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GARCH-type models have been widely used for forecasting crude oil price volatility, but often ignore the structural changes of time series, which may lead to spurious volatility persistence. Therefore, this paper focuses on the smooth and sharp structural changes in crude oil price volatility, i.e., smooth shift and regime switching, respectively, and investigates which structural change based GARCH models have better performance for forecasting crude oil price volatility. The empirical results indicate that, first, the flexible Fourier form (FFF) GARCH-type models considering smooth shift can accurately model structural changes and yield superior fitting and forecasting performance to traditional GARCH-type models. Second, the Markov regime switching (MRS) GARCH model incorporating regime switching exhibits superior fitting performance compared to the single-regime GARCH-type models, but it does not necessarily beat the counterparts for forecasting. Finally, the FFF-GARCH-type models outperform MRS-GARCH for forecasting crude oil price volatility and portfolio performance.

Regularity conditions are given for the consistency of the Poisson quasi-maximum likelihood estimator of the conditional mean parameter of a count time series model. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it lies at the boundary. Tests for the significance of the parameters and for constant conditional mean are deduced. Applications to specific integer-valued autoregressive (INAR) and integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models are considered. Numerical illustrations, Monte Carlo simulations and real data series are provided.

Over the past years, cryptocurrencies have drawn substantial attention from the media while attracting many investors. Since then, cryptocurrency prices have experienced high fluctuations. In this paper, we forecast the high-frequency 1 min volatility of four widely traded cryptocurrencies, i.e., Bitcoin, Ethereum, Litecoin, and Ripple, by modeling volatility to select the best model. We propose various generalized autoregressive conditional heteroscedasticity (GARCH) family models, including an sGARCH(1,1), GJR-GARCH(1,1), TGARCH(1,1), EGARCH(1,1), which we compare to a multivariate DCC-GARCH(1,1) model to forecast the intraday price volatility. We evaluate the results under the MSE and MAE loss functions. Statistical analyses demonstrate that the univariate GJR-GARCH model (1,1) shows a superior predictive accuracy at all horizons, followed closely by the TGARCH(1,1), which are the best models for modeling the volatility process on out-of-sample data and have more accurately indicated the asymmetric incidence of shocks in the cryptocurrency market. The study determines evidence of bidirectional shock transmission effects between the cryptocurrency pairs. Hence, the multivariate DCC-GARCH model can identify the cryptocurrency market’s cross-market volatility shocks and volatility transmissions. In addition, we introduce a comparison of the models using the improvement rate (IR) metric for comparing models. As a result, we compare the different forecasting models to the chosen benchmarking model to confirm the improvement trends for the model’s predictions.

The multivariate GARCH (MGARCH) model is popular for analyzing financial time series data. However, statistical inferences for MGARCH models are quite challenging, owing to the high dimension issue. To overcome this difficulty, we propose a network GARCH model that uses information derived from an appropriately defined network structure. This decreases the number of unknown parameters and reduces the computational complexity substantially. We also rigorously establish the strict and weak stationarity of the network GARCH model. In order to estimate the model, a quasi-maximum likelihood estimator (QMLE) is developed, and its asymptotic properties are investigated. Simulation studies are carried out to assess the performance of the QMLE in finite samples, and empirical examples are analyzed to illustrate the usefulness of network GARCH models.

ARMA-GARCH models are widely used to model the conditional mean and conditional variance dynamics of returns on risky assets. Empirical results suggest heavy-tailed innovations with positive extreme value index for these models. Hence, one may use extreme value theory to estimate extreme quantiles of residuals. Using weak convergence of the weighted sequential tail empirical process of the residuals, we derive the limiting distribution of extreme conditional Value-at-Risk (CVaR) and conditional expected shortfall (CES) estimates for a wide range of extreme value index estimators. To construct confidence intervals, we propose to use self-normalization. This leads to improved coverage vis-à-vis the normal approximation, while delivering slightly wider confidence intervals. A data-driven choice of the number of upper order statistics in the estimation is suggested and shown to work well in simulations. An application to stock index returns documents the improvements of CVaR and CES forecasts.

Our paper presents the first optimal analytical solution for an investor maximizing both consumption and terminal wealth within expected utility theory in the realm of GARCH models. Working in a general family of affine GARCH models, we derive an affine GARCH optimal wealth process, providing analytical representations for optimal allocation, consumption and value functions. In particular, the optimal consumption ratio avoids the undesirable scenario of investors consuming all wealth prior to maturity. Our numerical study highlights the importance of formally accounting for consumption as it disrupts the level of optimal risky allocations. It also shows a larger impact of stochastic conditional variance (heteroscedasticity) on risky allocations in comparison to the impact of non-Gaussianity. We find, in a numerical study based on S&P 500 index data over a 5-years horizon, that an investor following a Gaussian GARCH strategy can achieve 10% more total consumption and at the same time 8% more terminal wealth than another investor following a constant variance (homoscedastic) strategy.

Using standard GARCH-type, Markov Switching GARCH-type, and autoregressive distributed lag (ARDL) models, this study employs quarterly dataset from 1995 to 2023 to investigate the volatility shifts of macroeconomic variables, incorporating crude oil prices in Spain. The empirical results of the study clearly confirm that MSGARCH-type models extend beyond the capabilities of standard GARCH-type models, providing enhanced flexibility in modeling the volatility process. The estimated MSGARCH-type models effectively identify breakpoints in all macroeconomic variables volatilities, specifically during significant events such as the global financial crisis (GFC) in 2008, the European debt crisis in 2011, and the Covid-19 pandemic of 2020, Russia-Ukraine War in 2022. In addition, our results indicate that high crude oil price shocks during the global events are important drivers of uncertainty. There is strong evidence that the effects of crude oil price shocks on macroeconomic uncertainty are highly dependent on the prevailing regime. These impacts vary based on investor sentiment and the level of perceived volatility within financial markets. The responses of economic uncertainty to crude oil shocks appear to experience a dramatic change in the major global events, such as the post-global financial crisis (GFC), COVID-19 pandemic, and the Russia-Ukrainian war.

The presence of volatility in residential property market prices helps investors generate substantial profit while also causing fear among investors since high volatility implies a high return with a high risk. In a financial time series, volatility refers to the degree to which the residential property market price increases or decreases during a particular period. The present study aims to forecast the volatility returns of real residential property prices (RRPP) in Malaysia using three different families of generalized autoregressive conditional heteroskedasticity (GARCH) models. The study compared the standard GARCH, EGARCH, and GJR-GARCH models to determine which model offers a better volatility forecasting ability. The results revealed that the GJR-GARCH (1,1) model is the most suitable to forecast the volatility of the Malaysian RRPP index based on the goodness-of-fit metric. Finally, the volatility forecast using the rolling window shows that the volatility of the quarterly index decreased in the third quarter (Q3) of 2021 and stabilized at the beginning of the first quarter (Q1) of 2023. Therefore, the best time to start investing in the purchase of real residential property in Malaysia would be the first quarter of 2023. The findings of this study can help Malaysian policymakers, developers, and investors understand the high and low volatility periods in the prices of residential properties to make better investment decisions.

One of the perennial questions in the scientific study of war is how war affects the economy. The authors examine the influence that the political developments within three war regions had on global financial markets (CAC, Dow Jones, FTSE) from 1990 to 2000. They embed a rational expectation framework within commercial liberalism, a theoretical strand that tries to assess the interrelationship between war and economic exchanges. Time-series analyses account for the effects that the conflict between Israel and the Palestinians, the first confrontation of a U.S.-led alliance against Iraq, and the wars fought in Ex-Yugoslavia exerted. Using daily stock market data, the authors show that the conflicts affected the interactions at the core financial markets in the Western world negatively, if they had any systematic influence at all. They argue that these results lend some support to the rational expectations version of commercial liberalism.

PurposeThe purpose of the research is to assess the risk of the financial market in the digital economy through the quantitative analysis model in the big data era. It is a big challenge for the government to carry out financial market risk management in the big data era.Design/methodology/approachIn this study, a generalized autoregressive conditional heteroskedasticity-vector autoregression (GARCH-VaR) model is constructed to analyze the big data financial market in the digital economy. Additionally, the correlation test and stationarity test are carried out to construct the best fit model and get the corresponding VaR value.FindingsOwing to the conditional heteroscedasticity, the index return series shows the leptokurtic and fat tail phenomenon. According to the AIC (Akaike information criterion), the fitting degree of the GARCH model is measured. The AIC value difference of the models under the three distributions is not obvious, and the differences between them can be ignored.Originality/valueUsing the GARCH-VaR model can better measure and predict the risk of the big data finance market and provide a reliable and quantitative basis for the current technology-driven regulation in the digital economy.