Testing for Long Memory Using Penalized Splines and Adaptive Neyman Methods

Abstract

AbstractTesting procedures for the null hypothesis of short memory against long memory alternatives are investigated. Our new test statistic is constructed using penalized splines method and Fan’s (1996) canonical multivariate normal hypothesis testing procedure. Using penalized splines method, we are able to eliminate the effects of nuisance parameters typically induced by short memory autocorrelation. Therefore, under the null hypothesis of any short memory processes, our new test statistic has a known asymptotic distribution. The proposed test statistic is completely data-driven or adaptive, which avoids the need to select any smoothing parameters. Since the convergence of our test statistic toward its asymptotic distribution is relatively slow, Monte Carlo methods are investigated to determine the corresponding critical value. The finite-sample properties of our procedure are compared to other well-known tests in the literature. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.KeywordsAdaptive Neyman testLong memoryPenalized splinePeriodogramShort memorySpectral density