient regression parameters in thick-tail data. The empirical and theoretical results presented in this paper show that when skewness is present in the data, symmetric robust estimation techniques produce biased regression intercepts. The simulation results favor the T and GT regression estimators in leptokurtic symmetric data and the skewed T and skewed GT regression estimators in skewed data. In normal data, the OLS estimators are preferred because of their simplicity (JEL: G12, C13, C14, C15).

Frontiers in Applied Mathematics and Statistics, 2016

In this analysis of the risk and return of stocks in global markets, we apply several applications of robust regression techniques in producing stock selection models and several optimization techniques in portfolio construction in global stock universes. We find that (1) that robust regression applications are appropriate for modeling stock returns in global markets; and (2) mean-variance techniques continue to produce portfolios capable of generating excess returns above transactions costs and statistically significant asset selection. We estimate expected return models in a global equity markets using a given stock selection model and generate statistically significant active returns from various portfolio construction techniques.

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 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.

2017

Empirical evidence on the predictability of aggregate stock returns has shown that many commonly used predictor variables have little power to predict the market out-of-sample. However, a recent paper by Kelly and Pruitt (2013) find that predictors with strong out-of-sample performance can be constructed, using a partial least squares methodology, from the valuation ratios of portfolios. This paper shows that the statistical significance of this out-of-sample predictability is overstated for two reasons. Firstly, the analysis is conducted on gross returns rather than excess returns, and this raises the apparent predictability of the equity premium due to inclusion predictable movements of interest rates. Secondly, the bootstrap statistics used to assess out-of-sample significance do not account for small-sample bias in the estimated coefficients. This bias is well known to affect tests of in-sample significance (Stambaugh (1986)) and I show it is also important for out-of-sample tes...

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.