A goodness-of-fit test of the errors in nonlinear autoregressive time series models

2008 ◽  
Vol 78 (1) ◽  
pp. 50-59 ◽  
Author(s):  
Fuxia Cheng ◽  
Shuxia Sun
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Time Series Models ◽  
Goodness Of Fit Test ◽  
Autoregressive Time Series ◽  
Nonlinear Autoregressive

MINIMUM DISTANCE ESTIMATION OF NONSTATIONARY TIME SERIES MODELS

2002 ◽  
Vol 18 (6) ◽  
pp. 1385-1407 ◽  
Author(s):  
Hyungsik Roger Moon ◽  
Frank Schorfheide
Keyword(s):  
Time Series ◽  
Minimum Distance ◽  
Goodness Of Fit ◽  
Distance Estimation ◽  
Nonstationary Time Series ◽  
Regularity Conditions ◽  
Time Series Models ◽  
Goodness Of Fit Test ◽  
Restricted Parameter Space ◽  
Income Model

This paper analyzes the limit distribution of minimum distance (MD) estimators for nonstationary time series models that involve nonlinear parameter restrictions. A rotation for the restricted parameter space is constructed to separate the components of the MD estimator that converge at different rates. We derive regularity conditions for the restriction function that are easier to verify than the stochastic equicontinuity conditions that arise from direct estimation of the restricted parameters. The sequence of matrices that is used to weigh the discrepancy between the unrestricted estimates and the restriction function is allowed to have a stochastic limit. For MD estimators based on unrestricted estimators with a mixed normal asymptotic distribution the optimal weight matrix is derived and a goodness-of-fit test is proposed. Our estimation theory is illustrated in the context of a permanent-income model and a present-value model.

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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