Tests for Conditional Heteroscedasticity of Functional Data

26 Pages Posted: 6 Oct 2020

See all articles by Gregory Rice

Gregory Rice

University of Waterloo - Department of Statistics and Actuarial Science

Tony S. Wirjanto

University of Waterloo - School of Accounting and Finance; University of Waterloo, Department of Statistics & Actuarial Science

Yuqian Zhao

University of Essex

Date Written: November 1, 2020

Abstract

Functional data objects derived from high‐frequency financial data often exhibit volatility clustering. Versions of functional generalized autoregressive conditionally heteroscedastic (FGARCH) models have recently been proposed to describe such data, however so far basic diagnostic tests for these models are not available. We propose two portmanteau type tests to measure conditional heteroscedasticity in the squares of asset return curves. A complete asymptotic theory is provided for each test. We also show how such tests can be adapted and applied to model residuals to evaluate adequacy, and inform order selection, of FGARCH models. Simulation results show that both tests have good size and power to detect conditional heteroscedasticity and model mis‐specification in finite samples. In an application, the tests show that intra‐day asset return curves exhibit conditional heteroscedasticity. This conditional heteroscedasticity cannot be explained by the magnitude of inter‐daily returns alone, but it can be adequately modeled by an FGARCH(1,1) model.

Keywords: Functional time series, heteroscedasticity testing, model diagnostic checking, high‐frequency volatility models, intra‐day asset price

Suggested Citation

Rice, Gregory and Wirjanto, Tony S. and Zhao, Yuqian, Tests for Conditional Heteroscedasticity of Functional Data (November 1, 2020). Journal of Time Series Analysis, Vol. 41, Issue 6, pp. 733-758, 2020, Available at SSRN: https://ssrn.com/abstract=3705429 or http://dx.doi.org/10.1111/jtsa.12532

Gregory Rice

University of Waterloo - Department of Statistics and Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Croatia

Tony S. Wirjanto

University of Waterloo - School of Accounting and Finance ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
519-888-4567 x35210 (Phone)

HOME PAGE: http://https://uwaterloo.ca/statistics-and-actuarial-science/people-profiles/tony-wirjanto

University of Waterloo, Department of Statistics & Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
519-888-4567 x35210 (Phone)
519-746-1875 (Fax)

HOME PAGE: http://math.uwaterloo.ca/statistics-and-actuarial-science/people-profiles/tony-wirjanto

Yuqian Zhao (Contact Author)

University of Essex

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