Tests for conditional heteroscedasticity with functional data and goodness-of-fit tests for FGARCH models

Rice, Gregory and Wirjanto, Tony and Zhao, Yuqian (2019): Tests for conditional heteroscedasticity with functional data and goodness-of-fit tests for FGARCH models.

Abstract

Functional data objects that are derived from high-frequency financial data often exhibit volatility clustering characteristic of conditionally heteroscedastic time series. Versions of functional generalized autoregressive conditionally heteroscedastic (FGARCH) models have recently been proposed to describe such data, but 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 financial asset return curves. A complete asymptotic theory is provided for each test, and we further show how they can be applied to model residuals in order to evaluate the adequacy, and aid in 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 proposed tests reveal that intra-day asset return curves exhibit conditional heteroscedasticity. Additionally, we found that this conditional heteroscedasticity cannot be explained by the magnitude of inter-daily returns alone, but that it can be adequately modeled by an FGARCH(1,1) model.

• Item Type: MPRA Paper
• Language: English
• Keywords: Functional time series, Heteroscedasticity testing, Model diagnostic checking, High-frequency volatility models, Intra-day asset price
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; G - Financial Economics > G1 - General Financial Markets > G10 - General

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