Developments in Multivariate Time Series Modeling

We consider modeling procedures for multiple time series which aim to address the challenge of providing both a good representation of the structure, and an efficient parameterization. We first review a method, applied to vector autoregressions of low order, which uses conditional independence graphs to identify a sparse structural autoregressive representation. We show by an example how this may be extended to identify a sparse structural form of an ARMA(1,1) model for a series of seven daily US dollar term rates. The identified structure reveals the pivotal role of the series of two year rates, and highlights sources of heteroscedasticity. Vector autoregressions of high order are widely used to provide an empirical approximation to multiple time series structure, but the large number of parameters in these models restricts the possible maximum lag when the series is of moderate length. We present, and illustrate by example, a simple extension of the vector autoregression in which the predictors are smoothed functions of the past variables. This allows information from higher lags to be used in a model of relatively low order, and can improve forecasts at higher lead times.