Date of Award
5-2012
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Legacy Department
Mathematical Science
Committee Chair/Advisor
Lund, Robert
Committee Member
Gallagher , Colin
Committee Member
Park , Chanseok
Committee Member
Kulasekera , K.B.
Abstract
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.
Recommended Citation
Su, Nan, "New Results in Multivariate Time Series with Applications" (2012). All Dissertations. 954.
https://tigerprints.clemson.edu/all_dissertations/954