Test for parameter change in stochastic processes based on conditional least-squares estimator

A sequence of first-order integer-valued autoregressive (INAR(1)) processes is investigated, where the autoregressive-type coefficient converges to 1. It is shown that the limiting distribution of the conditional least squares estimator for this coefficient is normal and the rate of convergence is n3/2. Nearly critical Galton–Watson processes with unobservable immigration are also discussed.

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Asymptotic inference for nearly unstable INAR(1) models

Journal of Applied Probability ◽

10.1017/s0021900200019689 ◽

2003 ◽

Vol 40 (03) ◽

pp. 750-765 ◽

Cited By ~ 7

Author(s):

M. Ispány ◽

G. Pap ◽

M. C. A. van Zuijlen

Keyword(s):

Least Squares ◽

Rate Of Convergence ◽

Limiting Distribution ◽

Least Squares Estimator ◽

Asymptotic Inference ◽

First Order ◽

Conditional Least Squares ◽

Conditional Least Squares Estimator

A sequence of first-order integer-valued autoregressive (INAR(1)) processes is investigated, where the autoregressive-type coefficient converges to 1. It is shown that the limiting distribution of the conditional least squares estimator for this coefficient is normal and the rate of convergence is n 3/2. Nearly critical Galton–Watson processes with unobservable immigration are also discussed.

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Fluctuation limit of branching processes with immigration and estimation of the means

Advances in Applied Probability ◽

10.1017/s000186780000029x ◽

2005 ◽

Vol 37 (02) ◽

pp. 523-538 ◽

Cited By ~ 13

Author(s):

M. Ispány ◽

G. Pap ◽

M. C. A. van Zuijlen

Keyword(s):

Least Squares ◽

Critical Case ◽

Branching Processes ◽

Critical Value ◽

Subcritical Case ◽

Asymptotically Normal ◽

Fluctuation Limit ◽

Conditional Least Squares ◽

Type Process ◽

Conditional Least Squares Estimator

We investigate a sequence of Galton-Watson branching processes with immigration, where the offspring mean tends to its critical value 1 and the offspring variance tends to 0. It is shown that the fluctuation limit is an Ornstein-Uhlenbeck-type process. As a consequence, in contrast to the case in which the offspring variance tends to a positive limit, it transpires that the conditional least-squares estimator of the offspring mean is asymptotically normal. The norming factor is n 3/2, in contrast to both the subcritical case, in which it is n 1/2, and the nearly critical case with positive limiting offspring variance, in which it is n.

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On Conditional Least Squares Estimation for Stochastic Processes

The Annals of Statistics ◽

10.1214/aos/1176344207 ◽

1978 ◽

Vol 6 (3) ◽

pp. 629-642 ◽

Cited By ~ 261

Author(s):

Lawrence A. Klimko ◽

Paul I. Nelson

Keyword(s):

Stochastic Processes ◽

Least Squares ◽

Least Squares Estimation ◽

Conditional Least Squares

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Fluctuation limit of branching processes with immigration and estimation of the means

Advances in Applied Probability ◽

10.1239/aap/1118858637 ◽

2005 ◽

Vol 37 (2) ◽

pp. 523-538 ◽

Cited By ~ 18

Author(s):

M. Ispány ◽

G. Pap ◽

M. C. A. van Zuijlen

Keyword(s):

Least Squares ◽

Critical Case ◽

Branching Processes ◽

Critical Value ◽

Subcritical Case ◽

Asymptotically Normal ◽

Fluctuation Limit ◽

Conditional Least Squares ◽

Type Process ◽

Conditional Least Squares Estimator

We investigate a sequence of Galton-Watson branching processes with immigration, where the offspring mean tends to its critical value 1 and the offspring variance tends to 0. It is shown that the fluctuation limit is an Ornstein-Uhlenbeck-type process. As a consequence, in contrast to the case in which the offspring variance tends to a positive limit, it transpires that the conditional least-squares estimator of the offspring mean is asymptotically normal. The norming factor is n3/2, in contrast to both the subcritical case, in which it is n1/2, and the nearly critical case with positive limiting offspring variance, in which it is n.

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