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This is my undergraduate thesis, which mainly refers to Zhi Y. P. and L. Liu. (2018). although it has successfully passed the graduation defense, there are still many problems in this thesis, so it is not recommended as a reference for academic purposes. Abstract: According to the Heterogeneous Market Hypothesis, a financial market is composed by participants having different trading frequencies. The trading behaviors of investors with various time horizons cause different types of volatility components. Therefore, the various types of investors are concerned about whether the different short-term or long-term component of stock return volatility is more strongly related to past negative return, also named as leverage effect. Therefore, it is meaningful to consider the short-term and long-term leverage effects in volatility prediction. This paper extended the GARCH-MIDAS model proposed by Engle et al. (2013). The short-term and long-term leverage effects in the Shanghai 180 Index and Shenzhen 100 Index series are detected by adding corresponding asymmetric terms in the model. The effect of short-term leverage effect is that negative returns in the past can cause greater short-term fluctuations than positive returns in the future. The effect of long-term leverage effect is that positive returns in the past will increase long-term fluctuations in the future, while negative returns will reduce long-term fluctuations in the future. This paper also finds that the addition of leverage effect can improve the accuracy of the prediction of volatility, which is mainly attributed to the short-term leverage effect. In the estimation method, this paper adopts the rolling window technology. By fixing the monthly window and moving by day, the model can contain more information about long-term fluctuations. This improves the persuasiveness of the model. In the evaluation method, six popular loss functions and success indicators are used to avoid the evaluation errors caused by a single standard. Keywords: volatility prediction; short-term leverage effects; long-term leverage effects; GARCH-MIDAS, As my first academic attempt, there are many problems in this paper. I just want to make a memorial here., {"references":["Zhi Y. P. and L. Liu. Forecasting stock return volatility: A comparison between the roles of short-term and long-term leverage effects [J]. Physica A: Statistical Mechanics and its Applications, 2018, 492: 168-180.","A.J. Patton, Volatility forecast comparison using imperfect volatility proxies, J. Econometrics 160 (2011) 246–256.","F.X. Diebold, R.S. Mariano, Comparing predictive accuracy, J. Bus. Econ. Stat. 13 (1995) 253–263.","Ding, Z., Granger, C., 1996. Modeling Volatility Persistence of Speculative Returns: A New Approach. Journal of Econometrics, 73, 185-215.","Engle, R. F., Lee, G., 1999. 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We consider the problem of testing for an omitted multiplicative long-term component in GARCH-type models. Under the alternative there is a two-component model with a short-term GARCH component that uctuates around a smoothly time-varying long-term component which is driven by the dynamics of an explanatory variable. We suggest a Lagrange Multiplier statistic for testing the null hypothesis that the variable has no explanatory power. We derive the asymptotic theory for our test statistic and investigate its finite sample properties by Monte-Carlo simulation. Our test also covers the mixed-frequency case in which the returns are observed at a higher frequency than the explanatory variable. The usefulness of our procedure is illustrated by empirical applications to S&P 500 return data.

Following generalized variance decomposition, we identify the transmission structure of financial shock among ten sectors in China. Then, we examine whether economic policy uncertainty (EPU) affects it through GARCH-MIDAS regression. We find that consumer discretionary, industrials, and materials sectors are systemically important industries during the sample period. Further research of dynamic analysis shows that each sector acts in a time-varying role in this structure. The results of the GARCH-MIDAS regression indicate that none of the selected EPU indexes has a significant long-term impact on the total volatility spillover of the inter-sector stock market in China. However, the EPUs do affect some sectors’ spillover indexes in the long run, and they are significantly heterogeneous. This paper can provide regulatory suggestions for policymakers and reasonable asset allocation and risk avoidance methods for investors.

Forecasting oil prices is not straightforward, such that it is convenient to build a confidence interval around the forecasted prices. To this end, the principal ingredient for obtaining a reliable crude oil confidence interval is its volatility. Moreover, accurate crude oil volatility estimation has fundamental implications in terms of risk management, asset pricing and portfolio handling. Generally, current studies consider volatility models based on lagged crude oil price realizations and, at most, one additional macroeconomic variable as crude oil determinant. This paper aims to fill this gap, jointly considering not only traditional crude oil driving forces, such as the aggregate demand and oil supply, but also the monetary policy rate. Thus, this work aims to contribute to the debate concerning the potential impact of (lagged) US monetary policy as well as the other crude oil future price (COFP) determinants on daily COFP volatility. By means of the recently proposed generalized autoregressive conditional heteroskedasticity mixed data sampling model, different proxies of the US monetary policy alongside US industrial production (proxy of the US aggregate demand) and oil supply are included in the COFP volatility equation. Strong evidence that an expansionary (restrictive) variation in monetary policy anticipates a positive (negative) variation in COFP volatility is found. We also find that a negative (positive) variation of industrial production increases (decreases) COFP volatility. This means that volatility behaves counter-cyclically, according to the literature. Furthermore, the out-of-sample forecasting procedure shows that including these additional macroeconomic variables generally improves the forecasting performance.

This paper shows the application of MIDAS based models in systemic risk assessment in banking sector. We consider two popular measures of systemic risk i.e. Marginal Expected Shortfall and Delta Conditional Value at Risk. The GARCH-MIDAS model is used in modelling conditional volatilities. The long-run component is modeled using realized volatility. The conditional correlation, second step of modelling, is described with DCC-MIDAS model. This is novel approach in respect to classical TARCH and DCC modelling. Whereas the information contained in macroeconomic variables, if available, can help to predict short and long-term components, this is the promising option in improvement of systemic risk assessment.

We examine the statistical properties of multiplicative GARCH models. First, we show that in multiplicative models, returns have higher kurtosis and squared returns have a more persistent autocorrelation function than in the nested GARCH model. Second, we extend the results of Andersen and Bollerslev (1998) on the upper bound of the R2 in a Mincer-Zarnowitz regression to the case of a multiplicative GARCH model, using squared returns as a proxy for the true but unobservable conditional variance. Our theoretical results imply that multiplicative GARCH models provide an explanation for stylized facts that cannot be captured by classical GARCH modeling.

We use the GARCH-MIDAS model to extract the long- and short-term volatility components of cryptocurrencies. As potential drivers of Bitcoin volatility, we consider measures of volatility and risk in the US stock market as well as a measure of global economic activity. We find that S&P 500 realized volatility has a negative and highly significant effect on long-term Bitcoin volatility. The finding is atypical for volatility co-movements across financial markets. Moreover, we find that the S&P 500 volatility risk premium has a significantly positive effect on long-term Bitcoin volatility. Finally, we find a strong positive association between the Baltic dry index and long-term Bitcoin volatility. This result shows that Bitcoin volatility is closely linked to global economic activity. Overall, our findings can be used to construct improved forecasts of long-term Bitcoin volatility.

We propose a new measure of the expected variance risk premium that is based on a forecast of the conditional variance from a GARCH-MIDAS model. We find that the new measure has strong predictive ability for future U.S. aggregate stock market returns and rationalize this result by showing that the new measure effectively isolates fundamental uncertainty as the factor that drives the variance risk premium.

We propose a new measure of the expected variance risk premium that is based on a forecast of the conditional variance from a GARCH-MIDAS model. We find that the new measure has strong predictive ability for future U.S. aggregate stock market returns and rationalize this result by showing that the new measure effectively isolates fundamental uncertainty as the factor that drives the variance risk premium.

Modeling crude oil volatility is of substantial interest for both energy researchers and policy makers. This paper aims to investigate the impact of the U.S. monetary policy on crude oil future price (COFP) volatility. By means of the recently proposed generalized autoregressive conditional hetroskedasticity mixed data sampling (GARCH-MIDAS) model, a proxy of the U.S. monetary policy is included into the COFP volatility equation, alongside with other macroeconomic determinants. Strong evidence that an expansionary monetary policy is associated with an increase of the COFP volatility is found. In particular, an expansionary (restrictive) variation in monetary policy anticipates a positive (negative) variation in COFP volatility. Furthermore, an out of sample forecasting procedure shows that the estimated GARCH-MIDAS model has a superior predictive ability with respect to that of the GARCH(1,1), when the U.S. monetary policy exhibits severe changes in the run-up period.

This paper investigates the main drivers of the agricultural commodity price volatility using the GARCH-MIDAS model of Engel et al. (2013), a new class of component models that allows for isolating the low-frequency component of volatility and taking into consideration macroeconomic factors via mixed data sampling. We show that modelling the agricultural price volatility as the product of high and low frequency components is more efficient than filtering it through a standard GARCH(1,1) model. After combing wheat, corn and soybean daily prices with monthly market-specific and common macroeconomic drivers over the period 1986-2012, it appears that supply-demand indicators and conventional speculation proxies are crucial in explaining the low-frequency component of volatility while monetary factors and energy markets play significant but less important role. Nevertheless, when we consider only the period following the recent price spikes (2006-2012), the monetary factors –especially interest rate – become essential to describe agricultural price fluctuations, suggesting also that the heterogeneity in the effects of the drivers on different crops is decreasing.

Using a modified DCC-MIDAS specification, we endogenize the long-term correlation between crude oil and stock price returns with respect to the stance of the U.S. macroeconomy. We find that variables which contain information on current and future economic activity are helpful predictors for changes in the oil-stock correlation. For the period 1993-2011 there is strong evidence for a counter cyclical behavior of the long-term correlation. For prolonged periods with strong growth above trend our model predicts a negative long-term correlation, while before and during recessions the sign changes and remains positive throughout the economic recovery. Our results strongly suggest that crude oil prices cannot be viewed as being exogenous with respect to the U.S. macroeconomy and explain the controversial results concerning the oil-stock relationship in previous studies.