Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science


Lund, Robert

Committee Member

Gallagher , Colin

Committee Member

Park , Chanseok

Committee Member

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.