Nonlinear Generalized Autoregressive Conditional Heteroscedasticity Research Articles

Comparison of linear and non-linear GARCH models for forecasting volatility of select emerging countries

PurposeSeveral empirical studies have proven that emerging countries are attractive destinations for Foreign Institutional Investors (FIIs) because of high expected returns, weak market efficiency and high growth that make them attractive destination for diversification of funds. But higher expected returns come coupled with high risk arising from political and economic instability. This study aims to compare the linear (symmetric) and non-linear (asymmetric) Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models in forecasting the volatility of top five major emerging countries among E7, that is, China, India, Indonesia, Brazil and Mexico.Design/methodology/approachThe volatility of financial markets of five major emerging countries has been empirically investigated for a period of two decades from January 2000 to December 2019 using univariate volatility models including GARCH 1, 1, Exponential Generalized Autoregressive Conditional Heteroscedasticity (E-GARCH 1, 1) and Threshold Generalized Autoregressive Conditional Heteroscedasticity (T-GARCH-1, 1) models. Further, to examine time-varying volatility, the distinctions of structural break have been captured in view of the global financial crisis of 2008. Thus, the period under the study has been segregated into pre- and post-crisis, that is, January 2001–December 2008 and January 2009–December 2019, respectively.FindingsThe findings indicate that GARCH (1, 1) model is superior to non-linear GARCH models for forecasting volatility because the effect of leverage is insignificant. China has been considered as most volatile, whereas India is volatile but positively skewed and Indonesia is the least volatile country. The results can help investors in better international diversification of their portfolio and identifying best suitable hedging opportunities.Practical implicationsThis study can help investors to construct a more risk-adjusted returns international portfolio. Further, it adds to the scant literature available on the inconclusive debate on the choice of linear versus non-linear models to forecast market volatility.Originality/valueEarlier studies related to univariate volatility models are mostly applications of the models. Only few studies have considered the robustness while applying the models. However, none of the studies to the best of the authors’ searches have considered these models for identifying the diversification opportunity among the emerging countries. Hence, this study is able to derive diversification and hedging opportunities by applying wide ranges of the statistical applications and models, that is, descriptive, correlations and univariate volatility models. It makes the study more rigorous and unique compared to the previous literature.

Modeling streamflow time series using nonlinear SETAR-GARCH models

Although hydrological processes are generally nonlinear, linear time series models are commonly adopted in the field of water sciences. Nonlinear approaches such as threshold time series and conditional heteroscedasticity models are still seldom used. In this study, first, two- and three-regime Self-Exciting Threshold Autoregressive (SETAR) models are used to model the mean behavior of daily streamflows. The residual time series computed from the difference between observations and lag-one time-ahead best-estimates of the fitted models are also obtained. Second, the conditional variance behavior of the residual series obtained from the two- and three-regime SETAR models is modeled using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The GARCH model is hence used to capture the time-varying variance behavior of residuals as a nonlinear phenomenon and thus it removes the existence of autoregressive conditional heteroscedasticity so-called ARCH effect. Finally, the performance of SETAR models and their combination with the GARCH model are evaluated. Six deseasonalized daily streamflow series from upstream watershed rivers of Zarrineh Rood dam, in the southern part of Lake Urmia in Iran, are used to illustrate and test the procedure. The McLeod-Li test, a formal test for demonstrating the ARCH effect, indicates that the ARCH effect exists in all residual series, which means that the residuals of streamflow time series are nonstationary in terms of the variance. Results indicate that the hybrid SETAR-GARCH models performed better than the models without GARCH component. Results demonstrate also that the use of nonlinear SETAR and GARCH improves streamflow modeling efficiency by capturing the heteroscedasticity in the residuals of nonlinear threshold time series.

Timing of resources exploration in the behavior of firm—Empirical simulation by intelligent hybrid model

We have insight into the importance of resource exploration derived from the quest for sustaining competitive advantage as well as the growth of the firm, which are well-explicated in the resources point of view. However, we really do not know when the firm will seriously commit to this kind of activities. Therefore, this study proposes an intelligent hybrid model using quantum minimization (QM) to tune a composite model adaptive support vector regression (ASVR) and nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) such that it constitutes the relationship among five indicators, the growth rate of long-term investment, the firm size, the return on total asset, the return on common equity, and the return on sales. In particular, this proposed approach outperforms several typical methods such as auto-regressive moving-average regression (ARMAX), back-propagation neural network (BPNN), or adaptive neuron-fuzzy inference system (ANFIS) for this timing problem in term of comparing their achievement and the goodness of fit. Consequently, the preceding methods involved in this problem truly explain the timing of resources exploration in the behavior of firm. Meanwhile, the performance summary among methods is compared quantitatively.

Estimation and forecasting of machine health condition using ARMA/GARCH model

This paper proposes the hybrid model of autoregressive moving average (ARMA) and generalized autoregressive conditional heteroscedasticity (GARCH) to estimate and forecast the machine state based on vibration signal. The main idea in this study is to employ the linear ARMA model and the nonlinear GARCH model to explain the wear and fault condition of machine, respectively. The successful outcomes of the ARMA/GARCH prediction model can give obvious explanation for future states of machine, which enhance the worth of machine condition monitoring as well as condition-based maintenance in practical applications. The advance of the proposed model is verified in empirical results as applying for a real system of a methane compressor in a petrochemical plant.

Novel hybrid approach to data-packet-flow prediction for improving network traffic analysis

Forecast of the flow of data packets between client and server for a network traffic analysis is viewed as a part of web analytics. Thousands of web-smart businesses depend on web analytics to improve website conversions, reduce marketing costs, facilitate website optimization, speed-up website monitoring and provide a higher level of service to their customers and partners. This paper particularly intends to develop a high accurate prediction as one of core component of network traffic analysis. In this study, a novel hybrid approach, combining adaptive neuro-fuzzy inference system (ANFIS) with nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH), is tuned optimally by quantum minimization (QM) and then applied to forecasting the flow of data packets around website. The composite model (QM-ANFIS/NGARCH) is setup in the forecast point of view to improve the predictive accuracy because it can resolve the problems of the overshoot and volatility clustering simultaneously within time series. As part of real-time intelligence web analytics, the high accurate prediction will aid webmaster to improve the throughput of data-packet-flow up to around 20%, with helping each webmaster to optimize their website, maximize online marketing conversions, and lead campaign tracking.

Quantum-minimized BWGC/NGARCH approach to financial time series forecast

In this study, a novel approach to time series forecast is introduced in order to overcome the crucial problems of the overshoot phenomenon and the effect of volatility clustering at the same time. The prediction using grey model (GM) has encountered the overshoot phenomenon that results in big residual errors. To the contrary a method called cumulated 3-point least square polynomial model (C3LSP) may yield the underestimated output in the prediction. Thus we can utilize the predicted result from C3LSP to compensate the output of grey prediction so as for reducing the overshoot significantly. It is applicable to combine GM and C3LSP linearly and tune this combination optimally by back-propagation neural network (BPNN). This model denotes BPNN-weighted GM–C3LSP (BWGC). However, an effect of volatility clustering suggests a time series where successive disturbance, even if uncorrelated, are yet serially dependent. Consequently, this effect not only decreases the predictive accuracy but also deteriorates the localization for time series. Thus, incorporating a nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) into BWGC is proposed so that NGARCH is used to tackle the problem of volatility clustering effect during the time series forecast. For the purpose of simplicity, both BWGC and NGARCH models are composed linearly and then an algorithm called quantum-based minimization (QM) is particularly employed to regularize this composite model BWGC/NGARCH to best fit time series. As a result, the proposed approach can resolve the overshoot and volatility clustering effects simultaneously and outperforms the alternative models for time series forecasts.

Improving network traffic analysis by foreseeing data-packet-flow with hybrid fuzzy-based model prediction

Forecast of the flow of data packets on a computer network gives valuable information about the change of data-packet-flow to the website at the next upcoming period, which is a way to enhance the capability of network traffic analysis. Thousands of web-smart businesses depend on network traffic analysis to improve network conversions, reduce marketing costs, facilitate network optimization, speed-up network monitoring and provide a higher level of service to their customers and partners. In this study, an intelligent-based hybrid model prediction is introduced for foreseeing data-packet-flow on a network. This is to combine adaptive neuro-fuzzy inference system (ANFIS) with nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH), tuned optimally by adaptive support vector regression (ASVR). The hybrid model is chosen for resolving the problems of the overshoot and volatility clustering simultaneously so as to improve the predictive accuracy and we denote it as ASVR-ANFIS/NGARCH in this paper. Once we start on the scheme of foreseeing data-packet-flow on a network, the throughput ratio of foreseeing and non-foreseeing data-packet-flow is increased roughly up to 20%. We thereby drew the conclusion that the proposed scheme above can aid webmaster to improve network bandwidth allocation effectively and efficiently and then help web analytics to optimize their website, maximize online marketing conversions, and lead campaign tracking.

Resolving the forecasting problems of overshoot and volatility clustering using ANFIS coupling nonlinear heteroscedasticity with quantum tuning

In this paper, an approach to resolving two crucial problems of the overshoot and volatility clustering effects in time-series forecast has been proposed. In time-series prediction, big residuals round the turning-point region of a data sequence due to the overshoot phenomenon. Volatility clustering effect suggests a time series with successive disturbances being serially dependent. Both effects degrade the efficiency and effectiveness of time-series prediction and give rise to large residual errors. To overcome the overshoot and volatility clustering problems, an adaptive neuro-fuzzy inference system (ANFIS) coupling a nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH), which is adapted by quantum minimization (QM), is introduced to resolve the drawbacks of the predicted outputs with big residuals around the inflection points of a data sequence and time-varying conditional variance in residual errors. Besides, the trial of two distinct quantum amplitude amplification (QAA) techniques called by QM is also considered to show their different computational complexity. Two experiments on the financial time series were taken and a performance evaluation was made between the proposed one and several well-known alternative methods. Results show that our proposed method gains the best predictive accuracy to outperform the others. Goodness of fit of the proposed method was tested successfully by Ljung–Box Q-test. It followed that the proposed method in fact can reduce large residual errors significantly in time-series forecast because the overshoot and volatility clustering effects are simultaneously regulated to the trivial levels.

Timing of resources exploration in the behavior of firm – Innovative approach and empirical simulation

We have insight into the importance of resource exploration derived from the quest for sustaining competitive advantage as well as the growth of the firm, which are well-explicated in the resources point of view. However, we really do not know when the firm will seriously commit to this kind of activities. Therefore, this study proposes an innovative approach using quantum minimization (QM) to tune a composite model comprising adaptive neuron-fuzzy inference system (ANFIS) and nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) such that it constitutes the relationship among five indicators, the growth rate of long-term investment, the firm size, the return on total asset, the return on common equity, and the return on sales. In particularly, this proposed approach outperforms several typical methods such as auto-regressive moving-average regression (ARMAX), back-propagation neural network (BPNN), or adaptive support vector regression (ASVR) for this timing problem in term of comparing their achievement and the goodness-of-fit. Consequently, the preceding methods involved in this problem truly explain the timing of resources exploration in the behavior of firm. Meanwhile, the performance summary among methods is compared quantitatively.

Diversity of quantum optimizations for training adaptive support vector regression and its prediction applications

Three kinds of quantum optimizations are introduced in this paper as follows: quantum minimization (QM), neuromorphic quantum-based optimization (NQO), and logarithmic search with quantum existence testing (LSQET). In order to compare their optimization ability for training adaptive support vector regression, the performance evaluation is accomplished in the basis of forecasting the complex time series through two real world experiments. The model used for this complex time series prediction comprises both BPNN-Weighted Grey-C3LSP (BWGC) and nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) that is tuned perfectly by quantum-optimized adaptive support vector regression. Finally, according to the predictive accuracy of time series forecast and the cost of the computational complexity, the concluding remark will be made to illustrate and discuss these quantum optimizations.

Composite of adaptive support vector regression and nonlinear conditional heteroscedasticity tuned by quantum minimization for forecasts

Adaptive support vector regression (ASVR) applied to the forecast of complex time series is superior to the other traditional prediction methods. However, the effect of volatility clustering occurred in time-series actually deteriorates ASVR prediction accuracy. Therefore, incorporating nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) model into ASVR is employed for dealing with the problem of volatility clustering to best fit the forecast's system. Interestingly, quantum-based minimization algorithm is proposed in this study to tune the resulting coefficients between ASVR and NGARCH, in such a way that the ASVR/NGARCH composite model can achieve the best accuracy of prediction. Quantum optimization here tackles so-called NP-completeness problem and outperforms the real-coded genetic algorithm on the same problem because it accomplishes better approach to the optimal or near-optimal coefficient-found. It follows that the proposed method definitely obtains the satisfactory results because of highly balancing generalization and localization for composite model and thus improving forecast accuracy.

Adaptive Support Vector Regression Tuning Composite Model of BWCG and NGARCH for Applications of Time-Series Prediction

Grey model (GM) has encountered the crucial problem of overshoot when applying to the non-periodic short-term prediction. At the same period, cumulated 3-point least squared linear prediction (C3LSP) alternatively confronts the opposite situation, i.e. underestimation. Nevertheless, a method of combining both preceding models is proposed for resolving the overshoot and underestimation phenomena significantly that is hybrid BPNN-weighted GREY-C3LSP prediction (BWGC) model. However, some predicted outcomes resulted from BWGC are not accurate enough as few observations deviate far away from both GM and C3LSP outputs. Thus, compensation is figured out to deal with the time-varying variance of the residuals in BWGC. That is, incorporating a non-linear generalized autoregressive conditional heteroscedasticity (NGARCH) into BWGC is applied, and then adaptive support vector regression (ASVR) is employed for tuning the appropriate coefficients for both BWGC and NGARCH to effectively improve the predictive accuracy.

Applying nonlinear generalized autoregressive conditional heteroscedasticity to compensate ANFIS outputs tuned by adaptive support vector regression

Volatility clustering degrades the efficiency and effectiveness of time series prediction and gives rise to large residual errors. This is because volatility clustering suggests a time series where successive disturbances, even if uncorrelated, are yet serially dependent. To overcome volatility clustering problems, an adaptive neuro-fuzzy inference system (ANFIS) is combined with a nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) model that is tuned by adaptive support vector regression (ASVR) so as to tackle the problem of time-varying conditional variance in residual errors. The proposed method significantly reduces large residual errors in forecasts because volatility clustering effects are regulated to trivial levels. Two experiments using real financial data series compare the proposed method and a number of well-known alternative methods. Results show that forecasting performance by the proposed method produces superior results, with good speed of computation. Goodness of fit of the proposed method is tested by Ljung–Box Q-test. It is concluded that the ANFIS/NGARCH composite model tuned by ASVR performs very well for improved predictive accuracy of irregular non-periodic short-term time series forecast and will be of interest to the science of statistical prediction of time series.