Uniform Test for Predictive Regression With AR Errors

Testing predictability is known to be an important issue for the balanced predictive regression model. Some unified testing statistics of desirable properties have been proposed, though their validity depends on a predefined assumption regarding whether or not an intercept term nevertheless exists. In fact, most financial data have endogenous or heteroscedasticity structure, and the existing intercept term test does not perform well in these cases. In this paper, we consider the testing for the intercept of the balanced predictive regression model. An empirical likelihood based testing statistic is developed, and its limit distribution is also derived under some mild conditions. We also provide some simulations and a real application to illustrate its merits in terms of both size and power properties.

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“…Note that, similar to [ 23 ], one may take

to construct the test. Here, we however use an another weight

in order to increase the local power of the proposed test for the non-stationary cases.…”

Section: Methodology and Main Resultsmentioning

confidence: 99%

Testing the Intercept of a Balanced Predictive Regression Model

Wang

Liu

Fan

et al. 2022

Entropy

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“…Here, for the purpose of unifying the cases of stationary, nearly integrated and unit root, one can follow the idea in Li et al (2017) to take the model structure of {U t } into account by employing either empirical likelihood method or jackknife empirical likelihood method in Jing et al (2009).…”

Section: The Empirical Likelihood Functionmentioning

confidence: 99%

Unified Tests for a Dynamic Predictive Regression

Yang

Liu

Peng

et al. 2020

Journal of Business & Economic Statistics

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Testing for predictability of asset returns has been a long history in economics and finance. Recently, based on a simple predictive regression, Kostakis, Magdalinos and Stamatogiannis (2015, Review of Financial Studies) derived a Wald type test based on the context of the extended instrumental variable (IVX) methodology for testing predictability of stock returns and Demetrescu (2014) showed that the local power of the standard IVX-based test could be improved in some cases when a lagged predicted variable is added to the predictive regression on purpose, which poses a general important question on whether a lagged predicted variable should be included in the model or not. This paper proposes novel robust procedures for testing both the existence of a lagged predicted variable and the predictability of asset returns in a predictive regression regardless of regressors being stationary or nearly integrated or unit root and the AR model for regressors with or without intercept. A simulation study confirms the good finite sample performance of the proposed tests before applying the proposed tests to some real datasets in finance to illustrate their practical usefulness.

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“…To improve the efficiency of the estimation, a natural idea is to take into account the special structure of the errors if available. Note that it is common to assume that the errors further follow an AR process when they are correlated, while the performance of some testing procedures can be greatly improved once the AR structure has been addressed sufficiently, as shown in [13,14].…”

Section: Introductionmentioning

confidence: 99%

A Unified Test for the AR Error Structure of an Autoregressive Model

Wei

Liu

Fan

et al. 2022

Axioms

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A direct application of autoregressive (AR) models with independent and identically distributed (iid) errors is sometimes inadequate to fit the time series data well. A natural alternative is further to assume the model errors following an AR process, whose structure however has essential impacts on the statistical inferences related to the autoregressive models. In this paper, we construct a new unified test for checking the AR error structure based on the empirical likelihood method. The proposed test is desirable because its limit distribution is always chi-squared regardless of whether the autoregressive model is stationary or non-stationary, with or without an intercept term. Some simulations are also provided to illustrate the finite sample performance of this test. Finally, we apply the proposed test to a financial real data set.

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Uniform Test for Predictive Regression With AR Errors

Cited by 7 publications

References 23 publications

Testing the Intercept of a Balanced Predictive Regression Model

Testing the Intercept of a Balanced Predictive Regression Model

Unified Tests for a Dynamic Predictive Regression

A Unified Test for the AR Error Structure of an Autoregressive Model

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