An Evaluation of Kan and Wang's Adjusted Box-Pierce Test Using Seasonal Time Series

• Activity Number: 124
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Brian Carl Monsell*+
• Companies: U.S. Census Bureau
• Keywords: Autocorrelation ; regARIMA model ; Kalman filter ; modeling diagnostics ; elliptical distributions

Abstract

Kan and Wang (2010) develop an exact distribution for the sample autocorrelation coefficients. Using this distribution, the authors propose an adjustment to the Box-Pierce diagnostic commonly used to test the randomness of time series, and show it has superior size properties to the traditional Box-Pierce and Ljung-Box statistics. In this paper, I will examine the size and power properties of this new diagnostic for seasonal lags, and will examine the performance of the adjusted diagnostic versus the Box-Pierce and Ljung-Box statistics for simulated and Census Bureau time series. Also, Ansley and Newbold (1979) showed that Box-Pierce or Ljung-Box statistics computed from autocorrelations of Kalman filter innovations had better properties than those derived from the residuals of MLE for ARMA models. I will seek to confirm this, and compare such statistics to the Kan and Wang statistic.