Limit theorems on a linear explosive stochastic model for time series with moving average error |
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Authors: | K N Venkataraman K Suresh Chandra |
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Institution: | (1) University of Madras, Madras, India |
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Abstract: | Summary LetX(t) be a linear autoregressively generated explosive time series, with autoregressive coefficientsb
1,…,bq, and a constant termb
0, and an error term
; a0=1. Where ε(t),t≧1 are independent, Eε(t)=0, and Eε
2(t)=σ2 is positive and finite. In this paper two categories of
-consisent and asymptotically singularly normal estimators are proposed for (b
1,…,bq, b0) thus settling an open problem since the publication of the paper (Venkataraman 5]). Based on these estimators several additional
limit theorems based on estimated error residuals are proved. The parameter-free limit theorems of Spectral and Quenouille
types of this paper serve as asymptotic goodness of fit tests for the model generatingX(t). |
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Keywords: | |
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