Discrete Samples and Moving Sums in Stationary Stochastic Processes
作者:
L.G. Telser,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1967)
卷期:
Volume 62,
issue 318
页码: 484-499
ISSN:0162-1459
年代: 1967
DOI:10.1080/01621459.1967.10482922
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Assume that an autoregression generates the basic data but that the observations are an equi-spaced sample of moving sums of the basic data for non-overlapping discrete intervals. Simple least squares estimates of the underlying autoregression are not consistent. It is shown that it is possible to estimate consistently the coefficients of the underlying autoregression based on the equi-spaced sample. These results are equivalent to showing how to interpolate a finite number of missing values between adjacent sample observations if it is assumed that the underlying model is an autoregression of a specified order. It is not possible to interpolate a continuum of missing observations on the basis of an equi-spaced sample; this assertion is equivalent to the aliasing problem well known in spectral analysis. Finally, the analysis is extended to an autoregression including exogenous variables.
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