New Results in Multivariate Time Series with Applications

This dissertation presents some new results in stationary multivariate time series. The asymptotic properties of the sample autocovariance are established, that is, we derive a multivariate version of Bartlett’s Classic Formula. The estimation of the autocovariance function plays a crucial role in time series analysis, in particular for the identification problem. Explicit formula for vector autoregressive (p) and vector moving average (q) processes are presented as examples. We also address linear processes driven by nonindependent errors, a feature that permits consideration of multivariate GARCH processes. We next compare several techniques to discriminate two multivariate stationary signals. The compared methods include Gaussian likelihood ratio variance/covariance matrix tests and spectral-based tests gauging equality of the autocovariance function of the two signals. A simulation study is presented that illuminates the various properties of the methods. An analysis of experimentally collected gearbox data is also presented.