Statistical Properties of an Integrated Stationary Stochastic Process
Abstract
This report examines some statistical properties of a first-order, stationary time series (x sub t) and of a series (y sub t) consisting of disjoint sums of (x sub t). A connection between continuous stochastic processes and discrete time series is made via the concept of correlation time interval. Expressions for the variances of the sum and average of (x sub t) for n terms are derived. An asymptotic variance estimate of the average is derived and is shown to be a reasonable upper bound. General expressions are derived for the variance and autocovariance of the integrated process (y sub t) in terms of the same properties for any stationary process. These results are particularized for the case in which (x sub t) is first order. Expressions for the spectral densities of x sub t and y sub t are given when (x sub t) is first order. A computer program to calculate the autocovariance and autospectrum of y sub t is attached.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1983
- Accession Number
- ADA134180
Entities
People
- George J. Schlenker