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Tests for conditional heteroscedasticity of functional data

Rice, Gregory and Wirjanto, Tony and Zhao, Yuqian (2020) 'Tests for conditional heteroscedasticity of functional data.' Journal of Time Series Analysis, 41 (6). pp. 733-758. ISSN 0143-9782

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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.

Item Type: Article
Uncontrolled Keywords: Functional time series; heteroscedasticity testing; model diagnostic checking; high‐frequency volatility models; intra‐day asset price
Divisions: Faculty of Social Sciences
Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Essex Finance Centre
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 27 Apr 2020 13:49
Last Modified: 06 Jan 2022 14:13

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