scholarly journals Quasi- and pseudo-maximum likelihood estimators for discretely observed continuous-time Markov branching processes

2011 ◽  
Vol 141 (7) ◽  
pp. 2209-2227 ◽  
Author(s):  
Rui Chen ◽  
Ollivier Hyrien
Keyword(s):  
Maximum Likelihood ◽  
Continuous Time ◽  
Branching Processes ◽  
Maximum Likelihood Estimators ◽  
Pseudo Maximum Likelihood

Maximum likelihood estimation for branching processes with immigration

1981 ◽  
Vol 13 (3) ◽  
pp. 498-509 ◽  
Author(s):  
B. R. Bhat ◽  
S. R. Adke
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Continuous Time ◽  
Strong Consistency ◽  
Branching Process ◽  
Branching Processes ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Asymptotic Distributions ◽  
Branching Process With Immigration

This paper establishes the strong consistency of the maximum likelihood estimators of the parameters of discrete- and continuous-time Markov branching processes with immigration. The asymptotic distributions of the maximum likelihood estimators of the parameters of a Galton–Watson branching process with immigration are also obtained.

Maximum likelihood estimation for branching processes with immigration

1981 ◽  
Vol 13 (03) ◽  
pp. 498-509 ◽  
Author(s):  
B. R. Bhat ◽  
S. R. Adke
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Continuous Time ◽  
Strong Consistency ◽  
Branching Process ◽  
Branching Processes ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Asymptotic Distributions ◽  
Branching Process With Immigration

This paper establishes the strong consistency of the maximum likelihood estimators of the parameters of discrete- and continuous-time Markov branching processes with immigration. The asymptotic distributions of the maximum likelihood estimators of the parameters of a Galton–Watson branching process with immigration are also obtained.

Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models

1991 ◽  
Vol 7 (4) ◽  
pp. 435-449 ◽  
Author(s):  
B.M. Pötscher
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Function ◽  
Moving Average ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Arma Models ◽  
Limiting Behavior ◽  
Pseudo Likelihood ◽  
Moving Average Model ◽  
Pseudo Maximum Likelihood

Recently Tanaka and Satchell [11] investigated the limiting properties of local maximizers of the Gaussian pseudo-likelihood function of a misspecified moving average model of order one in case the spectral density of the data process has a zero at frequency zero. We show that pseudo-maximum likelihood estimators in the narrower sense, that is, global maximizers of the Gaussian pseudo-likelihood function, may exhibit behavior drastically different from that of the local maximizers. Some general results on the limiting behavior of pseudo-maximum likelihood estimators in potentially misspecified ARMA models are also presented.

scholarly journals Asymmetric COGARCH processes

2014 ◽  
Vol 51 (A) ◽  
pp. 161-173 ◽  
Author(s):  
Anita Behme ◽  
Claudia Klüppelberg ◽  
Kathrin Mayr
Keyword(s):  
Maximum Likelihood ◽  
Continuous Time ◽  
High Frequency ◽  
Likelihood Estimation ◽  
Econometric Models ◽  
Financial Data ◽  
Model Parameters ◽  
Moment Estimation ◽  
Pseudo Maximum Likelihood Estimation ◽  
Pseudo Maximum Likelihood

Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time GARCH model, concentrating then on the GJR-COGARCH model. We calculate higher-order moments and extend the first-jump approximation. These results are prerequisites for moment estimation and pseudo maximum likelihood estimation of the GJR-COGARCH model parameters, respectively, which we derive in detail.

scholarly journals Asymmetric COGARCH processes

2014 ◽  
Vol 51 (A) ◽  
pp. 161-173 ◽  
Author(s):  
Anita Behme ◽  
Claudia Klüppelberg ◽  
Kathrin Mayr
Keyword(s):  
Maximum Likelihood ◽  
Continuous Time ◽  
High Frequency ◽  
Likelihood Estimation ◽  
Econometric Models ◽  
Financial Data ◽  
Model Parameters ◽  
Moment Estimation ◽  
Pseudo Maximum Likelihood Estimation ◽  
Pseudo Maximum Likelihood

Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time GARCH model, concentrating then on the GJR-COGARCH model. We calculate higher-order moments and extend the first-jump approximation. These results are prerequisites for moment estimation and pseudo maximum likelihood estimation of the GJR-COGARCH model parameters, respectively, which we derive in detail.

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