scholarly journals Asymptotic properties of conditional least-squares estimators for array time series

2021 ◽  
Author(s):  
Rajae Azrak ◽  
Guy Mélard
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Asymptotic Properties ◽  
Least Squares Estimators ◽  
Conditional Least Squares

Estimation in the Cox-Ingersoll-Ross Model

1997 ◽  
Vol 13 (3) ◽  
pp. 430-461 ◽  
Author(s):  
Ludger Overbeck ◽  
Tobias Rydén
Keyword(s):  
Maximum Likelihood ◽  
Interest Rates ◽  
Least Squares ◽  
Term Structure ◽  
Asymptotic Properties ◽  
Likelihood Estimator ◽  
Time Points ◽  
Least Squares Estimators ◽  
Conditional Least Squares ◽  
One Step

The Cox-Ingersoll-Ross model is a diffusion process suitable for modeling the term structure of interest rates. In this paper, we consider estimation of the parameters of this process from observations at equidistant time points. We study two estimators based on conditional least squares as well as a one-step improvement of these, two weighted conditional least-squares estimators, and the maximum likelihood estimator. Asymptotic properties of the various estimators are discussed, and we also compare their performance in a simulation study.

On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle

1991 ◽  
Vol 7 (3) ◽  
pp. 269-306 ◽  
Author(s):  
P. Jeganathan
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Least Squares ◽  
Unit Circle ◽  
Asymptotic Expansions ◽  
Asymptotic Properties ◽  
Ar Model ◽  
Convergence In Distribution ◽  
Least Squares Estimators ◽  
The Given

Some asymptotic properties of the least-squares estimator of the parameters of an AR model of order p, p ≥ 1, are studied when the roots of the characteristic polynomial of the given AR model are on or near the unit circle. Specifically, the convergence in distribution is established and the corresponding limiting random variables are represented in terms of functionals of suitable Brownian motions.Further, the preceding convergence in distribution is strengthened to that of convergence uniformly over all Borel subsets. It is indicated that the method employed for this purpose has the potential of being applicable in the wider context of obtaining suitable asymptotic expansions of the distributions of leastsquares estimators.

scholarly journals On estimation of the variances for critical branching processes with immigration

2010 ◽  
Vol 47 (02) ◽  
pp. 526-542
Author(s):  
Chunhua Ma ◽  
Longmin Wang
Keyword(s):  
Least Squares ◽  
Branching Process ◽  
Branching Processes ◽  
Limiting Distributions ◽  
Least Squares Estimators ◽  
Conditional Least Squares ◽  
Regularly Varying ◽  
Branching Process With Immigration ◽  
Critical Branching Process

The conditional least-squares estimators of the variances are studied for a critical branching process with immigration that allows the offspring distributions to have infinite fourth moments. We derive different forms of limiting distributions for these estimators when the offspring distributions have regularly varying tails with index α. In particular, in the case in which 2 < α < 8/3, the normalizing factor of the estimator for the offspring variance is smaller than √n, which is different from that of Winnicki (1991).

scholarly journals Asymptotic Optimality of Estimating Function Estimator for CHARN Model

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Tomoyuki Amano
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Financial Time Series ◽  
Asymptotic Optimality ◽  
Time Series Models ◽  
Estimating Function ◽  
Asymptotically Optimal ◽  
Financial Time ◽  
Conditional Least Squares ◽  
Better Than

CHARN model is a famous and important model in the finance, which includes many financial time series models and can be assumed as the return processes of assets. One of the most fundamental estimators for financial time series models is the conditional least squares (CL) estimator. However, recently, it was shown that the optimal estimating function estimator (G estimator) is better than CL estimator for some time series models in the sense of efficiency. In this paper, we examine efficiencies of CL and G estimators for CHARN model and derive the condition that G estimator is asymptotically optimal.

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