We argue that the current framework for predictive ability testing (e.g.,West, 1996) is not necessarily useful for real-time forecast selection, i.e., for assessing which of two competing forecasting methods will perform better in the future. We propose an alternative framework for out-of-sample comparison of predictive ability which delivers more practically relevant conclusions. Our approach is based on inference about conditional expectations of forecasts and forecast errors rather than the unconditional expectations that are the focus of the existing literature. We capture important determinants of forecast performance that are neglected in the existing literature by evaluating what we call the forecasting method (the model and the parameter estimation procedure), rather than just the forecasting model. Compared to previous approaches, our tests are valid under more general data assumptions (heterogeneity rather than stationarity) and estimation methods, and they can handle comparison of both nested and non-nested models, which is not currently possible. To illustrate the usefulness of the proposed tests, we compare the forecast performance of three leading parameter-reduction methods for macroeconomic forecasting using a large number of predictors: a sequential model selection approach,

Entropy is a classical statistical concept with appealing properties. Establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time-series context. We use this theory to derive the limiting distribution of Granger and Lin's (1994) normalized entropy measure of serial dependence, which was previously not available in the literature. We also apply our theory to construct a new entropy-based test for serial dependence, providing an alternative to Robinson's (1991) approach. To obtain accurate inferences, we propose and justify a consistent smoothed bootstrap procedure. The naive bootstrap is not consistent for our test. Our test is useful in, for example, testing the random walk hypothesis, evaluating density forecasts, and identifying important lags of a time series. It is asymptotically locally more powerful than Robinson's (1991) test, as is confirmed in our simulation. An application to the daily S&P 500 stock price index illustrates our approach.

This paper is organized as follows. In Section 2, we motivate and discuss the sequential testing approach. Section 3 discusses invariance principles of the past and present, and the CUSUM and fluctuation instability detectors. Section 4 contains some illustrative Monte Carlo experiments. A summary and concluding remarks are given in Section 5. Proofs are gathered into the Mathematical Appendix

This paper proposes two consistent one-sided specification tests for parametric regression models, one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values; the other based on the difference in sums of squared residuals between the parametric and nonparametric models. We estimate the nonparametric model by series regression

We analyze use of a quasi-likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a Markov regime-switching context. This test exploits mixture properties implied by the regime-switching process, but ignores certain implied serial correlation properties. When formulated in the natural way, the setting is nonstandard, involving nuisance parameters on the boundary of the parameter space, nuisance parameters identified only under the alternative, or approximations using derivatives higher than second order. We exploit recent advances by Andrews (2001) and contribute to the literature by extending the scope of mixture models, obtaining asymptotic null distributions different from those in the literature. We further provide critical values for popular models or bounds for tail probabilities that are useful in constructing conservative critical values for regime-switching tests. We compare the size and power of our statistics to other useful tests for regime switching via Monte Carlo methods and find relatively good performance. We apply our methods to reexamine the classic cartel study of Porter (1983) and reaffirm Porter's findings.