zbMATH — the first resource for mathematics

A nonparametric goodness-of-fit-based test for conditional heteroskedasticity. (English) Zbl 1316.62058
Summary: In this paper we propose a new nonparametric test for conditional heteroskedasticity based on a measure of nonparametric goodness-of-fit ($$R^2$$) that is obtained from the local polynomial regression of the residuals from a parametric regression on some covariates. We show that after being appropriately standardized, the nonparametric $$R^2$$ is asymptotically normally distributed under the null hypothesis and a sequence of Pitman local alternatives. We also prove the consistency of the test and propose a bootstrap method to obtain the bootstrap $$p$$-values. We conduct a small set of simulations and compare our test with some popular parametric and nonparametric tests in the literature.

MSC:
 62G10 Nonparametric hypothesis testing 62G08 Nonparametric regression and quantile regression
Full Text:
References:
 [1] DOI: 10.1017/S0266466612000011 · Zbl 1369.62075 [2] DOI: 10.1016/S0304-4076(02)00198-7 · Zbl 1027.62027 [3] DOI: 10.1214/07-AOS531 · Zbl 1148.62055 [4] DOI: 10.1017/S0266466601171069 · Zbl 0976.62087 [5] DOI: 10.1111/1468-0262.00207 · Zbl 1017.62012 [6] DOI: 10.1016/0304-4076(78)90031-3 · Zbl 0401.62087 [7] DOI: 10.1080/01621459.1969.10500976 [8] Econometric Theory 24 pp 726– (2008) [9] DOI: 10.1214/aop/1176990862 · Zbl 0706.62017 [10] DOI: 10.1016/S0304-4076(99)00068-8 · Zbl 1122.62326 [11] Nonlinear Time Series: Semiparametric and Nonparametric Methods (2007) [12] Econometric Analysis (2000) [13] DOI: 10.1007/BF00354037 · Zbl 0596.60022 [14] DOI: 10.1080/01621459.1965.10480811 [15] DOI: 10.1016/j.jeconom.2006.12.002 · Zbl 1418.62191 [16] DOI: 10.2307/1911963 · Zbl 0416.62021 [17] Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (2005) · Zbl 1075.15001 [18] DOI: 10.1017/S0266466600009427 · Zbl 04527667 [19] Yokohama Mathematical 40 pp 1– (1992) [20] DOI: 10.2307/1911465 · Zbl 0533.62055 [21] Econometrica 48 pp 452– (1980) [22] DOI: 10.1017/S0266466609990788 · Zbl 1230.62123 [23] DOI: 10.1198/jbes.2009.0002 [24] Handbook of Statistics 11 pp 489– (1993) [25] DOI: 10.2307/1911031 · Zbl 0625.62047 [26] DOI: 10.1016/S0167-7152(00)00091-2 · Zbl 0966.62029 [27] DOI: 10.1111/j.1467-9892.1996.tb00294.x · Zbl 0876.62075 [28] Econometrica 50 pp 159– (1982)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.