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A Non‐parametric Test for Generalized First‐order Autoregressive Models
Author(s) -
Diebolt Jean,
Ngatchou Wandji Joseph
Publication year - 1997
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00061
Subject(s) - mathematics , autoregressive model , parametric statistics , parametric model , star model , robustness (evolution) , statistics , autoregressive integrated moving average , time series , biochemistry , chemistry , gene
We derive a non‐parametric test for testing the presence of V(X i ,ε i ) in the non‐parametric first‐order autoregressive model X i+1 =T(X i )+V(X i ,ε i )+U(X i )ε i+1 , where the function T(x) is assumed known. The test is constructed as a functional of a basic process for which we establish a weak invariance principle, under the null hypothesis and under stationarity and mixing assumptions. Bounds for the local and non‐local powers are provided under a condition which ensures that the power tends to one as the sample size tends to infinity.The testing procedure can be applied, e.g. to bilinear models, ARCH models, EXPAR models and to some other uncommon models. Our results confirm the robustness of the test constructed in Ngatchou Wandji (1995) and in Diebolt & Ngatchou Wandji (1995).