Date of Award
Doctor of Philosophy (PhD)
Gallagher , Colin
Park , Chanseok
Kulasekera , K.B.
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 non-independent 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.
Su, Nan, "New Results in Multivariate Time Series with Applications" (2012). All Dissertations. 954.