Statistical Properties of an Integrated Stationary Stochastic Process
ARMY ARMAMENT MUNITIONS AND CHEMICAL COMMAND ROCK ISLAND IL SYSTEMS AND OPERATIONS ANALYSIS DIRECTORATE
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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.
- Statistics and Probability
- Computer Programming and Software