Representation of Multiplicative Seasonal Vector Autoregressive Moving Average Models


AMERICAN STATISTICIAN, vol.63, no.4, pp.328-334, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 4
  • Publication Date: 2009
  • Doi Number: 10.1198/tast.2009.08040
  • Title of Journal : AMERICAN STATISTICIAN
  • Page Numbers: pp.328-334


Time series often contain observations of several variables and multivariate time series models are used to represent the relationship between these variables. There are many studies on vector autoregressive moving average (VARMA) models, but the representation of multiplicative seasonal VARMA models has not been seriously studied. In a multiplicative vector model, such as a seasonal VARMA model, the representation is not unique because of the noncommutative property of matrix multiplication. In this article, we carefully examine the consequences of different model representations on parameter estimation and forecasting through numerical illustrations, simulation, and the analysis of a housing starts and housing sales dataset.