Vector and Multidimensional Time Series Analysis
Binod Kumar Sahu · 2021
This chapter considers the basic properties of stationary multivariate time series having multivariate white noise and estimation of mean vector, covariance matrices at different lags and testing serial independence based on multivariate observations. It discusses the multivariate ARMA models and their identification which is simplified by restricting our attention to vector autoregressive processes. The chapter explains model by using multivariate Yule-Walker equations and by generalizing Durbin-Levison algorithm. An intervention model analysis is useful in case of either level change in the time series which may arise out of policy changes in economic time series or due to faulting in geological/stratigraphic/drilling data. The iron ores in Goa are worked as an opencast mine at Bicholim, Goa. This mine was sampled at 1 m intervals vertically and 3 m intervals along strike for the time series modelling. Transfer function models establish a relation between the output time series and a set of related input random time series through a linear filter.