scholarly journals Extensions of Rosenblatt's results on the asymptotic behavior of the prediction error for deterministic stationary sequences

2020 ◽  
Author(s):  
Nikolay M. Babayan ◽  
Mamikon S. Ginovyan ◽  
Murad S. Taqqu
Keyword(s):  
Asymptotic Behavior ◽  
Prediction Error ◽  
Stationary Sequences

Stationary Sequences in a Random Time Scenery

2019 ◽  
pp. 319-344
Author(s):  
Florence Merlevède ◽  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Asymptotic Behavior ◽  
Markov Chain ◽  
Random Walk ◽  
Random Time ◽  
Partial Sums ◽  
Stationary Sequences ◽  
Invariance Principles ◽  
Weak Invariance ◽  
Functional Clt ◽  
Random Scenery

In this chapter, we analyze the asymptotic behavior of the partial sums process associated with examples of stationary sequences in a random time scenery. The examples considered are stationary sequences sampled by shifted renewal Markov chains and random walks in a strictly stationary scenery. The asymptotic behavior of the partial sums process is essentially investigated with the help of the weak invariance principles stated in Chapter 4. More precisely, for the partial sums process associated with a stationary process sampled by a renewal Markov chain stated at zero, due to the non-stationarity of the underlying sequence, the functional CLT is obtained as an application of the functional CLT for non-stationary sequences developed in Section 4.4. In the case where we are sampling a strictly stationary random scenery by a random walk, stationarity is preserved, and the invariance principle is then derived by using the functional CLT under Maxwell–Woodroofe condition.

Asymptotic behavior of the prediction error

1984 ◽  
Vol 27 (6) ◽  
pp. 3170-3181 ◽  
Author(s):  
N. M. Babayan
Keyword(s):  
Asymptotic Behavior ◽  
Prediction Error
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