Accession Number : AD0715129

Title :   Asymptotically Efficient Estimates of the Parameters of a Moving Average Time Series.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Clevenson,M. Lawrence

Report Date : 31 JUL 1970

Pagination or Media Count : 101

Abstract : The thesis is concerned with the estimation of the parameters of a moving average time series, (x sub t, t= 0, plus or minus 1, plus or minus 2, ...), of order M. By definition, such a series has the representation x sub t = (eta sub t) + (b sub 1)(eta sub (t-1)) + (b sub 2)(eta sub (t-2)) +...+ (b sub M)(eta sub (+-M)) for some series of uncorrelated, identically distributed random variables eta sub t, t = 0, plus or minus 1, plus or minus 2, ...). It is assumed that the process has mean zero and is a Gaussian process; hence eta sub t has a normal distribution with mean and some unknown variance (sigma sub n) squared. The goal is to find asymptotically normal and efficient estimates of the parameters of the model. (Author)

Descriptors :   (*TIME SERIES ANALYSIS, MATHEMATICAL PREDICTION), STATISTICAL DISTRIBUTIONS, STOCHASTIC PROCESSES, DECISION THEORY, FOURIER ANALYSIS, INTEGRAL TRANSFORMS, MATRICES(MATHEMATICS), THEOREMS, THESES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE