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Temporal Aggregation, Bandwidth Selection and Long Memory for Volatility Models

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  • Pierre Perron

    (Boston University)

  • Wendong Shi

    (Renmin University of China)

Abstract

The effects of temporal aggregation and choice of sampling frequency are of great interest in modeling the dynamics of asset price volatility. We show how the squared low-frequency returns can be expressed in terms of the temporal aggregation of a high frequency series. Based on the theory of temporal aggregation, we provide the link between the spectral density function of the squared low-frequency returns and that of the squared high-frequency returns. Furthermore, we analyze the properties of the spectral density function of realized volatility series, constructed from squared returns with different frequencies under temporal aggregation. Our theoretical results allow us to explain some Öndings reported recently and uncover new features of volatility in financial market indices. The theoretical findings are illustrated via the analysis of both low-frequency daily S&P 500 returns from 1928 to 2011 and high-frequency 1-minute S&P 500 returns from 1986 to 2007.

Suggested Citation

  • Pierre Perron & Wendong Shi, 2014. "Temporal Aggregation, Bandwidth Selection and Long Memory for Volatility Models," Boston University - Department of Economics - Working Papers Series wp2014-009, Boston University - Department of Economics.
    • Handle: RePEc:bos:wpaper:wp2014-009
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    File URL: http://people.bu.edu/perron/papers/Aggregation-SP500-11June2014.pdf
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    References listed on IDEAS

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    Cited by:

    1. Shi, Wendong & Sun, Jingwei, 2016. "Aggregation and long-memory: An analysis based on the discrete Fourier transform," Economic Modelling, Elsevier, vol. 53(C), pages 470-476.

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    More about this item

    Keywords

    long memory; stochasyic volatility; temporal aggregation; semiparametric estimators; level shifts;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • 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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