Fast fractional differencing in modeling long memory of conditional variance for high-frequency data

The goal of this paper is twofold. First, using five of the most actively traded stocks in the Brazilian financial market, this paper shows that the normality assumption commonly used in the risk management area to describe the distributions of returns standardized by volatilities is not compatible with volatilities estimated by EWMA or GARCH models. In sharp contrast, when the information contained in high frequency data is used to construct the realized volatility measures, we attain the normality of the standardized returns, giving promise of improvements in Value-at-Risk statistics. We also describe the distributions of volatilities of the Brazilian stocks, showing that they are nearly lognormal. Second, we estimate a simple model of the log of realized volatilities that differs from the ones in other studies. The main difference is that we do not find evidence of long memory. The estimated model is compared with commonly used alternatives in out-of-sample forecasting experiment.

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Parsimonious Heterogeneous ARCH Models for High Frequency Modeling

Journal of Risk and Financial Management ◽

10.3390/jrfm13020038 ◽

2020 ◽

Vol 13 (2) ◽

pp. 38

Author(s):

Juan Carlos Ruilova ◽

Pedro Alberto Morettin

Keyword(s):

Financial Market ◽

Long Memory ◽

High Frequency ◽

High Frequency Data ◽

Frequency Data ◽

Arch Models ◽

Heterogeneous Information ◽

Modeling Process ◽

Proposed Model ◽

The Garch Model

In this work we study a variant of the GARCH model when we consider the arrival of heterogeneous information in high-frequency data. This model is known as HARCH(n). We modify the HARCH(n) model when taking into consideration some market components that we consider important to the modeling process. This model, called parsimonious HARCH(m,p), takes into account the heterogeneous information present in the financial market and the long memory of volatility. Some theoretical properties of this model are studied. We used maximum likelihood and Griddy-Gibbs sampling to estimate the parameters of the proposed model and apply it to model the Euro-Dollar exchange rate series.

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Bivariate Volatility Modeling with High-Frequency Data

Econometrics ◽

10.3390/econometrics7030041 ◽

2019 ◽

Vol 7 (3) ◽

pp. 41 ◽

Cited By ~ 1

Author(s):

Matei ◽

Rovira ◽

Agell

Keyword(s):

High Frequency ◽

Mathematical Structure ◽

Conditional Variance ◽

High Frequency Data ◽

Conditional Heteroskedasticity ◽

Frequency Data ◽

Volatility Estimation ◽

Structure Information ◽

Volatility Modeling ◽

Bivariate Models

We propose a methodology to include night volatility estimates in the day volatility modeling problem with high-frequency data in a realized generalized autoregressive conditional heteroskedasticity (GARCH) framework, which takes advantage of the natural relationship between the realized measure and the conditional variance. This improves volatility modeling by adding, in a two-factor structure, information on latent processes that occur while markets are closed but captures the leverage effect and maintains a mathematical structure that facilitates volatility estimation. A class of bivariate models that includes intraday, day, and night volatility estimates is proposed and was empirically tested to confirm whether using night volatility information improves the day volatility estimation. The results indicate a forecasting improvement using bivariate models over those that do not include night volatility estimates.

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