THE SPECTRAL THEORY OF DISCRETE STOCHASTIC PROCESSES
成果类型：
Article
署名作者：
MORAN, PAP
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/36.1-2.63
发表日期：
1949
页码：
6370
关键词：
摘要：
Given a stochastic process, {xt}, generated by a moving average whose weights are dominated by a convergent geometric series, define a new process[image]where [image] is also dominatedby a convergent geometric series. It is proven that the serial covariances [image] of the new process are generated by[image]where S(z) is the covariance generating function of the original process. The result is applied to stochastic difference equations to show that the process {xt}, defined by xt + a1xt-1 + ... + akxt-k=[eta]t where {[eta]t} is completely random, is reversible. The result also is used to provide short proofs of Slutzky''s and Romanovsky''s sinusoidal limit theorems. The last application gives the matrix covariance generating function for a stationary p-dimensional process.