scholarly journals Asymptotic Behavior of Conditional Least Squares Estimators for Unstable Integer-valued Autoregressive Models of Order 2

2014 ◽  
Vol 41 (4) ◽  
pp. 866-892 ◽  
Author(s):  
Mátyás Barczy ◽  
Márton Ispány ◽  
Gyula Pap
Keyword(s):  
Asymptotic Behavior ◽  
Least Squares ◽  
Autoregressive Models ◽  
Least Squares Estimators ◽  
Conditional Least Squares

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).

Functional least squares estimators in an additive effects outliers model

1990 ◽  
Vol 48 (2) ◽  
pp. 299-319 ◽  
Author(s):  
Sunil K. Dhar
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Gaussian Process ◽  
Least Squares ◽  
Strong Consistency ◽  
Additive Effects ◽  
Uniform Consistency ◽  
Least Squares Estimators

AbstractConsider the additive effects outliers (A.O.) model where one observes , with The sequence of r.v.s is independent of and , are i.i.d. with d.f. , where the d.f.s Ln, n ≦ 0, are not necessarily known and εj's are i.i.d.. This paper discusses the asymptotic behavior of functional least squares estimators under the above model. Uniform consistency and uniform strong consistency of these estimators are proven. The weak convergence of these estimators to a Gaussian process and their asymptotic biases are also discussed under the above A.O. model.

CONSISTENCY AND EFFICIENCY OF LEAST SQUARES ESTIMATION FOR MIXED REGRESSIVE, SPATIAL AUTOREGRESSIVE MODELS

2002 ◽  
Vol 18 (2) ◽  
pp. 252-277 ◽  
Author(s):  
Lung-Fei Lee
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Instrumental Variables ◽  
Estimation Method ◽  
Least Squares Estimation ◽  
Autoregressive Models ◽  
Least Squares Estimators ◽  
Spatial Autoregressive ◽  
Spatial Autoregressive Models ◽  
Asymptotically Efficient

Least squares estimation has casually been dismissed as an inconsistent estimation method for mixed regressive, spatial autoregressive models with or without spatial correlated disturbances. Although this statement is correct for a wide class of models, we show that, in economic spatial environments where each unit can be influenced aggregately by a significant portion of units in the population, least squares estimators can be consistent. Indeed, they can even be asymptotically efficient relative to some other estimators. Their computations are easier than alternative instrumental variables and maximum likelihood approaches.

scholarly journals Bootstrapping periodically autoregressive models

2017 ◽  
Vol 21 ◽  
pp. 394-411
Author(s):  
Gabriela Ciołek ◽  
Paweł Potorski
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Autoregressive Models ◽  
Wild Bootstrap ◽  
Autoregressive Time Series ◽  
Least Squares Estimators ◽  
Theoretical Considerations

The main objective of this paper is to establish the residual and the wild bootstrap procedures for periodically autoregressive models. We use the least squares estimators of model’s parameters and generate their bootstrap equivalents. We prove that the bootstrap procedures for causal periodic autoregressive time series with finite fourth moments are weakly consistent. Finally, we confirm our theoretical considerations by simulations.

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.

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