scholarly journals Consistency and Asymptotic Normality of Maximum Likelihood Estimators of a Multiplicative Time-Varying Smooth Transition Correlation GARCH Model

2021 ◽  
Author(s):  
Annastiina Silvennoinen ◽  
Timo Teräsvirta
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Garch Model ◽  
Maximum Likelihood Estimators ◽  
Smooth Transition ◽  
Time Varying ◽  
Consistency And Asymptotic Normality

scholarly journals Maximum Likelihood Estimation in the Fractional Vasicek Model

2017 ◽  
Vol 56 (1) ◽  
pp. 77-87 ◽  
Author(s):  
Stanislav Lohvinenko ◽  
Kostiantyn Ralchenko
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Hurst Parameter ◽  
Unknown Parameters ◽  
Vasicek Model ◽  
Consistency And Asymptotic Normality

We consider the fractional Vasicek model of the form dXt = (α-βXt)dt +γdBHt , driven by fractional Brownian motion BH with Hurst parameter H ∈ (1/2,1). We construct the maximum likelihood estimators for unknown parameters α and β, and prove their consistency and asymptotic normality.

New Ways to Prove Central Limit Theorems

1985 ◽  
Vol 1 (3) ◽  
pp. 295-313 ◽  
Author(s):  
David Pollard
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Limit Theorems ◽  
Maximum Likelihood Estimators ◽  
Empirical Processes ◽  
Central Limit Theorems ◽  
Criterion Function ◽  
Nonstandard Conditions

This paper describes some techniques for proving asymptotic normality of statistics defined by maximization of random criterion function. The techniques are based on a combination of recent results from the theory of empirical processes and a method of Huber for the study of maximum likelihood estimators under nonstandard conditions.

Regression for randomly sampled spatial series: the trigonometric case

1986 ◽  
Vol 23 (A) ◽  
pp. 275-289 ◽  
Author(s):  
David R. Brillinger
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Point Process ◽  
Maximum Likelihood Estimates ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
Spatial Series ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Asymptotically Efficient

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j in a subset of Rp and θ is a finite-dimensional parameter. The particular cases of 0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j} are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient.Contributions of the paper include: study of the Rp case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j} is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.

Regression for randomly sampled spatial series: the trigonometric case

1986 ◽  
Vol 23 (A) ◽  
pp. 275-289
Author(s):  
David R. Brillinger
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Point Process ◽  
Maximum Likelihood Estimates ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
Spatial Series ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Asymptotically Efficient

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j in a subset of Rp and θ is a finite-dimensional parameter. The particular cases of 0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j } are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient. Contributions of the paper include: study of the Rp case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j } is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.

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