Wavelet analysis of change-points in a non-parametric regression with heteroscedastic variance
In this paper we develop wavelet methods for detecting and estimating jumps and cusps in the mean function of a non-parametric regression model. An important characteristic of the model considered here is that it allows for conditional heteroscedastic variance, a feature frequently encountered with economic and financial data. Wavelet analysis of change-points in this model has been considered in a limited way in a recent study by Chen etÂ al. (2008) with a focus on jumps only. One problem with the aforementioned paper is that the test statistic developed there has an extreme value null limit distribution. The results of other studies have shown that the rate of convergence to the extreme value distribution is usually very slow, and critical values derived from this distribution tend to be much larger than the true ones. Here, we develop a new test and show that the test statistic has a convenient null limit N(0,1) distribution. This feature gives the proposed approach an appealing advantage over the existing approach. Another attractive feature of our results is that the asymptotic theory developed here holds for both jumps and cusps. Implementation of the proposed method for multiple jumps and cusps is also examined. The results from a simulation study show that the new test has excellent power and the estimators developed also yield very accurate estimates of the positions of the discontinuities.
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- Berkes, Istv n & Gombay, Edit & Horv th, Lajos & Kokoszka, Piotr, 2004. "SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1140-1167, December.
- Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2008. "Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility," Journal of Econometrics, Elsevier, vol. 143(2), pages 227-262, April.
- Ait-Sahalia, Yacine, 1996.
"Nonparametric Pricing of Interest Rate Derivative Securities,"
Econometric Society, vol. 64(3), pages 527-60, May.
- Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
- Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-65, September.
- Wong, Heung & Ip, Waicheung & Li, Yuan, 2001. "Detection of jumps by wavelets in a heteroscedastic autoregressive model," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 365-372, May.
- Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
- Donald W.K. Andrews, 1990.
"Tests for Parameter Instability and Structural Change with Unknown Change Point,"
Cowles Foundation Discussion Papers
943, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
- Hong, Yongmiao & Lee, Jin, 2001. "One-Sided Testing For Arch Effects Using Wavelets," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1051-1081, December.
- Duchesne, Pierre, 2006. "On Testing For Serial Correlation With A Wavelet-Based Spectral Density Estimator In Multivariate Time Series," Econometric Theory, Cambridge University Press, vol. 22(04), pages 633-676, August.
- Ho, Thomas S Y & Saunders, Anthony, 1980. " A Catastrophe Model of Bank Failure," Journal of Finance, American Finance Association, vol. 35(5), pages 1189-1207, December.
- Fan, Jianqing & Masry, Elias, 1992. "Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 237-271, November.
- Park, Cheol-Woo & Kim, Woo-Chul, 2004. "Estimation of a regression function with a sharp change point using boundary wavelets," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 435-448, March.
- Hall, Peter & Nason, Guy P., 1997. "On choosing a non-integer resolution level when using wavelet methods," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 5-11, May.
- Ip, Wai-Cheung & Wong, Heung & Li, Yuan & Xie, Zhongjie, 1999. "Threshold variable selection by wavelets in open-loop threshold autoregressive models," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 375-392, May.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
- Yongmiao Hong & Chihwa Kao, 2004.
"Wavelet-Based Testing for Serial Correlation of Unknown Form in Panel Models,"
Econometric Society, vol. 72(5), pages 1519-1563, 09.
- Yongmiao Hong & Chihwa Kao, 2000. "Wavelet-Based Testing for Serial Correlation of Unknown Form in Panel Models," Center for Policy Research Working Papers 32, Center for Policy Research, Maxwell School, Syracuse University.
- Dufour, Jean-Marie, 1982. "Recursive stability analysis of linear regression relationships: An exploratory methodology," Journal of Econometrics, Elsevier, vol. 19(1), pages 31-76, May.
- Jianqing Fan & Qiwei Yao, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
- Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
- Lee, Jin & Hong, Yongmiao, 2001. "Testing For Serial Correlation Of Unknown Form Using Wavelet Methods," Econometric Theory, Cambridge University Press, vol. 17(02), pages 386-423, April.
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