Comparing predictive accuracy in small samples

We consider fixed-b and fixed-m asymptotics for the Diebold and Mariano (1995) test of predictive accuracy. We show that this approach allows to obtain predictive accuracy tests that are correctly sized even in small samples. We apply the alternative asympotics for the Diebold and Mariano (1995) test to evaluate the predictive accuracy of the Survey of Professional Forecasters (SPF) against a simple random walk. Our results show that the predictive ability of the SPF was partially spurious, especially in the last decade.

[1]  Paul Newbold,et al.  Testing the equality of prediction mean squared errors , 1997 .

[2]  Ulrich K. Müller.  HAC Corrections for Strongly Autocorrelated Time Series , 2014 .

[3]  Andrew J. Patton,et al.  Asymptotic Inference about Predictive Accuracy Using High Frequency Data , 2013 .

[4]  Todd E. Clark.  Finite‐sample properties of tests for equal forecast accuracy , 1999 .

[5]  E. J. Hannan,et al.  Multiple time series , 1970 .

[6]  F. Iacone,et al.  Autocorrelation robust inference using the Daniell kernel with fixed bandwidth , 2015 .

[7]  Nicholas M. Kiefer,et al.  A NEW ASYMPTOTIC THEORY FOR HETEROSKEDASTICITY-AUTOCORRELATION ROBUST TESTS , 2005, Econometric Theory.

[8]  P. Kokoszka,et al.  The periodogram at the Fourier frequencies , 2000 .

[9]  Yixiao Sun.  A Heteroskedasticity and Autocorrelation Robust F Test Using an Orthonormal Series Variance Estimator , 2013 .

[10]  Todd E. Clark,et al.  Tests of Equal Forecast Accuracy and Encompassing for Nested Models , 1999 .

[11]  Victor Solo,et al.  Asymptotics for Linear Processes , 1992 .

[12]  Realistic evaluation of real-time forecasts in the Survey of Professional Forecasters , 2010 .

[13]  Barbara Rossi,et al.  Forecast comparisons in unstable environments , 2010 .

[14]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[15]  Kerstin Vogler,et al.  Table Of Integrals Series And Products , 2016 .

[16]  W. Newey,et al.  Automatic Lag Selection in Covariance Matrix Estimation , 1994 .

[17]  Francis X. Diebold,et al.  Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold–Mariano Tests , 2012 .