Vector ARMA Models Research Articles

APPROACHES TO MULTIVARIATE MODELING OF WATER RESOURCES TIME SERIES1

ABSTRACT: Alternative approaches suggested for modeling multiseries of water resources systems are reviewed and compared. Most approaches fall within the general framework of multivariate ARMA models. Formal modeling procedures suggest a three‐stage iterative process, namely: model identification, parameter estimation and diagnostic checks. Although a number of statistical tools are already available to follow such modeling process, in general, it is not an easy task, especially if high order vector ARMA models are used. However, simpler ARMA models such as the contemporaneous and the transfer‐function models may be sufficient for most applications in water resources. Two examples of modeling bivariate and trivariate streamflow series are included. Alternative modeling procedures are used and compared by using data generation techniques. The results obtained suggest that low order models, as well as contemporaneous ARMA models, reproduce quite well the main statistical characteristics of the time series analyzed. It is assumed that the same conclusions apply for most water resources time series.

Distribution of the Residual Autocorrelations in Multivariate Arma Time Series Models

SUMMARY The large-sample distribution of the multivariate residual autocorrelations in the vector arma model is derived. This result is somewhat less complicated for the vector autoregressive model. A new multivariate portmanteau test for checking the adequacy of fitted vector arma models is developed. A simulation study shows that a simple modification of the portmanteau test improves its accuracy in small samples.

Corrections and extensions to "An innovations approach to least squares estimations--Part VII: Some applications of vector ARMA models"

In this technical note, we point out certain corrections to [1] and then give some extensions to its results for the prediction problem in ARMA models. The notation will follow closely that of [1].