Testing for multivariate autoregressive conditional heteroskedasticity using wavelets

Computational Statistics and Data Analysis

Volumn 51, Issue 4, 2006, Pages 2142-2163

  Duchesne, Pierre ^a,b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b GERAD   (Canada)

Author keywords

Autoregressive conditional heteroskedasticity; Kernel spectrum estimator; Multivariate time series; Wavelet spectrum estimator

Indexed keywords

ASYMPTOTIC STABILITY; DENSITY (OPTICAL); MULTIVARIABLE SYSTEMS; NORMAL DISTRIBUTION; PARAMETER ESTIMATION; WAVELET TRANSFORMS;

AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY; KERNEL SPECTRUM ESTIMATORS; MULTIVARIATE TIME SERIES; WAVELET SPECTRUM ESTIMATORS;

REGRESSION ANALYSIS;

EID: 33750978975     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.07.022     Document Type: Article

References (59)

1. Anderson T.W. The Statistical Analysis of Time Series (1971), Wiley, New York
2. Bahadur R.R. Stochastic comparison of tests. Ann. Math. Statist. 31 (1960) 276-295
3. Bauwens L., Laurent S., and Rombouts J.V.K. Multivariate GARCH models: a survey. J. Appl. Econometrics 21 (2006) 79-109
4. Bera A.K., and Higgins M.L. A test for conditional heteroskedasticity in time series models. J. Time Ser. Anal. 13 (1992) 501-519
5. Bera, A.K., Lee, S., 1989. On the formulation of a general structure for conditional heteroskedasticity. Working Paper, University of Illinois.
6. Bollerslev T. Generalized autoregressive conditional heteroskedasticity. J. Econometrics 31 (1986) 307-328
7. Bollerslev T. Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. Rev. Econom. Statist. 72 (1990) 468-505
8. Bollerslev T., and Engle R.F. Common persistence in conditional variances. Econometrica 61 (1993) 167-186
9. Bollerslev T., Engle R.F., and Wooldridge J.M. A capital asset pricing model with time varying covariances. J. Polit. Economy 96 (1988) 116-131
10. Bollerslev T., Chou R.Y., and Kroner K.F. ARCH modeling in finance. J. Econometrics 52 (1992) 5-59
11. Bollerslev, T., Engle, R.F., Nelson, D.B., 1994. In: Engle, R.F., McFadden, D.L. (Eds.), ARCH models in Handbook of Econometrics, vol. IV. Elsevier Science, Amsterdam, pp. 2959-3038.
12. Brillinger D.R. Time Series, Data Analysis and Theory. second ed (1981), Holden-Day, San Francisco
13. Butucea C., and Tribouley K. Nonparametric homogeneity tests. J. Statist. Plann. Inference 136 (2006) 597-639
14. Christodoulakis G., and Satchell S. Correlated ARCH: modelling the time-varying correlation between financial asset returns. European J. Oper. Res. 139 (2002) 351-370
15. Daubechies I. Ten Lectures on Wavelets (1992), SIAM, Philadelphia
16. Davidson R., and MacKinnon J.G. Graphical methods for investigating the size and power of hypothesis tests. The Manchester School 66 (1998) 1-26
17. Duchesne P. On matricial measures of dependence in vector ARCH models with applications to diagnostic checking. Statist. Probab. Lett. 68 (2004) 149-160
18. Duchesne P. On testing for serial correlation with a wavelet-based spectral density estimator in multivariate time series. Econometric Theory 22 (2006) 633-676
19. Duchesne P., and Lalancette S. On testing for multivariate ARCH effects in vector time series models. Canad. J. Statist. 31 (2003) 275-292
20. Duchesne P., and Roy R. On consistent testing for serial correlation of unknown form in vector time series models. J. Multivariate Anal. 89 (2004) 148-180
21. Engle R.F. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50 (1982) 987-1007
22. Engle R.F. Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J. Business Econom. Statist. 20 (2002) 339-350
23. Engle R.F., and Kroner K.F. Multivariate simultaneous generalized ARCH. Econometric Theory 11 (1995) 122-150
24. Engle R.F., Granger C.W.J., and Kraft D.F. Combining competing forecasts of inflation using a bivariate ARCH model. J. Econom. Dynamics Control 8 (1984) 151-165
25. Engle R.F., Hendry D.F., and Trumble D. Small-sample properties of ARCH estimators and tests. Canad. J. Econom. 18 (1985) 66-93
26. Engle R.F., Ng V.K., and Rothschild M. Asset pricing with a factor-ARCH covariance structure: empirical estimates for treasury bills. J. Econometrics 45 (1990) 213-238
27. Gao, H., 1993. Wavelet estimation of spectral densities in time series analysis. Ph.D. Dissertation, Department of Statistics, University of California, Berkeley.
28. Hannan E. Multiple Time Series (1970), Wiley, New York
29. Hernandez E., and Weiss G. A First Course on Wavelets (1996), CRC Press, New York
30. Hong Y. Consistent testing for serial correlation of unknown form. Econometrica 64 (1996) 837-864
31. Hong Y. One-sided testing for conditional heteroskedasticity in time series models. J. Time Ser. Anal. 18 (1997) 253-277
32. Hong, Y., 2000. Wavelet-based estimation for heteroskedasticity and autocorrelation consistent variance-covariance matrices. Working Paper, Department of Economics and Department of Statistical Science, Cornell University.
33. Hong Y., and Lee J. One-sided testing for ARCH effects using wavelets. Econometric Theory 17 (2001) 1051-1081
34. Hong Y., and Shehadeh R.D. A new test for ARCH effects and its finite-sample performance. J. Business Econom. Statist. 17 (1999) 91-108
35. Hosking J. The multivariate portmanteau statistic. J. Amer. Statist. Assoc. 75 (1980) 602-608
36. Ledoit O., Santa-Clara P., and Wolf M. Flexible multivariate GARCH modeling with an application to international stock markets. Rev. Econom. Statist. 85 (2003) 735-747
37. Lepski O.V., and Tsybakov A.B. Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point. Probab. Theory Related Fields 117 (2000) 17-48
38. Li W.K. Diagnostic Checks in Time Series (2004), Chapman & Hall/CRC, New York
39. Ling S., and Li W.K. Diagnostic checking of nonlinear multivariate time series with multivariate ARCH errors. J. Time Ser. Anal. 18 (1997) 447-464
40. Ling S., and McAleer M. Asymptotic theory for a vector ARMA-GARCH model. Econometric Theory 19 (2003) 280-310
41. Mallat S.G. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11 (1989) 674-693
42. McLeod A.I., and Li W.K. Diagnostic checking ARMA time series models using squared residual autocorrelations. J. Time Ser. Anal. 4 (1983) 269-273
43. Meyer Y. Wavelets and Operators. Cambridge Studies in Advanced Mathematics vol. 37 (1992), Cambridge University Press, New York
44. Müller P., and Vidakovic B. MCMC methods in wavelet shrinkage: non-equally spaced regression, density and spectral density estimation. In: Müller P., and Vidakovic B. (Eds). Bayesian Inference In Wavelet-Based Models, Lecture Notes in Statistics vol. 141 (1999), Springer, New York 187-202
45. Neumann M.H. Spectral density estimation via nonlinear wavelet methods for stationary non-gaussian time series. J. Time Ser. Anal. 17 (1996) 601-633
46. Newey W., and West K. Automatic lag selection in covariance matrix estimation. Rev. Econom. Stud. 61 (1994) 631-653
47. Priestley M.B. Univariate Series, Spectral Analysis and Time Series vol. 1 (1981), Academic Press, New York
48. Priestley M.B. Wavelets and time-dependent spectral analysis. J. Time Ser. Anal. 17 (1996) 85-103
49. Robinson P.M. Automatic frequency domain inference on semiparametric and non-parametric models. Econometrica 59 (1991) 1329-1363
50. Spokoiny V.G. Adaptive hypothesis testing using wavelets. Ann. Statist. 24 (1996) 2477-2498
51. Spokoiny V.G. Adaptive and spatially adaptive testing of a nonparametric hypothesis. Math. Methods Statist. 7 (1998) 245-273
52. Tsay R. Analysis of Financial Time Series (2002), Wiley, New York
53. Tse Y.K. Residual-based diagnostics for conditional heteroscedasticity models. Econometrics J. 5 (2002) 358-373
54. Tse Y.K., and Tsui A.K.C. A note on diagnosing multivariate conditional heteroskedasticity models. J. Time Ser. Anal. 20 (1999) 679-691
55. Tse Y.K., and Tsui A.K.C. A multivariate GARCH model with time-varying correlations. J. Business Econom. Statist. 20 (2002) 351-362
56. van der Weide R. GO-GARCH: a multivariate generalized orthogonal GARCH model. J. Appl. Econometrics 17 (2002) 549-564
57. Vidakovic B. Statistical Modeling by Wavelets (1999), Wiley, New York
58. Vrontos I., Dellaportas P., and Politis D. A full-factor multivariate GARCH model. Econometrics J. 6 (2003) 311-333
59. Wong H., and Li W.K. Detecting and diagnostic checking multivariate conditional heteroscedastic time series models. Ann. Inst. Statist. Math. 54 (2002) 45-59