Stochastic Volatility and Cointegration in Statistics Canada's Retail Trade Series

• Activity Number: 96
• Type: Topic Contributed
• Date/Time: Monday, August 7, 2006 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economics Statistics Section
• Author(s): Thierno A. Balde*+ and Ioana Schiopu-Kratina and Benoit Quenneville
• Companies: Statistics Canada and Statistics Canada and Statistics Canada
• Keywords: stochastic volatility ; ARCH-GARCH models ; cointegration ; ARIMA transfer functions ; linear regression

Abstract

In this paper, we illustrate the concepts of volatility and cointegration introduced by R. F. Engle and C. W. Granger on Statistics Canada's Retail Trade Series. Although these concepts have been used extensively for economic time series, they do not seem to have been applied to seasonally adjusted time series typically produced by statistical agencies. We show that there is volatility in the New Motor Vehicle Survey series (NMVS). We fit a GARCH- and an ARIMA-type model and compare their performances. We find that the GARCH model gives better predictions than the ARIMA model, as it takes into account the existing volatility. We also find a cointegration relationship among the Monthly Retail Trade Survey series and two of its components, namely NMVS and Large Monthly Retailers series. Then, We use ARIMA transfer functions to model this cointegration relationship.