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Fourier Analysis of Periodic Weakly Stationary Processes: A Note on Slutsky's Observation
被引：0
|作者：
Maruyama, Toru
[1
]
机构：
[1] Keio Univ, Tokyo, Japan
来源：
ADVANCES IN MATHEMATICAL ECONOMICS, VOL 20
|
2016年
/
20卷
关键词：
Weakly stationary process;
Periodicity;
Almost periodicity;
Spectral measure;
SERIES;
D O I：
10.1007/978-981-10-0476-6_7
中图分类号：
F [经济];
学科分类号：
02 ;
摘要：
The periodic behavior of a specific weakly stationary stochastic process (w.s.p.) is examined from a viewpoint of classical Fourier analysis. (1) A w.s.p. has a spectral measure which is absolutely continuous with respect to the Lebesgue measure if and only if it is a moving average of a white noise. (2) A periodic or almost periodic w.s.p. must have a "discrete" spectral measure. Combining these two, we can conclude that any moving average of a white noise can neither be periodic nor almost periodic. However any w.s.p. can be approximated by a sequence of almost periodic w.s.p.'s in some specific sense.
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页码：151 / 180
页数：30
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