On Testing Goodness-of-Fit of AR(P) Model Through the Serial Dependence of the Residual Process

• Activity Number: 338 - Time Series and Forecasting
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Phyllis Wan* and Richard A. Davis and Muneya Matsui and Thomas Mikosch
• Companies: Columbia University and Columbia University and Nanzan University and University of Copenhagen
• Keywords: time series ; testing independence ; auto- and cross-distance covariance ; AR process ; residuals ; Fourier anaylsis

Abstract

In recent years, distance covariance as a dependence measure has received considerable attentions due to its many advantages, among which most notably, the ability to detect nonlinear dependence. We implement this concept in auto-distance correlation function (ADCF) as a replacement for autocorrelation function (ACF), in measuring serial dependence in time series. We find that for a time series generated from an AR(p) model, the limit distribution of the empirical ADCF of the residual process differs markedly from that of an iid sequence when innovation process has finite variance. Meanwhile if the innovations are regularly varying with indices alpha in (0,2), the difference will not be observed. One could use this test the goodness-of-fit of AR(p) model. The idea of ADCF was first proposed in Zhou (2012) using the distance covariance with weight measure in Székely et al. (2007). In the case of ADCF for residuals we note that the convergence of the limit does not hold for all choices of weight function -- in particular, the one in Székely et al. (2007) may not be suitable.