On same-realization prediction in an infinite-order autoregressive process
Journal of Multivariate Analysis
New Introduction to Multiple Time Series Analysis
New Introduction to Multiple Time Series Analysis
On the maximum of covariance estimators
Journal of Multivariate Analysis
Paper: Modeling by shortest data description
Automatica (Journal of IFAC)
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Let {X"k,k@?Z} be a zero mean causal AR(~) process with parameter @Q@?R^~. A very common fitting procedure is to employ the Yule-Walker equations in connection with the Durbin-Levinson algorithm, which yields the (recursive) sequence of estimators @Q@^"m:=(@q@^"m","1,...,@q@^"m","m)^@?, m=1,2,..... Under mild conditions, simultaneous confidence bands for @Q@^"m, @Q@^"m"+"1,... are derived. More precisely, it is shown that max"d"""n"-"@k"""n"@?"m"@?"d"""nmax"1"@?"h"@?"m|@q@^"m","h-@q"h| converges to an extreme value distribution, where d"n=O(n^@d), @d0, and n denotes the sample size. The relation of @k"n and d"n depends on the bias term @?"i"="d"""n"-"2"@k"""n^~|@q"i|. This significantly extends a recent result in Jirak (2012). Moreover, extensions of results of An et al. (1982) and Bhansali (1978) are obtained. In addition, the behavior of Information criteria in the AR(~) setting is briefly discussed.