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.

GOODNESS-OF-FIT TEST FOR NONLINEAR TIME SERIES MODELS

2017 ◽  
Vol 12 (02) ◽  
pp. 1750006
Author(s):  
NGAI SZE HAN ◽  
SHIQING LING
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Nonlinear Time Series ◽  
Garch Models ◽  
Time Series Models ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Conditional Mean ◽  
The Family ◽  
Functional Forms

Many time series models have been used extensively in modeling economic and financial data. However, it is difficult to determine the functional forms of the conditional mean and conditional variance in these models. In this paper, a test statistic based on the squared conditional residuals is proposed for testing these functional forms, and the asymptotic distribution of the test statistic is obtained. The test statistic is applicable not only to the family of GARCH models but also to other nonlinear time series models. Simulation results show that the proposed tests are powerful and have reasonable sizes. Two real examples are also given to illustrate our theory.

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