Forecasting the oil price realized volatility: A multivariate heterogeneous autoregressive model

International tourism is a major source of export receipts for many countries worldwide. Although it is not yet one of the most important industries in Taiwan (or the Republic of China), an island in East Asia off the coast of mainland China (or the People's Republic of China), the leading tourism source countries for Taiwan are Japan, followed by USA, Republic of Korea, Malaysia, Singapore, UK, Germany and Australia. These countries reflect short, medium and long haul tourist destinations. Although the People's Republic of China and Hong Kong are large sources of tourism to Taiwan, the political situation is such that tourists from these two sources to Taiwan are reported as domestic tourists. Daily data from 1 January 1990 to 30 June 2007 are obtained from the National Immigration Agency of Taiwan. The heterogeneous autoregressive (HAR) model is used to capture long memory properties in the data. In comparison with the HAR(1) model, the estimated asymmetry coefficients for GJR(1,1) are not statistically significant for the HAR(1,7) and HAR(1,7,28) models, so that their respective GARCH(1,1) counterparts are to be preferred. These empirical results show that the conditional volatility estimates are sensitive to the long memory nature of the conditional mean specifications. Although asymmetry is observed for the HAR(1) model, there is no evidence of leverage. The quasi-maximum likelihood estimators (QMLE) for the GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for international tourist arrivals to Taiwan are statistically adequate and have sensible interpretations. However, asymmetry (though not leverage) was found only for the HAR(1) model and not for the HAR(1,7) and HAR(1,7,28) models.

The Properties of Realized Correlation: Evidence from the Greek Equity Market

• HAR models are used to forecast Realized Volatility (RV) for a portfolio of stocks. • Low-, medium-, and high-frequency components of RV are isolated using wavelet decomposition. • Low-frequency volatility forecasts improve utility and reduce portfolio turnover. • Benefits are robust to direct forecasts of portfolio weights and jump robust RV. • Results stress the distinction between statistical and practical performance metrics in volatility forecasting. This study proposes a wavelet-based approach to forecasting Realized Volatility (RV) and evaluates its economic value within a volatility-timing framework. We apply wavelet decomposition to separate short-, medium-, and long-term components and generate forecasts using Heterogeneous Autoregressive (HAR) models. Forecasts based on the low-frequency component consistently lead to better portfolio outcomes, reducing turnover and enhancing investor utility without increasing risk. These results hold even when portfolio weights are forecast directly after being constructed from RV, or when jump-robust volatility estimates are used. The results highlight the importance of aligning forecast evaluation with practical investment objectives. Forecasts delivering the greatest welfare gains may not minimize conventional statistical loss functions.

The role of higher moments in predicting China's oil futures volatility: Evidence from machine learning models

In the international monetary system, gold plays a significant role. Predicting gold prices is a useful and unique skill for anybody. As a result, improving one's ability to anticipate gold futures is critical. The study presented in this paper relates to gold futures predictions, based on heterogeneous autoregressive (HAR) theory, and Heterogeneous Autoregressive model of Realized Volatility (HAR-RV model), coupled with gold's daily trade volume and CBOE Volatility Index (VIX) to create three unique models: Heterogeneous Autoregressive model of Realized Volatility and Trading volume (HAR-RV-T model), Heterogeneous Autoregressive model of Realized Volatility and Volatility Index (HAR- RV-VIX model), and Heterogeneous Autoregressive model of Realized Volatility, Trading Volume, and Volatility Index (HAR-RV-T&VIX model). This paper mainly explores a method to predict the volatility of gold futures. Improve the ability to forecasting the volatility of gold prices is obviously conducive to effectively play the futures, including hedging, risk management, price analysis, and other tasks. The research concludes that adding trading volume and sentiment indicator contributes to a more robust HAR model and performs better on forecasting.

Modeling CAC40 volatility using ultra-high frequency data

Since Bitcoin price is highly volatile, forecasting its volatility is crucial for many applications, such as risk management or hedging. We study which model is the most suitable for forecasting Bitcoin volatility. We consider several GARCH and two heterogeneous autoregressive (HAR) models and compare them. Since we utilize realized variance estimated from high frequency data as a proxy for true volatility, we can draw sharper conclusions than studies which use only daily data. We find that EGARCH and APARCH perform best among the GARCH models. HAR models based on realized variance perform better than GARCH models based on daily data. Superiority of HAR models over GARCH models is strongest for short-term volatility forecasts.

Exploiting the heteroskedasticity in measurement error to improve volatility predictions in oil and biofuel feedstock markets

Networks are ubiquitous throughout biology, spanning the entire range from molecules to food webs and global environmental systems. Yet, despite substantial efforts by the scientific community, the inference of these networks from data still presents a problem that is unsolved in general. One frequent strategy of addressing the structure of networks is the assumption that the interactions among molecular or organismal populations are static and correlative. While often successful, these static methods are no panacea. They usually ignore the asymmetry of relationships between two species and inferences become more challenging if the network nodes represent dynamically changing quantities. Overcoming these challenges, two very different network inference approaches have been proposed in the literature: Lotka-Volterra (LV) models and Multivariate Autoregressive (MAR) models. These models are computational frameworks with different mathematical structures which, nevertheless, have both been proposed for the same purpose of inferring the interactions within coexisting population networks from observed time-series data. Here, we assess these dynamic network inference methods for the first time in a side-by-side comparison, using both synthetically generated and ecological datasets. Multivariate Autoregressive and Lotka-Volterra models are mathematically equivalent at the steady state, but the results of our comparison suggest that Lotka-Volterra models are generally superior in capturing the dynamics of networks with non-linear dynamics, whereas Multivariate Autoregressive models are better suited for analyses of networks of populations with process noise and close-to linear behavior. To the best of our knowledge, this is the first study comparing LV and MAR approaches. Both frameworks are valuable tools that address slightly different aspects of dynamic networks.

We propose moving average threshold heterogeneous autoregressive (MAT‐HAR) models as a novel combination of heterogeneous autoregression (HAR) and threshold autoregression (TAR). The MAT‐HAR has multiple groups of lags of a target series, and a threshold term can appear in each group. The threshold is a moving average of lagged target series, which guarantees time‐varying thresholds and simple estimation via least squares. We show via Monte Carlo simulations that the MAT‐HAR has sharp in‐sample and out‐of‐sample performance. An empirical application on the industrial production of Japan suggests that significant threshold effects exist, and the MAT‐HAR has a higher forecast accuracy than the HAR.

We apply heterogeneous autoregressive (HAR) models—including nine univariate, two multivariate and three combination models—to high-frequency data to predict the one-day forward volatilities of two strategically linked commodities, gold and silver. We provide evidence that it is difficult to beat the benchmark HAR model using univariate models and that, a much better strategy is to average the forecasts from many models. In addition, the forecasts are not improved by using volatilities from strategically linked commodities; thus, no volatility spillovers are detected. Interestingly, when the two strategically linked commodities are modelled together using the generalized HAR model, the forecasts are comparable to those of combination forecast models.

Improving stock market volatility forecasts with complete subset linear and quantile HAR models

We analyze the predictability of daily data on the CBOE VIX and SKEW indices, used to capture the average level of risk-neutral risk and downside risk, respectively, as implied by S&P 500 index options. In particular, we use forecast models from the Heterogeneous Autoregressive (HAR) class to test whether and how lagged values of the VIX and of the SKEW may increase the forecasting power of HAR for the SKEW and the VIX. We find that a simple HAR is very hard to beat in out-of-sample experiments aimed at forecasting the VIX. In the case of the SKEW, the benchmarks (the random walk and an AR(1)) are clearly outperformed by HAR models at all the forecast horizons considered and there is evidence that special definitions of the SKEW index based on put options data only yield superior forecasts at all horizons.

This study explores the connectedness between selected emerging equity markets (BRIC-T) and the Emerging Markets Financial Stress Index (EMFSI). We aim to reveal the extent of spillovers from stock market indices to aggregated financial tension in these countries. Empirical investigations are executed through Quantile Vector Autoregression analysis. Results show that spillovers occur mainly during extreme negative and positive return periods. When we focus on four important phases, namely Global Financial Crisis (GFC), the Euro Area Sovereign Debt Crisis, the COVID-19 pandemic, and the Russia-Ukraine war, three countries come to the fore. While Brazil has had a substantial and persistent impact across the years, during the GFC, two other countries, Russia and Türkiye, seem to induce positive return spillovers toward emerging markets’ stress. This impact becomes bilateral in Russia (both in positive and negative returns) during the pandemic and the Russia-Ukraine war. Thus, we conclude that among the examined market economies, negative or positive return transmissions to emerging market stress are led mainly by Brazil and Russia. The importance of energy sources and political factors can account for this result.

The authors explore the separate momentum effect in the positive and negative return environments at both the time domain and the frequency domain. Using the power spectrums and daily returns of sixteen representative exchange-traded funds (ETFs), the authors attempt to answer whether the momentum strategies have equal endurance gain and loss markets with assets that represent different market capitalizations, value, and industry. The authors’ results provide evidence that the US equity market carries strong negative-return resistance. The probability of realizing positive return is increasingly higher when the market carries longer consecutive negative returns. Small-cap stocks exhibit momentum effect in positive return environment but mean reversion effect in negative returns. For value stocks, the probabilities of continuing positive returns are 16.83% higher; for growth stocks, the probabilities of flipping over from negative returns are 16.4% higher. The power spectrums from the Merlot wavelet transformation suggest that the density of transaction activities is high at the high-frequency level, proving that the momentum strategy is less effective within a month-wide window. TOPICS:Exchange-traded funds and applications, mutual fund performance Key Findings • The average probability of the equity market realizing another positive return after the previous positive return is 51.80%, the probability of the third positive return after two positive days is 50.64%, 47.98% after three days, and 45.98% after four days. • The US equity market carries negative return resistance. The average probabilities of the market realizing positive return after one, two, three, four, and five days of consecutive negative returns are 52.88%, 54.63%, 56.55%, 57.17%, and 60.09% across the 11 sectors. • Small-cap stocks exhibit momentum effect in positive return environment but mean reversion effect in negative returns. The probabilities of continuing positive trend are higher for value stocks; yet the probabilities of stopping negative trend are higher for growth stocks.