HAR Model Research Articles

Forecasting Realised Volatility: Does the LASSO approach outperform HAR?

The HAR model dominates current volatility forecasting. This model implies a restricted lag approach, with three parameters accounting for an AR(22) structure. This paper uses the Lasso method, which selects a parsimonious lag structure, while allowing both a flexible lag structure and lags greater than 22. In-sample results suggest that while significance is largely found among the first 22 lags, consistent with the HAR model, there is evidence that longer lags contain information, as Lasso models providing an improved fit. Out-of-sample forecasts for daily, weekly and monthly volatility, evaluated using MSE, QLIKE, MCS and VaR measures suggest that the ordered Lasso model provides the preferred forecasts using an AR(100) at the daily level and an AR(22) for the weekly and monthly horizons. The results support the view that a more flexible lag structure is preferred over the HAR approach.

A generalized simplified modeling method for electromagnetic coupling effects of uncertainty strapping cable harness

<sec>The cable harness provides a main gateway for electromagnetic interference(EMI) in electromechanical system. The unreasonable electromagnetic compatibility (EMC) design of cable harness will produce EMI to other on-board electronic equipment, bringing great safety risks to the system. Theoretical research and engineering practice indicate that most of the electromechanical systems cannot satisfy EMC standards, which can be attributed to the EMI generated by cables. As for the eletromagnetic(EM) illumination analysis, reliably and efficiently generating a full numerical model of cable harness is becoming more prominent for the EMC designers. Therefore, it is necessary to develop a more effective method to solve the modeling problem of cable harness. </sec><sec>In the practical application, the cable harness has the characteristics of spatial layout, and its characteristics such as “large number of core wires”, “arbitrary curvature of space” and “randomness of wiring” bring challenges to the modeling of EM coupling to cable harness. The numerical simulation of the whole cable harness model requires severe conditions for computational resource and even makes the EM coupling analysis impossible. Thus, considering the uncertainty of wire position, this paper proposes a generalized simplified modeling method for the EM coupling effect of uncertainty strapping cable harness. Firstly, the Gaussian distribution and spline interpolation are used to determine the location of the core conductors in the random bundling. Then, the distribution parameters of the cable harness at different positions are established by using the transposition relationship between the subsegments of the wires. Finally, the effectiveness of the proposed method is verified by numerical examples of the arc-shaped and sine-shaped harness. </sec><sec>In conclusion, this paper proposes a generalized simplification technique to model the EM illumination on cable harness with uncertainty wiring factors. By grouping the conductors together, the required computation time is markedly reduced and the complexity of modeling the completely cable harness is significantly simplified within a good accuracy. The proposed method provides a way of solving the modeling problem caused by “uncertainty strapping” of the complex wiring harnesses in electromechanical systems.</sec>

An application of Lasso regression in Factor Augmented HAR models

An application of Lasso regression in Factor Augmented HAR models

Volatility Forecasting of China Silver Futures: the Contributions of Chinese Investor Sentiment and CBOE Gold and Silver ETF Volatility Indices

This paper is to detect the role of CBOE gold ETF volatility index (GVZ), CBOE silver ETF volatility index (VXSLV), and constructed Chinese investor sentiment (CnSENT) on the volatility forecasting of China silver futures over daily, weekly and monthly horizons. Different types of HAR models and ridge regression models are utilized to do the analysis, and the out-of-sample R-square statistics and different rolling window sizes are used to ensure the robustness of the conclusion. The empirical results suggest that GVZ and VXSLV have the explanatory power on the China silver futures. Particularly, VXSLV has a better performance than GVZ. However, the predictive power of CnSENT is doubtful as some results indicate that it cannot improve the prediction accuracy. Additionally, the ridge regression method does not achieve a better result than all types of HAR models.

A Note on the Asymptotic Normality Theory of the Least Squares Estimates in Multivariate HAR-RV Models

In this work, multivariate heterogeneous autoregressive-realized volatility (HAR-RV) models are discussed with their least squares estimations. We consider multivariate HAR models of order p with q multiple assets to explore the relationships between two or more assets’ volatility. The strictly stationary solution of the HAR(p,q) model is investigated as well as the asymptotic normality theories of the least squares estimates are established in the cases of i.i.d. and correlated errors. In addition, an exponentially weighted multivariate HAR model with a common decay rate on the coefficients is discussed together with the common rate estimation. A Monte Carlo simulation is conducted to validate the estimations: sample mean and standard error of the estimates as well as empirical coverage and average length of confidence intervals are calculated. Lastly, real data of volatility of Gold spot price and S&P index are applied to the model and it is shown that the bivariate HAR model fitted by selected optimal lags and estimated coefficients is well matched with the volatility of the financial data.

Does VPIN provide predictive information for realized volatility forecasting: evidence from Chinese stock index futures market

PurposeUsing intraday data, the authors explore the forecast ability of one high frequency order flow imbalance measure (OI) based on the volume-synchronized probability of informed trading metric (VPIN) for predicting the realized volatility of the index futures on the China Securities Index 300 (CSI 300).Design/methodology/approachThe authors employ the heterogeneous autoregressive model for realized volatility (HAR-RV) and compare the forecast ability of models with and without the predictive variable, OI.FindingsThe empirical results demonstrate that the augmented HAR model incorporating OI (HARX-RV) can generate more precise forecasts, which implies that the order imbalance measure contains substantial information for describing the volatility dynamics.Originality/valueThe study sheds light on the relation between high frequency trading behavior and volatility forecasting in China's index futures market and reveals the underlying market mechanisms of liquidity-induced volatility.

Forecasting Realized Volatility of Crude Oil Futures Prices based on Variable Selection Approaches

We augment the HAR model with additional information channels to forecast realized volatility of WTI futures prices. These channels include stock markets, sentiment indices, commodity and FX markets, and text-based Google indices. We then apply four differing machine learning techniques to identify the most suitable endo- and exogenous factors which improve baseline model forecasts. We show that machine learning generated forecasts provide better forecasting quality and that portfolios which are constructed with these forecasts outperform their competing models. We find LASSO and SSVS to provide outperforming forecasts and portfolio weights. Analyzing the selection process, we show that variable choices vary across forecasting horizon. Variable selection produces clusters and provides evidence that there are structural changes with regard to the significance of information channels.

The Contribution of Jump Activity and Sign to Forecasting Stock Price Volatility

This paper proposes a novel approach to decompose realized jump measures by type of activity (finite/infinite) and by sign. We also provide noise-robust versions of the ABD jump test (Andersen et al. 2007) and realized semivariance measures for use at high frequency sampling intervals. The volatility forecasting exercise involves the use of different types of jumps, forecast horizons, sampling frequencies, calendar and transaction time-based sampling schemes, as well as standard and noise-robust volatility measures. We find that infinite (finite) jumps improve the forecasts at shorter (longer) horizons; but the contribution of signed jumps is limited. Noise-robust estimators, that identify jumps in the presence of microstructure noise, deliver substantial forecast improvements at higher sampling frequencies. However, standard volatility measures at the 300-second frequency generate the smallest MSPEs. Since no single model dominates across sampling frequency and forecast horizon, we show that model averaged volatility forecasts - using time-varying weights and models from the model confidence set - generally outperform forecasts from both the benchmark and single best extended HAR model.

Machine Learning for Realised Volatility Forecasting

This paper compares machine learning and HAR models for forecasting realised volatility of 23 NASDAQ stocks using 146 variables extracted from limit order book (LOBSTER) and stock-specific news (Dow Jones Newswires) from 27 July 2007 to 18 November 2016. We find simpler ML to outperform HARs on normal volatility days. With SHAP, an Explainable AI technique, we find simple mid prices at all limit order book levels and mean bid/ask prices drive RV forecasts for many stocks. An ML model with a larger number of units and complex idiosyncratic LOB variables are needed for forecasting volatility jumps.

The role of oil futures intraday information on predicting US stock market volatility

This study investigates the role of oil futures price information on forecasting the US stock market volatility using the HAR framework. In-sample results indicate that oil futures intraday information is helpful to increase the predictability. Moreover, compared to the benchmark model, the proposed models improve their predictive ability with the help of oil futures realized volatility. In particular, the multivariate HAR model outperforms the univariate model. Accordingly, considering the contemporaneous connection is useful to predict the US stock market volatility. Furthermore, these findings are consistent across a variety of robust checks.

A Dynamic Model for Simulating Elephant-Lifting by Using a Tilting Frame

A rigid multi-body dynamic model of an elephant was developed for motion analysis during tilt-lifting. The elephant lifting to standing position is required by veterinarians to perform surgery and bedsores treatment. The elephant mechanism dynamic model (EMDM) was developed by simplifying the skeleton to simple straight linkages connected by joints. The model consisted of 10 bones and 9 joints. A mechanical harness model (MHM) was developed. Two harnesses were attached to the tilt-frame mechanism model (FMM) and the EMDM; this assembly became the elephant dynamic during tilt-lifting model (EDTM). The developed EDTM permitted us to observe the displacement, velocity, and acceleration responses at any location on the elephant. The model allowed the virtual study of the motion, and avoided the real elephant testing; thus, the cost, time, and resources were reduced and no conflict with the animal experimental ethics. The simulation was found to be a valuable tool for engineers to design a suitable elephant bed. It permitted us to observe the operation, safety, and precaution of the equipment.

Volatility forecasts, proxies and loss functions

Abstract The main problem in volatility forecasting is that the variable of interest is unobservable, which complicates not only the construction of forecasts but also their comparison. This article challenges the common practice of using only proxy-robust loss functions, which have the nice property that they lead to the same ranking of forecasts regardless whether the unobservable true volatility is used or some unbiased proxy. It is shown that two proxy-robust loss functions need not necessarily produce similar rankings but may even produce completely contradictory rankings. Two likelihood-based loss functions are proposed instead, which are not exactly proxy-robust but are still robust in the classical sense. The first is based on a t-distribution and is meant for daily data. The second is based on an F-distribution and is meant for high-frequency data. In the latter case, the squared error loss function may also be used when a logarithmic transformation is applied to the realized variances in order to achieve approximate normality. An alternative transformation is proposed which allows the adaptation to the degree of non-normality. The forecasting procedures that are compared by the different loss functions include GARCH, HAR, HARQ, and MIDAS models as well as nonparametric techniques. Finally, the economic relevance of choosing the right forecast is illustrated with the problem of establishing the intertemporal risk–return tradeoff. All theoretical arguments are backed up with empirical evidence obtained from daily data as well as from high-frequency data.

Big Data Approach to Realised Volatility Forecasting Using HAR Model Augmented With Limit Order Book and News

The study determines if information extracted from a big data set that includes limit order book (LOB) and Dow Jones corporate news can help to improve realised volatility forecasting for 23 NASDAQ tickers over the sample from 27 July 2007 to 18 November 2016. The out-of-sample forecasting results indicate that the CHAR model outperformed all other models in the HAR-family of models, and there is strong evidence that news and LOB data provide statistically significant improvement in RV forecasts. Specifically, the slope of the bid-side of LOB has better predictive power than the slope from the ask-side. For normal volatility day, the ‘negative’ sentiment derived from the news has a clear impact, while ‘news count’, and to a lesser extent, ‘weak modal’, and ‘uncertainty’ can help to forecast volatility jumps. The depth of the LOB also helps to forecast volatility jumps. Indeed, the findings also suggest normal volatility and volatility jumps should be separately analysed as variables that improve the forecasting performance of normal days causes a degradation in the forecasting performance of volatility jumps and vice versa. On the other hand, increasing the estimation sample size causes statistically significant degradation in the forecasting performance of volatility on normal days, especially if it includes extreme volatility period such as the 2008 financial crisis, but a longer sample improves the forecast of volatility jumps.

Predicting the volatility of crude oil futures: The roles of leverage effects and structural changes

AbstractThis paper investigates whether leverage effects and structural changes have positive effects on the volatility prediction of crude oil futures. On the basis of existing HAR models, this paper proposes three classes of new HAR models by considering leverage effects, structural changes, or both. The in‐sample and out‐of‐sample results show that leverage effects and structural changes contain significant information for predicting oil volatility. In most cases, structural changes have more in‐sample and out‐of‐sample incremental information than leverage effect, whereas leverage effects have more out‐of‐sample information for predicting 1‐day volatility. In addition, HAR models with leverage effects and structural changes have better in‐sample and out‐of‐sample performances than the corresponding other three classes of HAR models. The above results mean that leverage effects and structural changes should be considered while modelling and forecasting oil volatility.

Volatility forecasting revisited using Markov‐switching with time‐varying probability transition

AbstractThis study proposes a novel model, Markov‐switching Heterogeneous Autoregressive (MS‐HAR) model with jump‐driven time‐varying transition probabilities (TVTP), to forecast the future volatility in Chinese stock market. The in‐sample results show that MS‐HAR models are more powerful than HAR‐RV‐type models; furthermore, the high‐volatility regime is short‐lived. Moreover, the out‐of‐sample results indicate that the MS‐HAR with TVTP model can achieve a superior forecasting performance and increase the economic value than the competing models including the simple HAR model and the MS‐HAR with fixed transition probabilities (FTP) model. The results are robust to several robustness checks including alternative forecast window, alternative evaluation method, alternative predictive model, sub‐sample analysis and alternative representative index.

A moving average heterogeneous autoregressive model for forecasting the realized volatility of the US stock market: Evidence from over a century of data

AbstractThis 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, Journal of Econometrics, 2007, 138, 291–311 forecast evaluation approach is employed to evaluate the forecast performance of the proposed predictive model vis‐à‐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 modelling 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.

A Simple Model Correction for Modelling and Forecasting (Un)Reliable Realized Volatility

We propose a dilution bias correction approach to deal with the errors-in-variables problem observed in realized volatility (RV) measures. The absolute difference between daily and monthly RV is shown to be proportional to the relative magnitude of the measurement error. Therefore, in implementing the latter metric, and in allowing the daily auto-regressive parameter to vary as a function of the error term, the result is more responsive forecasts with greater persistence (faster mean-reversion) when the measurement error is low (high). Empirical results indicate that our models outperform some of the most popular HAR and GARCH models across various forecasting horizons.

A Novel Multichannel Dilated Convolution Neural Network for Human Activity Recognition

A novel multichannel dilated convolution neural network for improving the accuracy of human activity recognition is proposed. The proposed model utilizes the multichannel convolution structure with multiple kernels of various sizes to extract multiscale features of high-dimensional data of human activity during convolution operation and not to consider the use of the pooling layers that are used in the traditional convolution with dilated convolution. Its advantage is that the dilated convolution can first capture intrinsical sequence information by expanding the field of convolution kernel without increasing the parameter amount of the model. And then, the multichannel structure can be employed to extract multiscale gait features by forming multiple convolution paths. The open human activity recognition dataset is used to evaluate the effectiveness of our proposed model. The experimental results showed that our model achieves an accuracy of 95.49%, with the time to identify a single sample being approximately 0.34 ms on a low-end machine. These results demonstrate that our model is an efficient real-time HAR model, which can gain the representative features from sensor signals at low computation and is hopeful for the effective tool in practical applications.

Forecasting Stock Market Realized Volatility using Decomposition

Empirical studies concerned with realized volatility reveal the presence of heterogeneous behavior within the stock market. The sum of this heterogeneous behavior takes a persistent form, which may be modeled and forecasted according to different time horizons by the class of HAR models. In this paper, we investigate the HAR-RV and HAR-RV-CJ models for high-frequency data based on five realized volatility indices. The aim here is to demonstrate that the predictability of realized volatility can be improved by decomposing realized variance into its continuous and jump components. What is more, the results show that this decomposition of the realized variance into its components does indeed enhance the modeling and forecasting of the indices’ realized volatility.

Realized volatility forecast with the Bayesian random compressed multivariate HAR model

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.