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.

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 Gaussian and Non-Gaussian Autoregressive Time Series Models with Rainfall Data

2019 ◽  
Vol 9 (1) ◽  
pp. 6699-6704
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Time Series Data ◽  
Autoregressive Models ◽  
Annual Rainfall ◽  
Series Data ◽  
Time Series Models ◽  
Chi Square ◽  
Autoregressive Time Series ◽  
Non Gaussian

The Gaussian and non- Gaussian autoregressive models are used in this paper for analyzing time series data. The autoregressive time series models with various distributions are considered here for analyzing the annual rainfall of Punjab, India. Three different types of autoregressive models are applied here for analyzing data namely autoregressive model with Gaussian, Gamma and Laplace distribution. For the goodness of fit the chi - square test is applied and the best fitted distribution is obtained for the data. Next the stationarity of data is checked, after that models are applied on data for comparing three distributions of AR models and lastly the best fitted model is obtained. The residual checking of selected model is also discussed and forecast the best fitted model based on simulated response comparison.

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