Bayesian estimation of the mean of an autoregressive process

1993 ◽  
Vol 20 (1) ◽  
pp. 25-39 ◽  
Author(s):  
Lyle D Broemeling ◽  
Peyton Cook
Keyword(s):  
Bayesian Estimation ◽  
Autoregressive Process ◽  
The Mean

On Some Asymptotic Results for Multivariate Autoregressive Models with Estimated Parameters

1986 ◽  
Vol 35 (3-4) ◽  
pp. 123-132 ◽  
Author(s):  
A. K. Basu ◽  
S. Sen Roy
Keyword(s):  
Mean Square Error ◽  
Autoregressive Process ◽  
Mean Square ◽  
Asymptotic Equivalence ◽  
Asymptotic Results ◽  
Stable Case ◽  
Estimated Parameters ◽  
Multivariate Autoregressive Models ◽  
The Mean ◽  
Dependent Error

In this paper the asymptotic equivalence of the estimated predictor and the optimal predictor of k-dimensional pth order autoregressive process in the stable case with dependent error variables bas been shown. An expression for the mean square error of the estimated predictor has also been derived.

scholarly journals Bayesian Estimation for Two Parameters of Gamma Distribution under Generalized Weighted Loss Function

2019 ◽  
Vol 60 (5) ◽  
pp. 1161-1171
Author(s):  
Loaiy F. Naji ◽  
Huda A. Rasheed
Keyword(s):  
Bayesian Estimation ◽  
Gamma Distribution ◽  
Loss Function ◽  
Maximum Likelihood Estimators ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Mean Squared Errors ◽  
Scale Parameters ◽  
The Mean ◽  
Two Parameters

This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on Gamma and Exponential priors for the shape and scale parameters, respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared in terms of the mean squared errors (MSE’s).

Intrinsic objective Bayesian estimation of the mean of the Tweedie family

2019 ◽  
Vol 2019 (7) ◽  
pp. 585-603
Author(s):  
Limor Langbord ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Bayesian Estimation ◽  
Tweedie Family ◽  
The Mean

scholarly journals Testing the epidemic change in nearly nonstationary autoregressive processes

2014 ◽  
Vol 19 (1) ◽  
pp. 67-82 ◽  
Author(s):  
Jurgita Markevičiūtė ◽  
Alfredas Račkauskas ◽  
Charles Suquet
Keyword(s):  
Autoregressive Process ◽  
Autoregressive Processes ◽  
Limit Distributions ◽  
First Order ◽  
Type Change ◽  
The Mean

Some tests for an epidemic type change in a first order nearly nonstationary autoregressive process are investigated. Limit distributions of the tests are found under no change. Consistencyis examined under short epidemics in the mean of innovations.

scholarly journals Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach

2020 ◽  
pp. 28-43
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Fadimatu Bawuro Mohammed ◽  
Ahmed Askira Sule
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Shape Parameter ◽  
Likelihood Estimation ◽  
Monte Carlo Study ◽  
Comparative Approach ◽  
The Mean ◽  
Inverse Exponential Distribution

This paper aims at making Bayesian analysis on the shape parameter of the exponential inverse exponential distribution using informative and non-informative priors. Bayesian estimation was carried out through a Monte Carlo study under 10,000 replications. To assess the effects of the assumed prior distributions and loss function on the Bayesian estimators, the mean square error has been used as a criterion. Overall, simulation results indicate that Bayesian estimation under QLF outperforms the maximum likelihood estimation and Bayesian estimation under alternative loss functions irrespective of the nature of the prior and the sample size. Also, for large sample sizes, all methods perform equally well.

On Asymptotic Prediction Problems for Autoregressive Models with Explosive and Other Roots

1989 ◽  
Vol 38 (1-2) ◽  
pp. 43-56 ◽  
Author(s):  
A. K. Basu ◽  
S. Sen Roy
Keyword(s):  
Mean Square Error ◽  
Asymptotic Properties ◽  
Autoregressive Process ◽  
Autoregressive Models ◽  
Mean Square ◽  
The Mean ◽  
Set Up ◽  
Prediction Problems ◽  
Dependent Error

In this paper the asymptotic properties of the estimated predictor of a k-dimensional, pth order autoregressive process with dependent error variables and a general set-up of the roots have been considered. An expression for the mean-square-error of the estimated predictor has also been obtained.

scholarly journals Impact of Algorithm Selection on Modeling Ozone Pollution: A Perspective on Box and Tiao (1975)

Forests ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1311
Author(s):  
Mihaela Paun ◽  
Nevine Gunaime ◽  
Bogdan M. Strimbu
Keyword(s):  
Maximum Likelihood ◽  
Los Angeles ◽  
Mean Square Error ◽  
Arima Model ◽  
Autoregressive Process ◽  
Least Square ◽  
Mean Square ◽  
Ozone Pollution ◽  
Complex Models ◽  
The Mean

Estimation using a suboptimal method can lead to imprecise models, with cascading effects in complex models, such as climate change or pollution. The goal of this study is to compare the solutions supplied by different algorithms used to model ozone pollution. Using Box and Tiao (1975) study, we have predicted ozone concentration in Los Angeles with an ARIMA and an autoregressive process. We have solved the ARIMA process with three algorithms (i.e., maximum likelihood, like Box and Tiao, conditional least square and unconditional least square) and the autoregressive process with four algorithms (i.e., Yule–Walker, iterative Yule–Walker, maximum likelihood, and unconditional least square). Our study shows that Box and Tiao chose the appropriate algorithm according to the AIC but not according to the mean square error. Furthermore, Yule–Walker, which is the default algorithm in many software, has the least reliable results, suggesting that the method of solving complex models could alter the findings. Finally, the model selection depends on the technical details and on the applicability of the model, as the ARIMA model is suitable from the AIC perspective but an autoregressive model could be preferred from the mean square error viewpoint. Our study shows that time series analysis should consider not only the model shape but also the model estimation, to ensure valid results.

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