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Extant empirical evidence suggests that variance risk might not be priced in markets that witness high retail participation. We examine and reject this hypothesis using data from Indian markets. We employ both model-dependent and model-free approaches in our analysis. Our result is robust to alternate specifications of volatility, sampling frequencies and sample periods. We then examine the dynamics of variance risk premium. Specifically, we split realized variance into its two components: jumps and continuous variance. We find that only past continuous variance is significant in forecasting short-term synthetic variance swap returns; realized jumps do not have any predictive power. These results survive inclusion of classical risk factors. These findings suggest that only the continuous component of realized variance has significant impact on variance risk premium.

The authors acquire a unique dataset of high-frequency traded prices for bitcoin call and put options from the Deribit cryptocurrency derivatives exchange, by 15-minute sampling via the application programming interface They use these prices to construct a term structure of bitcoin implied volatility indices using a variance swap fair-value formula that is employed by the CBOE for the VIX, an index commonly referred to as the “investor fear gauge” for the US stock market Employing over seven million option prices, they construct the bitcoin implied volatility indices with maturities from one week to three months, sampled every 15 minutes from March 2019 to March 2020 They discuss the features of the index and the associated bitcoin variance risk premia, with three different regular time partitions for realized variance, viz 15-minutes, hourly, and daily They also examine the relationship between bitcoin’s 30-day realized variance, volatility index, and variance risk premium, with their equivalent for US equities, oil, gold, the USD/EUR exchange rate, and the 10-year US Treasury note TOPICS: Options, currency, statistical methods Key Findings • The authors novel dataset of bitcoin option prices from Deribit is applied to quote bitcoin VIX indices with maturities from one-week to three months The short-maturity bitcoin VIX exceeded 200% after the global outbreak of Covid-19 • The indices provide indicative fair values for bitcoin variance swaps, which are traded on-chain Using realized volatility monitored at 15-minute, hourly, and daily frequencies, they examine the bitcoin variance risk premium at different maturities • Bitcoin’s 30-day realized volatility, volatility index, and variance risk premium are correlated with their equivalent for US equities, oil, gold, the USD/EUR exchange rate, and the 10-year US Treasury note Diversification potential decreased dramatically after the outbreak of Covid-19

PurposeThe purpose of this paper is to explore whether the out-of-sample model bias plays an important role in predicting volatility.Design/methodology/approachUnder the heterogeneous autoregressive realized volatility (HAR-RV) framework, we analyze the predictive power of out-of-sample model bias for the realized volatility (RV) of the Dow Jones Industrial Average (DJI) and the S&P 500 (SPX) indices from in-sample and out-of-sample perspectives respectively.FindingsThe in-sample results reveal that the prediction model including the model bias can obtain bigger R2, and the out-of-sample empirical results based on several evaluation methods suggest that the prediction model incorporating model bias can improve forecast accuracy for the RV of the DJI and the SPX indices. That is, model bias can enhance the predictability of original HAR family models.Originality/valueThe author introduce out-of-sample model bias into HAR family models to enhance model capability in predicting realized volatility.

Taking the unique advantage of the cryptocurrency market setting, this paper examines the relationships between blockchain participation and returns, trading volume and realized volatility of main cryptocurrencies (i.e., Bitcoin, Ethereum and Litecoin). Dissimilar to previous theoretical studies that model the influencing factors on participation, we employ the number of unique from addresses 1 as the proxy for cryptocurrency investors’ blockchain participation and further explore the impact of such participation. By using vector autoregressive (VAR) model, we find that the blockchain participation has a significant and positive impact on the next day’s trading volume and realized volatility for the main cryptocurrencies. Our results are robust to the Granger causality test and alternative measure for blockchain participation.

We propose a sparse vector heterogeneous autoregressive (VHAR) model for realized volatility forecasting. As a multivariate extension of a heterogeneous autoregressive model, a VHAR model can consider the dynamics of multinational stock volatilities in a compact manner. A sparse VHAR is estimated using adaptive lasso and some theoretical properties are provided. In practice, our sparse VHAR model can improve forecasting performance and explicitly show the connectivity between stock markets. In particular, our empirical analysis shows that the NASDAQ market had the strongest influence on stock market volatility worldwide in the 2010s.

We examine the impact of the introduction of traditional, non-U.S., real estate exchange traded funds (ETFs) on the realized volatility of real estate ETFs’ component stocks in a global setting. We...

Motivated by a common belief that the international stock market volatilities are synonymous with information flow, this paper proposes a parsimonious way to combine multiple market information flows and assess whether cross-national volatility flows contain important information content that can improve the accuracy of international volatility forecasting. We concentrate on realized volatilities (RV) derived from the intra-day prices of 22 international stock markets, and employ the heterogeneous autoregressive (HAR) framework, along with two common diffusion indices that are constructed based on the simple mean and first principal component (PC) of the 22 stock market RVs, to forecast future volatilities of each market for 1-day, 1-week, and 1-month ahead. We provide strong evidence that the use of the cross-national information reflected by the simple and parsimonious common indices enhances the predictive accuracy of international volatilities at all forecasting horizons. Alternative volatility measures, estimation window sizes, and forecasting evaluation tests confirm the robustness of our results. Finally, our strategy of constructing common diffusion indices is also feasible for international market jumps.

Fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, new realized stochastic volatility (RSV) models are developed: one is a RSV model with general Gegenbauer long memory (GGLM), while the other is a RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks, apart from the origin in the power spectrum. For estimating the RSV–GGLM model, a two step method is suggested: the location parameters for the peaks of the power spectrum are estimated in the first step, while the remaining parameters are estimated based on the Whittle likelihood in the second step. Monte Carlo experiments give results for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of the RSV–SLM model against the RSV–GGLM model. The RSV–GGLM and RSV–SLM models are applied to three stock market indices, for which the estimation and forecasting results indicate the adequacy of considering general long memory.

This study designs the Markov-switching (MS) mixed data sampling (MIDAS) models and then explores the effects of intraday and interday jumps on oil futures price realized volatility. The in-sample ...

We consider a GARCH-MIDAS model with short-term and long-term volatility components, in which the long-term volatility component depends on many macroeconomic and financial variables. We select the variables that exhibit the strongest effects on the long-term stock market volatility via maximizing the penalized log-likelihood function with an Adaptive-Lasso penalty. The GARCH-MIDAS model with variable selection enables us to incorporate many variables in a single model without estimating a large number of parameters. In the empirical analysis, three variables (namely, housing starts, default spread and realized volatility) are selected from a large set of macroeconomic and financial variables. The recursive out-of-sample forecasting evaluation shows that variable selection significantly improves the predictive ability of the GARCH-MIDAS model for the long-term stock market volatility.

We identify the VIX index is innately a risk-neutrally forward-looking measure of the polynomial (not quadratic) variation of market returns. Correspondingly, the VIX risk premium, squared VIX minuses the realized VIX (a physically conditional measure of the polynomial variation), compensates jointly for the risk of stochastic volatility and that of jump and tail. The VIX index consequently can be decomposed into four fundamentally different components: the realized variance (RV), the variance risk premium (VRP*), the realized tail (RT), and the tail risk premium (TRP), respectively. The empirical results reveal that VRP*, RT, and TRP (except RV) help predict future market returns.

This paper investigates the “spurious almost integration” effect of volatility under a threshold GARCH structure with realized volatility measures. To closely examine the effect, the realized persistence of volatility is proposed to be used as a threshold trigger for volatility regimes. Under the threshold framework, general closed‐form solutions of moment conditions are derived, which provide a convenient way to theoretically examine the “spurious almost integration” effect and its associated impacts. We find that introducing the volatility persistence‐driven threshold can capture regime‐specific characteristics well. It performs better than the traditional GARCH‐type models in terms of both in‐sample fitting and out‐of‐sample forecasting. Based on our Monte Carlo and empirical results, in general we find that overlooking the relatively low‐persistence regime(s) could lead to some misleading conclusions.

This paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures.

This study forecasts the monthly realized volatility of the US stock market covering the period of February, 1885 to September, 2019 using a recently developed novel approach – a moving average heterogeneous autoregressive (MAT-HAR) model, which treats threshold as a moving average generated time varying parameter rather than as a fixed or unknown parameter. The significance of asymmetric information in realized volatility of stock market forecasting is also considered by examining the case of good and bad realized volatility. The Clark and West (2007) forecast evaluation approach is employed to evaluate the forecast performance of the proposed predictive model vis-a-vis the conventional HAR and threshold HAR (T-HAR) models. We find evidence in favour of the MAT-HAR model relative to the HAR and T-HAR models. Also observed is the significant role of asymmetry in modeling the realized volatility as good realized volatility and bad realized volatility yield dissimilar predictability results. Our results are not sensitive to the choice of sample periods and realized volatility measures.

This paper investigates whether volatilities in oil prices influence consumer household consumption expenditure from 1995 to 2019, a period described in the literature by the weakening effect of oil price volatility on macroeconomic factors. The Vector autoregressive model's findings suggest that the unexpected changes in oil prices significantly influence household consumption expenditure in Nigeria. A one standard deviation unexpected for a change in oil prices corresponds to a 28.31 percent increase in Nigeria's consumption expenditure. Moreover, the decomposition of the variance did not affect the sign and significance of the household relationship between oil price volatility and consumption expenditure. The paper offers that the extent to which dependence on oil continues depends on the magnitude to which Nigeria's economies can continue developing alternative energy sources and improving energy conservation.JEL classification: D15, Q43 How to Cite:Ogede, J. S. (2020). Does Oil Price Volatility Drive Household Consumption Expenditures in Nigeria? Signifikan: Jurnal Ilmu Ekonomi, 9(2), 257-268. https://doi.org/10.15408/sjie.v9i2.15498.

Speculators who wish to bet on higher future volatility often purchase options to “go long volatility.” Should investors who buy options expect to profit when realized volatility increases? If so, under what conditions? To answer these questions, we conducted an analysis of the relationship between long volatility performance (buying options) and contemporaneous changes in volatility. We found that buying one-month S&P 500 options was only consistently profitable in the highest decile of changes in one-month volatility. Buying options consistently lost money in the lowest seven deciles of changes in volatility. We then studied the trade entry and exit timing required to retain the profits from long option positions during significant volatility increases. We found similar results between the S&P 500 options market and global equity option markets. TOPIC:Options Key Findings • We explore the relationship between buying options and contemporaneous changes in volatility, and find that buying one-month, delta-hedged S&P 500 options is only consistently profitable in the highest decile of changes in one-month volatility. • We also find that monetizing gains from long option positions during volatility spikes requires very precise trade entry and exit timing. • We find similar results between the S&P 500 option market and global equity option markets.

We analyze the role of the US–China trade war in forecasting out-of-sample daily realized volatility of Bitcoin returns. We study intraday data spanning from 1st July 2017 to 30th June 2019. We use the heterogeneous autoregressive realized volatility model (HAR-RV) as the benchmark model to capture stylized facts such as heterogeneity and long-memory. We then extend the HAR-RV model to include a metric of US–China trade tensions. This is our primary forecasting variable of interest, and it is based on Google Trends. We also control for jumps, realized skewness, and realized kurtosis. For our empirical analysis, we use a machine-learning technique that is known as random forests. Our findings reveal that US–China trade uncertainty does improve forecast accuracy for various configurations of random forests and forecast horizons.

This study investigates the existence of commonality of volatility risk premium in the index and individual stock options. Using data from the National Stock Exchange (NSE) India, the study finds t...

This paper formulates a new dynamic model for the variance risk premium based on a state space representation of a bivariate system for the observable ex-post realized variance and the ex-ante option implied variance expectation. A regime switching structure accommodates for periods of unusually high volatility, heterogeneous dynamics and changes in the dependence between the latent states. The model allows separating the continuous component of the variance risk premium from the impact of jumps on option implied variance expectations. Using options and high frequency returns for the S&P500 index, we explain what is generating return predictability by disentangling the part of the variance risk premium associated with normal sized price fluctuations from that associated with tail events. The latter component predicts to a significant extent, and asymmetrically with respect to their sign, future market return variations.

We study the prediction of realized volatility of non‐ferrous metals futures traded on the Shanghai Futures Exchange from March 2011 to December 2017. A dynamic model averaging model is employed to combine multiple prediction models using time‐varying weights based on individual model performance. Empirical results also reveal that models incorporating volatility spillovers across metals are important for forecast combinations, and short‐term spillovers have a stronger impact than long‐term spillovers. This approach offers the best forecasting performance and allows users to identify the most dominant model at any given time and demonstrate when and how volatility transmission from another metal is valuable for forecasting. We also find evidence of distinct trading behaviours in emerging and developed markets.

This paper evaluates the information content in daily volatility measures that utilize OHLC (Open‐High‐Low‐Close) price data. An encompassing regression framework is used to evaluate the absolute and relative information contain in such measures. 2‐step GMM (generalized method of moments) estimates using two sets of instruments are used to address potential bias from measurement errors. The evidence using S&P 500 index data suggest that volatility measures that use OHLC data encompass those based only on close‐to‐close returns or high‐minus‐low ranges. However, the proposed instruments do not all pass statistical tests of instrument validity and the identification robust confidence set can be quite large.

To forecast the volatility of Chinese stock market, we use information from 28 international markets rather than relying on the Chinese market alone. A common factor, which we call the international volatility index, is constructed by the first principal component of all the 28 cross‐national stock market volatilities. We then add the international volatility index into the prevailing heterogeneous autoregressive model of realized volatility (HAR‐RV). The in‐sample estimation results show that the impact of this common index on future Chinese market volatility is statistically significant and positive. More importantly, the out‐of‐sample forecasting results suggest that our proposed model outperforms competing models including the HAR‐RV, kitchen sink model, and combination approaches. The results are similar when we use a wide range of robustness checks. Furthermore, the international volatility index also yields the highest economic value from an asset allocation perspective.

PurposeWith the presence of pricing errors, the authors consider statistical inference on the variance risk premium (VRP) and the associated implied variance, constructed from the option prices and the historic returns.Design/methodology/approachThe authors propose a nonparametric kernel smoothing approach that removes the adverse effects of pricing errors and leads to consistent estimation for both the implied variance and the VRP. The asymptotic distributions of the proposed VRP estimator are developed under three asymptotic regimes regarding the relative sample sizes between the option data and historic return data.FindingsThis study reveals that existing methods for estimating the implied variance are adversely affected by pricing errors in the option prices, which causes the estimators for VRP statistically inconsistent. By analyzing the S&P 500 option and return data, it demonstrates that, compared with other implied variance and VRP estimators, the proposed implied variance and VRP estimators are more significant variables in explaining variations in the excess S&P 500 returns, and the proposed VRP estimates have the smallest out-of-sample forecasting root mean squared error.Research limitations/implicationsThis study contributes to the estimation of the implied variance and the VRP and helps in the predictions of future realized variance and equity premium.Originality/valueThis study is the first to propose consistent estimations for the implied variance and the VRP with the presence of option pricing errors.

Estimation of true volatility is a crucial part of equity investment, and there are many strategies for realizing this objective (e.g., the Parkinson realized volatility, the GARCH projected volatility, and stochastic implied volatility). Instead of treating volatility estimates as alternatives to one another, a recent series of studies has emphasized the return prediction performances of their paired differences, such as the variance risk premium, which subtracts the implied variance from the realized variance under a nonparametric framework. This article proposes a novel method of differencing variances that are computed on the basis of the holding-period return versus the logarithmic return. Via this approach, the authors provide a satisfactory substitute for the variance risk premium in cases in which its requirements for intraday and options data are not satisfied. They argue that the volatility differences can capture the information contained in logarithmic returns that involve continuous transactions. This argument is supported by follow-up empirical results—the proxy is demonstrated to be able to foreshadow the next-month market return and to perform well in adjusting holdings in long–short portfolio construction strategies. TOPICS:Volatility measures, exchanges/markets/clearinghouses, risk management Key Findings • The authors build a variance difference measure that is based on the holding-period versus logarithmic return for capturing information obtained from continuous trading activities. • This measure retains the return predictability of differencing volatility estimates, thereby providing a satisfactory alternative to the variance risk premium when its stringent data requirements cannot be satisfied. • The long–short portfolio strategies that are developed according to their variance difference are shown to outperform the market index, especially during market downtrend periods.

Este artigo tem por objetivo detalhar o protocolo de aplicação e avaliação dos modelos autorregressivos de heteroscedasticidade condicional generalizados (GARCH), com ênfase em especificar adequadamente a distribuição de probabilidade para os resíduos e o critério de avaliação da previsão. Com este intuito, aplicam-se modelos GARCH com distribuição normal e t de Student na modelagem da volatilidade da série de retornos das ações ABEV3. O melhor modelo seguindo a distribuição normal e o melhor seguindo a distribuição t de Student são executados para a previsão, em que os resultados são comparados com a volatilidade realizada, calculada a partir de retornos intradiários, e com os retornos absolutos. Os resultados evidenciam que o modelo GARCH(1,1) seguindo a distribuição t de Student possui a melhor performance, tanto no ajuste como na previsão. Além disso, os modelos possuem resultados significativamente melhores quando avaliados pelo critério da volatilidade realizada.

In this article, we consider the estimation of the structural change point in the nonparametric model with dependent observations. We introduce a maximum-CUSUM-estimation procedure, where the CUSUM statistic is constructed based on the sum-of-squares aggregation of the difference of the two Nadaraya-Watson estimates using the observations before and after a specific time point. Under some mild conditions, we prove that the statistic tends to zero almost surely if there is no change, and is larger than a threshold asymptotically almost surely otherwise, which helps us to obtain a threshold-detection strategy. Furthermore, we demonstrate the strong consistency of the change point estimator. In the simulation, we discuss the selection of the bandwidth and the threshold used in the estimation, and show the robustness of our method in the long-memory scenario. We implement our method to the data of Nasdaq 100 index and find that the relation between the realized volatility and the return exhibits several structural changes in 2007-2009., 34 pages, 20 figures, 1 tex file, 5 tex auxiliary files

We develop a Bayesian random compressed multivariate heterogeneous autoregressive (BRC-MHAR) model to forecast the realized covariance matrices of stock returns. The proposed model randomly compresses the predictors and reduces the number of parameters. We also construct several competing multivariate volatility models with the alternative shrinkage methods to compress the parameter’s dimensions. We compare the forecast performances of the proposed models with the competing models based on both statistical and economic evaluations. The results of statistical evaluation suggest that the BRC-MHAR models have the better forecast precision than the competing models for the short-term horizon. The results of economic evaluation suggest that the BRC-MHAR models are superior to the competing models in terms of the average return, the Shape ratio and the economic value.

This study analyzes volatility spillovers between European equity and foreign exchange markets over 2003–2019 by exploring causal linkages in realized volatility across the frequency domain. Daily volatility spillovers are bidirectional and asymmetric across the frequency domain in most cases. Spillovers from equity to foreign exchange markets are significant at high, mid-range, and low frequencies, whereas typically at lower frequencies in the opposite direction. Sub-sample estimations identify similar patterns of asymmetric frequency significance; however, volatility spillovers are primarily unidirectional prior to the Global Financial Crisis. Focusing on slower moving volatility, weekly analysis suggests weaker equity market driven spillovers.

The linkage among the realized volatilities of component stocks is important when modeling and forecasting the relevant index volatility. In this article, the linkage is measured via an extended Common Correlated Effects (CCEs) approach under a panel heterogeneous autoregression model where unobserved common factors in errors are assumed. Consistency of the CCE estimator is obtained. The common factors are extracted using the principal component analysis. Empirical studies show that realized volatility models exploiting the linkage effects lead to significantly better out-of-sample forecast performance, for example, an up to 32% increase in the pseudo R2. We also conduct various forecasting exercises on the linkage variables that compare conventional regression methods with popular machine learning techniques.

This paper studies a large number of bitcoin (BTC) options traded on the options exchange Deribit. We use the trades to calculate implied volatility (IV) and analyze if volatility forecasts can be improved using such information. IV is less accurate than AutoRegressive–Moving‐Average or Heterogeneous Auto‐Regressive model forecasts in predicting short‐term BTC volatility (1 day ahead), but superior in predicting long‐term volatility (7, 10, 15 days ahead). Furthermore, a combination of IV and model‐based forecasts provides the highest accuracy for all forecasting horizons revealing that the BTC options market contains unique information.

Numerous studies have proven that news media sentiment has an impact on stock market volatility, making topics such as how to quantify news media sentiment and use it to predict stock market volatility increasingly relevant. In this paper, a Chinese financial sentiment lexicon was constructed to quantify the emotions in the news media as a sentiment index to be added to the model and establish new prediction models HAR-RV-AI and GRU-AI. To compare the prediction ability of the models, we consider the loss function and model confidence set (MCS) test as the evaluation criterion and employ the rolling window strategy for out-of-sample forecasting. The prediction results of the GRU model are found to be better than the HAR-RV model, and the prediction effect of the model improved after the addition of the news media sentiment index.

We propose new asymmetric multivariate volatility models. The models exploit estimates of variances and covariances based on the signs of high-frequency returns, measures known as realized semivariances, semicovariances, and semicorrelations, to allow for more nuanced responses to positive and negative return shocks than threshold “leverage effect” terms traditionally used in the literature. Our empirical implementations of the new models, including extensions of widely-used bivariate GARCH specifications for a number of individual stocks and the aggregate market portfolio as well as larger dimensional dynamic conditional correlation type formulations for a cross-section of individual stocks, provide clear evidence of improved model fit and reveal new and interesting asymmetric joint dynamic dependencies.

This study investigates the impact of the local political uncertainty (LPU) on one-step-ahead volatility in the Chinese stock market using high-frequency data. The empirical findings indicate that ...

PurposeThe purpose of the study is to examine the dynamics in the troika of asset pricing, volatility, and the business cycle in the US and Japan.Design/methodology/approachThe study uses a six-factor asset pricing model to derive the realized volatility measure for the GARCH-type models.FindingsThe comprehensive empirical investigation led to the following conclusion. First, the results infer that the market portfolio and human capital are the primary discounting factors in asset return predictability during various phases of the subprime crisis phenomenon for the US and Japan. Second, the empirical estimates neither show any significant impact of past conditional volatility on the current conditional volatility nor any significant effect of subprime crisis episodes on the current conditional volatility in the US and Japan. Third, there is no asymmetric volatility effect during the subprime crisis phenomenon in the US and Japan except the asymmetric volatility effect during the post-subprime crisis period in the US and full period in Japan. Fourth, the volatility persistence is relatively higher during the subprime crisis period in the US, whereas during the subprime crisis transition period in Japan than the rest of the phases of the subprime crisis phenomenon.Originality/valueThe study argues that the empirical investigations that employed the autoregressive method to derive the realized volatility measure for the parameter estimation of GARCH-type models may result in incurring spurious estimates. Further, the empirical results of the study show that using the six-factor asset pricing model in an intertemporal framework to derive the realized volatility measure yields better estimation results while estimating the parameters of GARCH-type models.

Based on methods developed by Bollerslev et al. (2016), we explicitly accounted for the heteroskedasticity in the measurement errors and for the high volatility of Chinese stock prices; we proposed a new model, the LogHARQ model, as a way to appropriately forecast the realized volatility of the Chinese stock market. Out-of-sample findings suggest that the LogHARQ model performs better than existing logarithmic and linear forecast models, particularly when the realized quarticity is large. The better performance is also confirmed by the utility based economic value test through volatility timing.

By introducing a genetic algorithm learning with a classifier system, we construct an AI model for oil volatility forecasting on the basis of Internal Information and External Information. The model provides decision support for mark-to-market portfolio and risk management by forecasting whether 1-day-ahead volatility is above a given threshold. Moreover, we explore the dynamic influencing mechanism of different types of information through information usage frequency in the learning process. In particular, we find that the jump component of oil realized volatility is efficient only in bull market, and currency information contributes most rather than oil information in bear market. Therefore, this article provides an AI method to forecast oil volatility as well as to improve the information structure of forecasting models.

In this paper, we investigate whether the model-free implied volatility index iVX officially launched by the Shanghai Stock Exchange has incremental explanatory power for future volatility in the S...

This article introduces a volatility model with a component structure allowing for a realized measure based on high-frequency data (e.g., realized variance) to drive the short-run volatility dynamics. In a joint model of the daily return and the realized measure, the conditional variance of the daily return has a multiplicative component structure: the first component traces long-run (secular) volatility trends, while the second component captures short-run (transitory) movements in volatility. Despite being a fixed-parameter model, its component structure implies time-varying parameters, which are “data-driven” to capture changing volatility regimes. We discuss the model dynamics and estimation by maximum likelihood. The empirical analysis reveals statistically significant out-of-sample gains compared to benchmark models, particularly for short forecast horizons and during the financial crisis.

Forecasting the covolatility of asset return series is becoming the subject of extensive research among academics, practitioners, and portfolio managers. This paper estimates a variety of multivariate GARCH models using weekly closing price (in USD/barrel) of Brent crude oil and weekly closing prices (in USD/pound) of Coffee Arabica and compares the forecasting performance of these models based on high-frequency intraday data which allows for a more precise realized volatility measurement. The study used weekly price data to explicitly model covolatility and employed high-frequency intraday data to assess model forecasting performance. The analysis points to the conclusion that the varying conditional correlation (VCC) model with Student’s t distributed innovation terms is the most accurate volatility forecasting model in the context of our empirical setting. We recommend and encourage future researchers studying the forecasting performance of MGARCH models to pay particular attention to the measurement of realized volatility and employ high-frequency data whenever feasible.

In this paper, we develop econometric tools to analyze the integrated volatility of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent estimators of the variance and autocovariances of noise using a variant of realized volatility. Next, we employ these estimators to adapt the pre-averaging method and derive a consistent estimator of the integrated volatility, which converges stably to a mixed Gaussian distribution at the optimal rate $n^{1/4}$. To refine the finite sample performance, we propose a two-step approach that corrects the finite sample bias, which turns out to be crucial in applications. Our extensive simulation studies demonstrate the excellent performance of our two-step estimators. In an empirical study, we characterize the dependence structures of microstructure noise in several popular sampling schemes and provide intuitive economic interpretations; we also illustrate the importance of accounting for both the serial dependence in noise and the finite sample bias when estimating integrated volatility.