STATISTICAL INFERENCE FOR AUTOCOVARIANCE OF FUNCTIONAL TIME SERIES UNDER CONDITIONAL HETEROSCEDASTICITY

Gregory Kokoszka

doi:10.55640/gmj-abc111

Open Access

STATISTICAL INFERENCE FOR AUTOCOVARIANCE OF FUNCTIONAL TIME SERIES UNDER CONDITIONAL HETEROSCEDASTICITY

https://doi.org/10.55640/gmj-abc111

PDF

Gregory Kokoszka ¹ ,

⁴ Department of Statistics and Actuarial Science, University of Waterloo, Canada

Abstract

This paper investigates statistical inference methods for autocovariance estimation in functional time series under the presence of conditional heteroscedasticity. Functional time series data, which are characterized by observations evolving over continuous time or space, often exhibit complex dependencies and time-varying volatility patterns. In the presence of conditional heteroscedasticity, traditional autocovariance estimators may be biased or inefficient, necessitating the development of robust inference techniques. We propose a novel approach based on robust covariance estimation and bootstrap resampling to account for heteroscedasticity and provide reliable estimates of autocovariance. The efficacy of the proposed methodology is demonstrated through simulations and applications to real-world functional time series data, highlighting its ability to capture dynamic dependencies and volatility patterns under varying conditions.

Keywords

Functional time series, autocovariance, conditional heteroscedasticity

References

📄 Aue, S. Hörmann, L. Horváth, M. Reimherr, Break detection in the covariance structure of multivariate time series models, Ann. Statist. 37 (2009) 4046–4087.

📄 Aue, L. Horváth, D.F. Pellatt, Functional generalized autoregressive conditional heteroskedasticity, J. Time Ser. Anal. 38 (2017) 3–21.

📄 L. Bauwens, S. Laurent, J. Rombouts, Multivariate GARCH models: A survey, J. Appl. Econometrics 21 (2006) 79–109.

📄 Berkes, S. Hörmann, J. Schauer, Split invariance principles for stationary processes, Ann. Probab. 39 (2011) 2441–2473.

📄 V.I. Bogachev, Gaussian Measures, American Mathematical Society, 1998.

📄 T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, J. Econometrics 31 (1986) 307–327.

📄 D. Bosq, Linear Processes in Function Spaces, Springer, New York, 2000.

📄 Cerovecki, S. Hörmann, On the CLT for discrete Fourier transforms of functional time series, J. Multivariate Anal. 154 (2017) 282–295.

📄 P. Duchesne, Testing for multivariate autoregressive conditional heteroskedasticity using wavelets, Comput. Statist. Data Anal. 51 (2006) 2142–2163.

📄 R.F. Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50 (1982) 987–1007.

📄 Francq, R. Roy, J.-M. Zakoian, Diagnostic checking in ARMA models with uncorrelated errors, J. Amer.

📄 Francq, J.-M. Zakoian, GARCH Models, Wiley, New York, 2010.

📄 R. Gabrys, P. Kokoszka, Portmanteau test of independence for functional observations, J. Amer. Statist. Assoc. 102 (2007) 1338–1348.

📄 Gouriéroux, ARCH Models and Financial Applications, Springer, New York, 1997.

How to Cite

Gregory Kokoszka. (2022). STATISTICAL INFERENCE FOR AUTOCOVARIANCE OF FUNCTIONAL TIME SERIES UNDER CONDITIONAL HETEROSCEDASTICITY. Global Multidisciplinary Journal, 1(01), 01-06. https://doi.org/10.55640/gmj-abc111

Download Citation

Most read articles by the same author(s)

<< < 1 2 3 4 5 6 7 8 9 10 > >>

Global Multidisciplinary Journal

STATISTICAL INFERENCE FOR AUTOCOVARIANCE OF FUNCTIONAL TIME SERIES UNDER CONDITIONAL HETEROSCEDASTICITY

Abstract

Keywords

References

How to Cite

Most read articles by the same author(s)

Similar Articles