Principal Component Analysis of Time Series 1,2
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 y(in 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 x(t), x(t-1),...,x(t-n) x(t) 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 x(t) 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 x(t) obtains its maximum value. It is shown, moreover, that when the process x(t) contains deterministic components such as a trend or a periodic component, certain of the principal components processes tend to model those deterministic components.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1970
- Accession Number
- AD0716591
Entities
People
- J. Richard Stewart
Organizations
- Ohio State University