this paper are covered by U.S. Patent 5,893,069

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,

In this paper, we draw on both the consistent specification testing and the predictive ability testing literatures and propose a test for predictive accuracy which is consistent against generic nonlinear alternatives. Broadly speaking, given a particular reference model, assume that the objective is to test whether there exists any alternative model, among an infinite number of alternatives, that has better predictive accuracy than the reference model, for a given loss function. A typical example is the case in which the reference model is a simple autoregressive model and the objective is to check whether a more accurate forecasting model can be constructed by including possibly unknown (non) linear functions of the past of the process or of the past of some other process(es). We propose a statistic which is similar in spirit to that of White (2000), although our approach diers from his as we allow for an innite number of competing models that may be nested. In addition, we allow for non ...

A number of variants of seven procedures designed to check for the absence of causal ordering are summarized. Five are based on classical hypothesis testing principles, including: Wald F-tests designed for stationary and difference stationary data; sequential Wald tests that account for cointegration; surplus lag regression type tests; and nonparametric fully modied vector autoregressive type tests. The other two are based on model selection techniques, and include: complexity penalized likelihood criteria; and ex-ante model selection based on predictive ability. In addition, various other approaches to checking for the causal order of economic variables are briey discussed. A small set of Monte Carlo experiments is carried out in order to assess empirical size, and it is found that although all tests perform well in the environments where the true lag dynamics and cointegrating ranks are "accurately" estimated, simple surplus lag type tests of the variety discussed by Toda and Yamamoto ...

This not-for-publication appendix contains proofs of Theorems 3.1- 3.3 as discussed in the text. It also contains lemmas used to prove the theorems. In addition, the appendix contains

Forecasters and applied econometricians are often interested in comparing the predictive accuracy of nested competing models. A leading example of a context in which competing models are nested is when predictive ability is equated with “out-of-sample Granger causality”. In particular, it is often of interest to assess whether historical data from one variable are useful when constructing a forecasting model for another variable, and hence our use of terminology such as “out-of-sample Granger causality ” (see e.g. Ashley, Granger and Schmalensee (1980)). In this paper we examine and discuss three key issues one is faced with when constructing predictive accuracy tests, namely: the contribution of parameter estimation error, the choice of linear versus nonlinear models, and the issue of (dynamic) misspecification, with primary focus on the latter of these issues. One of our main conclusions is that there are a number of easy to apply statistics constructed using out of sample conditional moment conditions which are robust to the presence of dynamic misspecification under both hypothesis. We provide some new Monte Carlo findings and empirical evidence based on the use of such tests. In particular, we analyze the finite sample properties of the consistent out of sample test of Corradi and Swanson (2002) using data generating processes calibrated with

This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy and encompassing applied to predictions from nested long-horizon regression models. We first derive the asymptotic distributions of a set of tests of equal forecast accuracy and encompassing, showing that the tests have non-standard distributions that depend on the parameters of the data-generating process. Using a simple model-based bootstrap for inference, we then conduct Monte Carlo simulations of a range of data-generating processes to examine the finite-sample size and power of the tests. In these simulations, the bootstrap yields tests with good finite--sample size and power properties, with the encompassing test proposed by Clark and McCracken (2001) having superior power. The paper concludes with a reexamination of the predictive content of capacity utilization for core inflation.

In this paper, we draw on both the consistent speci¯cation testing and the predictive ability testing literatures and propose a test for predictive accuracy which is consistent against generic nonlinear alternatives. Broadly speaking, given a particular reference model, assume that the objective is to test whether there exists any alternative model, among an in¯nite number of alternatives, that has better predictive accuracy than the reference model, for a given loss function. A typical example is the case in which the reference model is a simple autoregressive model and the objective is to check whether amore accurate forecasting model can be constructed by including possibly unknown (non) linear functions of the past of the process or of the past of some other process(es). We propose a statistic which is similar in spirit to that of White (2000), although our approach di®ers from his as we allow for an in¯nite number of competing models that may be nested. In addition, we allow for non vanishing parameter estimation error. In order to construct valid asymptotic critical values, we implement a conditional p-value procedure which extends the work of Inoue (1999) by allowing for non vanishing parameter estimation error. In a series of Monte Carlo experiments, we focus on a version of our test which can be interpreted as an out of sample nonlinear Granger causality test,

This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy and encompassing applied to predictions from nested long-horizon regression models. We first derive the asymptotic distributions of a set of tests of equal forecast accuracy and encompassing, showing that the tests have non-standard distributions that depend on the parameters of the data-generating process. Using a simple model–based bootstrap for inference, we then conduct Monte Carlo simulations of a range of data-generating processes to examine the finite-sample size and power of the tests. In these simulations, the bootstrap yields tests with good finite–sample size and power properties, with the encompassing test proposed by Clark and McCracken (2001) having superior power. The paper concludes with a reexamination of the predictive content of capacity utilization for core inflation.

Todd E. Clark is an assistant vice president and economist at the Federal Reserve Bank of Kansas City. Michael W. McCracken is an assistant professor of economics at Louisiana State University. The authors gratefully acknowledge the helpful comments of: Ken West, anonymous