A Unified Test for the AR Error Structure of an Autoregressive Model
A direct application of autoregressive (AR) models with independent and identically distributed (iid) errors is sometimes inadequate to fit the time series data well. A natural alternative is further to assume the model errors following an AR process, whose structure however has essential impacts on...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/12/690 |
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| author | Xinyi Wei Xiaohui Liu Yawen Fan Li Tan Qing Liu |
| author_facet | Xinyi Wei Xiaohui Liu Yawen Fan Li Tan Qing Liu |
| author_sort | Xinyi Wei |
| collection | DOAJ |
| description | A direct application of autoregressive (AR) models with independent and identically distributed (iid) errors is sometimes inadequate to fit the time series data well. A natural alternative is further to assume the model errors following an AR process, whose structure however has essential impacts on the statistical inferences related to the autoregressive models. In this paper, we construct a new unified test for checking the AR error structure based on the empirical likelihood method. The proposed test is desirable because its limit distribution is always chi-squared regardless of whether the autoregressive model is stationary or non-stationary, with or without an intercept term. Some simulations are also provided to illustrate the finite sample performance of this test. Finally, we apply the proposed test to a financial real data set. |
| first_indexed | 2024-03-09T17:20:10Z |
| format | Article |
| id | doaj.art-725abf8440614c4eac60ba33c7b43ab3 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T17:20:10Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-725abf8440614c4eac60ba33c7b43ab32023-11-24T13:15:29ZengMDPI AGAxioms2075-16802022-12-01111269010.3390/axioms11120690A Unified Test for the AR Error Structure of an Autoregressive ModelXinyi Wei0Xiaohui Liu1Yawen Fan2Li Tan3Qing Liu4School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaA direct application of autoregressive (AR) models with independent and identically distributed (iid) errors is sometimes inadequate to fit the time series data well. A natural alternative is further to assume the model errors following an AR process, whose structure however has essential impacts on the statistical inferences related to the autoregressive models. In this paper, we construct a new unified test for checking the AR error structure based on the empirical likelihood method. The proposed test is desirable because its limit distribution is always chi-squared regardless of whether the autoregressive model is stationary or non-stationary, with or without an intercept term. Some simulations are also provided to illustrate the finite sample performance of this test. Finally, we apply the proposed test to a financial real data set.https://www.mdpi.com/2075-1680/11/12/690autoregressive modelAR errorsempirical likelihoodunified test |
| spellingShingle | Xinyi Wei Xiaohui Liu Yawen Fan Li Tan Qing Liu A Unified Test for the AR Error Structure of an Autoregressive Model Axioms autoregressive model AR errors empirical likelihood unified test |
| title | A Unified Test for the AR Error Structure of an Autoregressive Model |
| title_full | A Unified Test for the AR Error Structure of an Autoregressive Model |
| title_fullStr | A Unified Test for the AR Error Structure of an Autoregressive Model |
| title_full_unstemmed | A Unified Test for the AR Error Structure of an Autoregressive Model |
| title_short | A Unified Test for the AR Error Structure of an Autoregressive Model |
| title_sort | unified test for the ar error structure of an autoregressive model |
| topic | autoregressive model AR errors empirical likelihood unified test |
| url | https://www.mdpi.com/2075-1680/11/12/690 |
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