Practical Test for Goodness-of-Fit of Low-Order AR Models Applied to Pinot Noir Grape Harvest Dates

• Activity Number: 306
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Karim Rahim*+ and David Thomson
• Companies: Queen's University and Queen's University
• Keywords: Time Series ; Spectral Estimation ; Multitaper Method ; Autoregressive Coefficient ; Goodness of Fit

Abstract

This paper presents a practical test for goodness of fit of low-order Autoregressive (AR) models. The test compares the maximum absolute deviation between the estimated integrated spectrum and the theoretical integrated spectrum of an AR model. We demonstrate using simulation that the multitaper method results accurate estimates of AR model coefficients. Simulation is used to study the effectiveness of the goodness-of-fit test. Recently Tourre et al. (2011) presented a spectral analysis of the Burgundy Pinot Noir Grape Harvest Date (GHD) series using the multitaper method, and this analysis used an AR(1) model to prewhiten the data. We fit several AR models to the Pinot Noir series, then using our goodness-of-fit test, we determine that several AR models, including an AR(1), are reasonable for the GHD series.