We consider GLS and OLS estimation in a linear regression model with serially correlated errors, and we provide the following contributions. First, we clarify when OLS is consistent or not. Second, we give sufficient conditions such that GLS is valid without the assumption of exogenous regressors (uncorrelated with past innovations). Third, we devise a feasible GLS procedure valid whether or not the regressors are exogenous, and which achieves a MSE close to that of the correctly specified infeasible GLS. Fourth, we derive the asymptotic distribution of this feasible GLS estimate: with exogenous regressors, the limit distribution is the same as that of the infeasible GLS estimator. However, with non-exogenous regressors, an additional term is present in the asymptotic variance. We provide a variance estimator, free of tuning parameters, which delivers confidence intervals with asymptotically correct coverage in both cases. We also illustrate how GLS can be more robust than OLS when the regressors are exogenous, even when GLS is based on an incorrect correction. The main assumptions are: a) the regressors are pre-determined (uncorrelated with future innovations); b) the errors are stationary thereby admitting a Wold representation in terms of some unpredictable innovations; c) the moving-average representation of the errors is invertible and implies a short-memory process. We also briefly address issues related to heteroskedastic errors.
We develop the Sample Splitting Alpha (SSA) test, a formal out-of-sample (OOS) test for evaluating whether an asset pricing factor model satisfies the zero-alpha restriction in high-dimensional settings. The test uses sample splitting to separate portfolio weight estimation from model evaluation and ridge regularization to stabilize the portfolio problem when the number of test assets is large. We show that each single SSA statistic is asymptotically Gaussian under mild regularity conditions. For the aggregated SSA statistic used in implementation, we characterize the dependence across split statistics and compute p-values by resampling. Economically, the statistic relates to the OOS incremental spanning value of the chosen test assets relative to a candidate factor model, measured by the OOS squared information ratio. The simulation results accord with the asymptotic analysis. In empirical applications, SSA rejects some statistically constructed factor models more often than the in-sample benchmarks, despite those models’ strong in-sample fit.
Predictive regression models are often used to evaluate the predictive capability of economic fundamentals on bond and equity returns. Inferential procedures in these regressions typically employ parameter constancy or piecewise constancy in slope coefficients. Such formulations are prone to misspecification, more especially during periods of disturbance or evolution in prevailing economic and financial conditions, which can lead to size distortion and spurious evidence of predictability. To address these issues the present work proposes a semiparametric predictive regression model with mixed-root regressors and time-varying coefficients that allow for smooth evolution in the generating mechanism over time. For estimation and inference a novel variant of the self-generated instrument approach called sieve-IVX is introduced, giving a robust approach to inference concerning time-varying predictability that is applicable irrespective of the degrees of persistence. Asymptotic theory of the Sieve-IVX approach is based on a new infinite dimensional invariance principle that delivers limit theory for sieve-IVX estimation, validating pointwise and uniform inference procedures for testing predictability and model specification. Simulations show excellent performance characteristics of the resulting tests in finite samples. An empirical exercise is conducted examining excess S&P 500 returns, applying Sieve-IVX regression with pointwise and uniform tests to reveal evidence of time-varying patterns in the predictive capability of commonly used fundamental variables.
Consensus professional stock return forecasts are three times more volatile than those of non-professionals and econometricians. We show that this difference reflects professionals’ strong countercyclical responses to macro shocks, which explain 20–40% of forecast variation and are consistent with rational asset pricing models in which discount rates rise in bad times. We use macro shocks to identify the discount-rate component of professional forecasts and find that it closely matches realized returns. We conclude that professionals’ assessment of the discount-rate impact of macro shocks distinguishes them from other forecasts, challenging existing models of expectation formation.
This paper develops a test for coefficient variability in spatial regressions. The test is designed to have good power for a wide range of persistent patterns of coefficient variation, be applicable in a wide range of spatial designs, and accommodate spatial correlation in regressors and regression errors. The test approximates the locally best invariant test for coefficient stability in a Gaussian regression model with martingale-like coefficient variation under the alternative, and is thus a spatial generalization of the Nyblom (1989) test of coefficient stability in time series regressions.
