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The functional central limit theorem and structural change test for the HAR(∞) model

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  • Lee, Oesook

Abstract

In this paper, we study the functional central limit theorem (FCLT) for the infinite-order heterogeneous autoregressive model of realized volatility (HAR(∞)). We prove under proper assumptions that the process is L2-NED and then obeys the FCLT. As an application of the FCLT, we derive the limit distribution of the CUSUM statistics to detect the structural change of the model.

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  • Lee, Oesook, 2014. "The functional central limit theorem and structural change test for the HAR(∞) model," Economics Letters, Elsevier, vol. 124(3), pages 370-373.
    • Handle: RePEc:eee:ecolet:v:124:y:2014:i:3:p:370-373
    DOI: 10.1016/j.econlet.2014.06.029
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    1. Walter Kramer & Philipp Sibbertsen, 2002. "Testing for Structural Changes in the Presence of Long Memory," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 1(3), pages 235-242, December.
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    Cited by:

    1. Asai Manabu & Peiris Shelton & McAleer Michael & Allen David E., 2020. "Cointegrated Dynamics for a Generalized Long Memory Process: Application to Interest Rates," Journal of Time Series Econometrics, De Gruyter, vol. 12(1), pages 1-18, January.
    2. Hwang, Eunju & Shin, Dong Wan, 2015. "A CUSUMSQ test for structural breaks in error variance for a long memory heterogeneous autoregressive model," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 167-176.
    3. Min Liu & Wei‐Chong Choo & Chi‐Chuan Lee & Chien‐Chiang Lee, 2023. "Trading volume and realized volatility forecasting: Evidence from the China stock market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(1), pages 76-100, January.
    4. Asai, M. & Peiris, S. & McAleer, M.J. & Allen, D.E., 2018. "Cointegrated Dynamics for A Generalized Long Memory Process," Econometric Institute Research Papers EI 2018-32, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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    More about this item

    Keywords

    Functional central limit theorem; HAR(∞) model; L2-NED; Structural break; CUSUM;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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