Inference Based on the Vector Autoregressive and Moving Average Model

Abstract

Based on the stationary vector ARMA process, this chapter shows how the partial measures of interdependence introduced in Sect. 3.3 are numerically evaluated and applied to practical situations. Section 4.1 discusses the statistical inference on those measures using the standard asymptotic theory of the Whittle likelihood inference for stationary multivariate ARMA processes. The point is the use of simulation-based estimations of the covariance matrix of each measure-related statistic. In Sect. 4.2, we investigate the small sample performance of partial one-way effect measure estimates using Monte Carlo data generated by a pair of trivariate data generating processes, the VAR(2) and VARMA(1,1) models. All model parameter estimates are produced using an improved version of the Takimoto and Hosoya (2004, 2006) procedure. The partial frequency-wise measures of the one-way effect are evaluated using spectral factorization, and the parameters are substituted with a modified Whittle estimate. To illustrate the analysis of interdependence in the frequency domain, Sect. 4.3 provides an empirical analysis of US interest rates and economic growth data.