HAR Model Research Articles

Global equity market volatility spillovers: A broader role for the United States

Rapach et al. (2013) recently showed that U.S. equity market returns contain valuable information for improving return forecasts in global equity markets. In this study, we extend the work of Rapach et al. (2013) and examine whether U.S.-based equity market information can be used to improve realized volatility forecasts in a large cross-section of international equity markets. We use volatility data for the U.S. and 17 foreign equity markets from the Oxford Man Institute’s realized library, and augment our benchmark HAR model with U.S. equity market volatility information for each foreign equity market. We show that U.S. equity market volatility information improves the out-of-sample forecasts of realized volatility substantially in all 17 foreign equity markets that we consider. Not only are these forecast gains highly significant, they also produce out-of-sample R2 values of between 4.56% and 14.48%, with 9 being greater than 10%. The improvements in out-of-sample forecasts remain statistically significant for horizons up to one month ahead. A substantial part of these predictive gains is driven by forward-looking volatility, as captured by the VIX.

Implied volatility index for the Norwegian equity market

We introduce and evaluate the NOVIX - an implied volatility index for the Norwegian equity index OBX. NOVIX is created according to the VIX methodology. We compare the NOVIX to the German VDAX-NEW and the U.S. VIX and find that NOVIX has similar properties as these two indices. We also evaluate the VIX, VDAX-NEW and NOVIX in terms of volatility forecasting. As a benchmark model we use a precise HAR model of Corsi (2009) based on high-frequency data. All three implied volatility indices significantly improve daily, weekly and monthly forecasts of volatility of their underlying equity indices. This improvement is largest for the VIX, followed by VDAX-NEW and NOVIX.

A Vector Heterogeneous Autoregressive Index Model for Realized Volatility Measures

This paper introduces a new modelling for detecting the presence of commonalities in a set of realized volatility measures. In particular, we propose a multivariate generalization of the heterogeneous autoregressive model (HAR) that is endowed with a common index structure. The Vector Heterogeneous Autoregressive Index model has the property to generate a common index that preserves the same temporal cascade structure as in the HAR model, a feature that is not shared by other aggregation methods (e.g., principal components). The parameters of this model can be easily estimated by a proper switching algorithm that increases the Gaussian likelihood at each step. We illustrate our approach with an empirical analysis aiming at combining several realized volatility measures of the same equity index for three different markets.

Tax reforms and stock return volatility: The case of Japan

Although global financial turmoil in recent years has resulted in renewed interest in taxing financial markets, the existing evidence is inconclusive regarding the effect of stock transaction taxes (STT) on stock return volatility. In this respect, Japan provides an excellent opportunity to address the issue, as the country enacted major tax reforms during the long recession beginning in the early 1990s, not only abolishing STT in 1999, but also reducing the capital gains and dividend taxes in 2003. The present paper exploits these tax reform episodes and examines whether and how they affected stock return volatility. In so doing, it employs GARCH-type models using standard daily stock data, as well as HAR models based on realized volatility constructed from high-frequency, intraday data. The estimation results are consistent with the views that, in line with some earlier findings, the STT abolition in 1999 reduced volatility, and that the tax reforms in 2003 also reduced volatility through a cut in the dividend tax, but not in the capital gains tax.

Forecasting Daily Volatility on Bucharest Stock Exchange using HAR Model

In this paper we forecast realized volatility using a very liquid equity traded on Bucharest Stock Exchange, Property Fund (FP) which is a company that manages Romanian government real-estate properties and at that time had almost 40% market capitalization. Many research paper use strndard version of HAR model, with or without jumps to forecast volatility on markets with a high level of liquidity. Our result, based on Diebold an Mariano test show that forecast performance increase if we use a modified version of HAR model, allowing for average trade duration form prevoius day to play an important role in analysis.

Realised Volatility Forecasts for Stock Index Futures Using the HAR Models with Bayesian Approaches *

Abstract We investigate the realised volatility (RV) forecasts for the short, mid, and long term by developing the HAR models with Bayesian approaches and employing the high-frequency data of the China Stock Index 300 (CSI300) future for the period from 16 April 2010 to 21 May 2014. We also evaluate the performances of competing models for both in-sample forecasts and out-of-sample forecasts. We find that the proposed HAR-type models with Bayesian approaches capture the time-varying properties of parameters and predictor sets. We also find that the HAR-type models with Bayesian approaches have superior forecast performance for both in-sample forecasts and out-of-sample forecasts as compared with the benchmark HAR-type models.

Global Equity Market Volatility Spillovers: A Broader Role for the United States

Rapach et al. (2013) have recently shown that U.S. equity market returns carry valuable information to improve return forecasts in global equity markets. In this study, we extend the work of Rapach et al. (2013) and examine if U.S. based equity market information can be used to improve realized volatility forecasts in a large cross-section of international equity markets. We use volatility data for the U.S. and 17 foreign equity markets from the Oxford Man Institute’s realized library and augment for each foreign equity market our benchmark HAR model with U.S. equity market volatility information. We show that U.S. equity market volatility information substantially improves out-of-sample forecasts of realized volatility in all 17 foreign equity markets that we consider. Forecast gains are not only highly significant, but produce out-of-sample R 2 values between 4.56% and 14.48%, with 12 of these being greater than 10%. The improvements in out-of-sample forecasts remain statistically significant for horizons up to 1 month ahead. A substantial part of the predictive gains are driven by forward looking volatility as captured by the VIX.

Modeling Realized Volatility Dynamics with a Genetic Algorithm

AbstractThe heterogeneous autoregressive model of realized volatility (HAR‐RV) is inspired by the heterogeneous market hypothesis and characterizes realized volatility dynamics through a linear function of lagged daily, weekly and monthly realized volatilities with a (1, 5, 22) lag structure. Considering that different markets can have different heterogeneous structures and a market's heterogeneous structure can vary over time, we build an adaptive heterogeneous autoregressive model of realized volatility (AHAR‐RV), whose lag structure is optimized with a genetic algorithm. Using nine common loss functions and the superior predictive ability test, we find that our AHAR‐RV model and its extensions provide significantly better out‐of‐sample volatility forecasts for the CSI 300 index than the corresponding HAR models. Furthermore, the AHAR‐RV model significantly outperforms all the other models under most loss functions. Besides, we confirm that Chinese stock markets' heterogeneous structure varies over time and the (1, 5, 22) lag structure is not the optimal choice. Copyright © 2016 John Wiley & Sons, Ltd.

Sparse Change-Point Har Models for Realized Variance

Change-point time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an over-parametrization issue since typically only one latent state variable drives the switches in all parameters. This implies that all parameters have to change when a break happens. To gauge whether and where there are structural breaks in realized variance, we introduce the sparse change-point HAR model. The approach controls for model parsimony by limiting the number of parameters which evolve from one regime to another. Sparsity is achieved thanks to employing a nonstandard shrinkage prior distribution. We derive a Gibbs sampler for inferring the parameters of this process. Simulation studies illustrate the excellent performance of the sampler. Relying on this new framework, we study the stability of the HAR model using realized variance series of several major international indices between January 2000 and August 2015.

Incremental information of stock indicators

The present paper is the first to examine the incremental information of stock indicators in the spot and futures stock markets. The properties of volatility series of indicators in relation to spot and futures stock indices are examined. Correlations between either the spot or futures stock indices and the corresponding indicators are examined for their properties. The asymmetry, heterogeneity and jump properties of volatilities and correlations are studied. Indicators offer information not captured in the corresponding futures and spot stock indices. Volatility and correlation in the stock market are accurately in-sample predicted via asymmetric and HAR models. The inclusion of indicators improves the in-sample modeling of volatility and correlation in the stock market.

The course of realized volatility in the LME non-ferrous metal market

This study analyzes the volatility of LME futures contracts on aluminum, copper, lead, nickel and zinc using high-frequency data. The dynamics of realized volatility is studied over the period from January 2004 to September 2012 and is shown to be well captured with a rolling HAR-GARCH model. An increasing importance of short-term volatility components is evident across all metals in the aftermath of the global financial crisis and the related sharp decline in industrial metal prices. The heavier impact of short-term volatility corresponds consistently to a decreasing persistence of the volatility of realized volatility. In terms of predictive accuracy, even though leverage effects or GARCH-terms related to the volatility of realized volatility are characterized for the most part by significant in-sample parameters, the plain HAR model cannot be consistently outperformed by explicitly accounting for these stylized facts.

Recursive wind speed forecasting based on Hammerstein Auto-Regressive model

Abstract A new Wind Speed Forecasting (WSF) model, suitable for a short term 1–24 h forecast horizon, is developed by adapting Hammerstein model to an Autoregressive approach. The model is applied to real data collected for a period of three years (2004–2006) from two different sites. The performance of HAR model is evaluated by comparing its prediction with the classical Autoregressive Integrated Moving Average (ARIMA) model and a multi-layer perceptron Artificial Neural Network (ANN). Results show that the HAR model outperforms both the ARIMA model and ANN model in terms of root mean square error (RMSE), mean absolute error (MAE), and Mean Absolute Percentage Error (MAPE). When compared to the conventional models, the new HAR model can better capture various wind speed characteristics, including asymmetric (non-gaussian) wind speed distribution, non-stationary time series profile, and the chaotic dynamics. The new model is beneficial for various applications in the renewable energy area, particularly for power scheduling.

Realized range volatility forecasting: Dynamic features and predictive variables

In this paper, we estimate, model and forecast realized range volatility, a realized measure and estimator of the quadratic variation of financial prices. This quantity was introduced early in the literature and it is based on the high–low range observed at high frequency during the day. We consider the impact of the microstructure noise in high frequency data and correct our estimations, following a known procedure. Then, we model the realized range accounting for the well-known stylized effects present in financial data and we investigate the role that macroeconomic and financial variables play when forecasting daily stocks volatility. We consider an HAR model with asymmetric effects with respect to the volatility and the return, and GARCH and GJR specifications for the variance equation. Moreover, we consider a non-Gaussian distribution for the innovations. Finally, we extend the model including macroeconomic and financial variables that capture the present and the future state of the economy. We find that these variables are significantly correlated with the first common component of the volatility series and they have a highly in-sample explanatory power. The analysis of the forecast performance in 16 NYSE stocks suggests that the introduction of asymmetric effects with respect to the returns and the volatility in the HAR model result in a significant improvement in the point forecasting accuracy as well and the variables related with the U.S. stock market performance and proxies for the credit risk.

A CUSUMSQ test for structural breaks in error variance for a long memory heterogeneous autoregressive model

For testing error variance instability, a test based on CUSUM squares of the residuals in HAR model is constructed and its limiting null distribution is derived to be a simple function of the standard Brownian bridge. A finite sample Monte-Carlo experiment shows reasonable size and power performances of the proposed test. The test is applied to the log-return realized volatilities of some stock price index and exchange rate to find evidence for variance instability after adjusting long-memories.

Estimating dynamic copula dependence using intraday data

Abstract We estimate the dynamic daily dependence between assets by applying the Semiparametric Copula-Based Multivariate Dynamic (SCOMDY) model on intraday data. Using tick data of three stock returns of the period before and during the credit crisis, we find that our dependence estimator better captures the steep increase in dependence during the onset of the crisis as compared to other commonly used time-varying copula methods. Like other high-frequency estimators, we find that the dependence estimator exhibits long memory and forecast it using a HAR model. We show that for out-of-sample forecasts, our dependence estimator performs better than the constant estimator and other commonly used time-varying copula dependence estimators.

It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model

The persistent nature of equity volatility is investigated by means of a multi-factor stochastic volatility model with time varying parameters. The parameters are estimated by means of a sequential matching procedure which adopts as an auxiliary model a time-varying generalization of the HAR model for the realized volatility series. It emerges that during the recent financial crisis the relative weight of the daily component dominates over the monthly term. The estimates of the two factor stochastic volatility model suggest that the change in the dynamic structure of the realized volatility during the financial crisis is due to the increase in the volatility of the persistent volatility term. A set of Monte Carlo simulations highlights the robustness of the methodology adopted in tracking the dynamics of the parameters. • We study the dynamics of the log-realized volatility with a time-varying HAR. • Parameters are estimated with an on-line method. • The parameters of a two-factor stochastic volatility model are recursively estimated. • The vol-of-vol parameter of the slow factor increases during the financial crisis. • The increase of vol-of-vol generates higher persistence and higher variability.

The functional central limit theorem and structural change test for the HAR([formula omitted]) model

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.

The Analysis of Automotive Wiring Harness Dynamic Crosstalk

Since the installation and strapping of the harness, and the vehicle motion state of the automotive is different. The crosstalk automotive wire harness is not a fixed value, but a certain dynamic range in the actual situation. Through the analysis of the factors of influence cable crosstalk can draw a conclusion that the cable relative position and disturbed line termination impedance is a major factor in the production of dynamic change. We analyze the dynamic range of crosstalk of 14 core wire harness model by using a statistical method, as a result of the change of the relative position of cable far-end crosstalk (FEXT) range within 1 dB, but when the disturbed line termination impedance changes from 50Ω to 1000Ω, the cable far-end crosstalk range reached 15 dB. It provides reference basis for the automotive wiring harness electromagnetic compatibility design.

Obtaining and Predicting the Bounds of Realized Correlations

Summary This paper argues that the inherent data problems make precise point identification of realized correlation difficult but identification bounds in the spirit of Manski (1995) can be derived. These identification bounds allow for a more robust approach to inference especially when the realized correlation is used for estimating other risk measures. We forecast the identification bounds using the HAR model of Corsi (2003) using data during the year of onset of the credit crisis and find that the bounds provide good predictive coverage of the realized correlation for both 1- and 10-step forecasts even in volatile periods.

Obtaining and Predicting the Bounds of Realized Correlations

The problem of estimation of realized correlation, which is analogous to realized covariance, is compounded by effects of market microstructure, noise, and asynchronous trading. Various methods have been proposed to decrease the biases, but they require assumptions to be made that may be unrealistic. This paper argues that the inherent data problems make precise point identification of realized correlation difficult, but identification bounds in the spirit of Manski (1995) can be derived. These identification bounds allow for a more robust approach to inference, especially when the realized correlation is used for estimating other risk measures. We forecast the identification bounds using the HAR model of Corsi (2003) using data during the year of onset of the credit crisis, and find that the bounds provide good predictive coverage of the realized correlation for both one step and ten step forecasts, even in volatile periods.