Geodesic
Sufficient Statistics of Stationary Gaussian Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 2, pp. 216-218

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We prove that for a stationary Gaussian process with spectral density (1) the number of sufficient statistics is $(p+1)(p+2)/2$. A simple example shows that in the general case the number of sufficient statistics increases with the number of observations. 
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     author = {M. Arat\'o},
     title = {Sufficient {Statistics} of {Stationary} {Gaussian} {Processes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1961},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1961_6_2_a5/}
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M. Arató. Sufficient Statistics of Stationary Gaussian Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 2, pp. 216-218. http://geodesic.mathdoc.fr/item/TVP_1961_6_2_a5/