# Accession Number:

## AD0716591

# Title:

## Principal Component Analysis of Time Series 1,2

# Descriptive Note:

## Doctoral thesis

# Corporate Author:

## OHIO STATE UNIV COLUMBUS DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 1970-09-01

# Pagination or Media Count:

## 77.0

# Abstract:

The primary purpose of this dissertation is to investigate the properties of the principal components of a finite set of random variables comprising a part of a discrete time series. In the first chapter, the covariance structure between a set of random variables y, x sub 1,...,x sub p, which yields the result that the first k p principal components of x sub 1,.. .,x sub p provide a better predictor of yin the sense of expected squared error than do any k of the variables x sub 1,...,x sub p themselves, is examined. In the remaining chapters, principal component processes which are linear combinations of xt, xt-1,...,xt-n xt is a random process and n is an arbitrary positive integer, are defined and their properties investigated in terms of their frequency content. It is shown that when xt is a stationary moving average process, an autoregressive process, or a mixed moving average autoregressive process, the first principal component process tends as n approaches infinity to contain only the frequency at which the spectral density of xt obtains its maximum value. It is shown, moreover, that when the process xt contains deterministic components such as a trend or a periodic component, certain of the principal components processes tend to model those deterministic components.

# Descriptors:

# Subject Categories:

- Statistics and Probability