Nonlinear GARCH Models for Highly Persistent Volatility

Forecasting price of financial market crash via a new nonlinear potential GARCH model

Autoregressive Conditional Skewness

This paper evaluates the performances of Value-at-Risk (VaR) and expected shortfall, as well as volatility forecasts in a class of risk models, specifically focusing on GARCH, integrated GARCH, and asymmetric GARCH models (GJR-GARCH, exponential GARCH, and smooth transition GARCH models). Most of the models incorporate four error probability distributions: Gaussian, Student’s t, skew Student’s t, and generalized error distribution (GED). We employ Bayesian Markov chain Monte Carlo sampling methods for estimation and forecasting. We further present backtesting measures for both VaR and expected shortfall forecasts and implement two loss functions to evaluate volatility forecasts. The empirical results are based on the S&P500 in the U.S. and Japan’s Nikkei 225. A VaR forecasting study reveals that at the 1% level the smooth transition model with a second-order logistic function and skew Student’s t error compares most favorably in terms of violation rates for both markets. For the volatility predictive abilities, the EGARCH model with GED error is the best model in both markets.

PurposeThe purpose of this paper is to deal with the different phases of volatility behavior and the dependence of the variability of the time series on its own past, models allowing for heteroscedasticity like autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), or regime‐switching models have been suggested by reserachers. Both types of models are widely used in practice.Design/methodology/approachBoth regime‐switching models and GARCH are used in this paper to model and explain the behavior of crude oil prices in order to forecast their volatility. In regime‐switching models, the oil return volatility has a dynamic process whose mean is subject to shifts, which is governed by a two‐state first‐order Markov process.FindingsThe GARCH models are found to be very useful in modeling a unique stochastic process with conditional variance; regime‐switching models have the advantage of dividing the observed stochastic behavior of a time series into several separate phases with different underlying stochastic processes.Originality/valueThe regime‐switching models show similar goodness‐of‐fit result to GARCH modeling, while has the advantage of capturing major events affecting the oil market. Daily data of crude oil prices are used from NYMEX Crude Oil market for the period 13 February 2006 up to 21 July 2009.

ABSTRACTThis study considers the problem of testing for a parameter change in integer-valued time series models in which the conditional density of current observations is assumed to follow a Poisson distribution. As a test, we consider the CUSUM of the squares test based on the residuals from INGARCH models and find that the test converges weakly to the supremum of a Brownian bridge. A simulation study demonstrates its superiority to the residual and standardized residual-based CUSUM tests of Kang and Lee [Parameter change test for Poisson autoregressive models. Scand J Statist. 2014;41:1136–1152] and Lee and Lee [CUSUM tests for general nonlinear inter-valued GARCH models: comparison study. Ann Inst Stat Math. 2019;71:1033–1057.] as well as the CUSUM of squares test based on standardized residuals.

This paper attempts to model and forecast the sugar prices volatility in the India using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. Various types of GARCH models for instance; GARCH (1, 1), EGARCH(1, 1)were applied to sugar the period 1995–2015; to test the hypothesis of persistence, asymmetry and volatility of the spot and futuresprices. It is found that, the sum of ARCH and GARCH coefficients is not close to one, indicating that volatility shocks is not quite persistent, moreover volatility, in addition none of sugar spot and futures prices has an impact of bad news on the price volatility, while lastly leverage effect is not present on the conditional variance. Therefore (GARCH) models are appropriate in modeling and forecasting sugar prices volatility.

The Indonesian Sharia stock market has experienced significant growth over the past year, accompanied by an increase in market capitalization. However, high volatility remains a critical challenge for investors when deciding to invest in Sharia stocks. Modeling Sharia stock return volatility is essential to help investors minimize investment risks. This study aims to identify the most effective model for measuring volatility in the Sharia stock market by comparing classical models such as Generalized Autoregressive Conditional Heteroscedasticity (GARCH), asymmetric models including Exponential GARCH (EGARCH), Threshold GARCH (TGARCH), and Asymmetric Power GARCH (APGARCH), along with the Markov Switching GARCH (MSGARCH) and a Bayesian MSGARCH model that incorporates structural regime changes. The results indicate that the Bayesian MSGARCH model outperforms the other models in capturing the volatility of the Jakarta Islamic Index Sharia stock returns, achieving the lowest prediction error and improved accuracy in parameter estimation. Moreover, the study reveals that investment activities influence the volatility structure during periods of market appreciation and depreciation, with identifiable durations, thereby providing valuable insights for the formulation of effective investment strategies.

Is Bitcoin a Commodity? On price jumps, demand shocks, and certainty of supply

Volatility forecasting of financial market returns is vital for risk management and portfolio optimization. In the quest for accurate volatility modeling, this article introduces an Artificial Neural Network -Generalized Autoregressive Conditional Heteroscedasticity model (ANN-GARCH) that fuses the strengths of neural networks with the well-known GARCH framework to deliver superior volatility predictions. The approach integrates volatility captured by conventional GARCH models into a neural network framework, combining return and realized volatility series. Then, the ANN architecture is designed to learn and process patterns, ultimately generating enhanced volatility predictions. The proposed model consistently outperforms traditional volatility forecasting methods when applied to Dow Jones Index returns during the COVID-19 period and its aftermath. Across various error distributions, the ANN-GARCH model demonstrates superior forecasting accuracy, evidenced by significantly lower root mean square error (RMSE) and mean absolute error (MAE) compared to competing models. This underscores the model's reliability and effectiveness in volatility forecasting. This innovative model will help academics and finance practitioners make informed decisions when the market conditions are stressed.

Purpose- The primary purpose of this study is to model Bitcoin price volatility and forecast its future price returns using advanced econometric models such as ARCH and GARCH. The study aims to enhance risk management strategies and support informed investment decisions by addressing the time-varying nature of Bitcoin’s volatility. The research explores the persistence of volatility shocks and the clustering of price movements to provide insights into market dynamics. Methodology- This research examines daily Bitcoin closing prices over the period from January 2020 to October 2024. The data was preprocessed to ensure reliability, including applying logarithmic transformations to standardize the data and eliminate trends. Stationarity tests, such as the Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and KPSS tests, were conducted to confirm the series' stationarity. The ARCH-LM test was utilized to detect volatility clustering which is essential for validating the use of ARCH and GARCH models. Following this, ARIMA models were employed to define mean equations and GARCH models were used to estimate conditional variance and capture volatility dynamics. The dataset was split into training and validation subsets with data from July to October 2024 reserved for validation. Findings- The findings demonstrate that Bitcoin’s price movements exhibit significant volatility clustering and persistence of shocks which are key characteristics effectively captured by ARCH and GARCH models. These models provide valuable insights into the volatility patterns of Bitcoin, supporting their application in cryptocurrency analysis. Despite their robustness, the models face limitations in precise return forecasting during highly volatile periods, suggesting the need for further refinement or integration with advanced approaches. Conclusion- The research concludes that ARCH and GARCH models are effective tools for understanding and forecasting Bitcoin’s volatility. The study underscores the importance of acknowledging volatility persistence and clustering effects when analyzing cryptocurrency price behavior. However, it also highlights areas for improvement in econometric modelling by including the exploration of hybrid models and the integration of macroeconomic factors to enhance forecasting accuracy. Keywords: Bitcoin, ARCH models, GARCH Models, forecasting, ARIMA models JEL Codes: C58, G10, G12

In highly volatile market conditions it's always difficult to predict returns using heteroscedastic Garch models. This paper tries to investigate the impact of sample data inputs over forecast using nested conditional mean ARMAX(2,2,0) and conditional variance Garch(1,1), Gjr-garch(1,1) and Egarch(1,1) models. Research also tries to indentify relationship between outcome of formal hypothesis tests, the Ljung-Box-Pierce Q-test and Engle's ARCH test, sample input and forecast results. Study is conducted over two diversified stock markets index of America (NASDAQ Composite) and Asia (Nikkei 225). Returns are forecasted for the volatile month of aug-08 using sample inputs of last one month, two months up to seven months before aug-08 and a complete year before inputi.e from 1-aug-07 to 31-jul-08 of 246 trading days has also been taken. Graphical and correlative comparison of forecasted and observed returns is also done to identify any trend followed by Garch models in relation to size of sample inputs and forecast. Results show that forecast of mean of returns is far more accurate with Nikkei as compared to Nasdaq.

Volatility is a matter of concern for time series modeling. It provides valuable insights into the fluctuation and stability of concerning variables over time. Volatility patterns in historical data can provide valuable information for predicting future behaviour. Nonlinear time series models such as the autoregressive conditional heteroscedastic (ARCH) and the generalized version of the ARCH model, i.e. generalized ARCH (GARCH) models are popularly used for capturing the volatility of a time series. The realization of any time series may have significant statistical dependencies on its distant counterpart. This phenomenon is known as the long memory process. Long memory structure can also be present in volatility. Fractionally integrated volatility models such as the fractionally integrated GARCH (FIGARCH) model can be used to capture the long memory in volatility. In this paper, we derived the out-of-sample forecast formulae along with the forecast error variances for the AR (1) -FIGARCH (1, d, 1) model by recursive use of conditional expectations and conditional variances. For empirical illustration, the modal spot prices of onion for Delhi, Lasalgaon and Bengaluru markets, India and S&P 500 index (close) data are used.

This research article proposes an innovative strategy to improve long-term forecasting accuracy for gasoline sales in Canada. The SARIMA-GARCH model was used with the rolling window forecasting technique to successfully address varying seasons, changing patterns, and conditional variance on the historical data of gasoline sales in Canada (1993-01-01 to 2015-12-01) with the sample size of 276. The rolling window forecasting technique was used to forecast one-step-ahead value and update the model to fresh observations while minimizing look-back bias and attaining good long-term forecasting accuracy. The findings revealed considerable improvements in forecasting accuracy. The proposed SARIMA-GARCH model with rolling window forecasting produced a RMSE of 151026.28 and a Mean Absolute Percentage Error (MAPE) of 0.0340. This outperformed other baseline models, including simple SARIMA model which had a RMSE of 329,689.88 and a MAPE of 0.0786, and the GARCH model which had a RMSE of 316,168.33 and a MAPE of 0.0685. The data shows that the proposed approach is effective for accurate long-term forecasting of gasoline sales in Canada. The study provides significant data for politicians, industry professionals, and energy investors, assisting them in making informed decisions about resource allocation, strategic planning, and risk management.

Crude oil is an important energy commodity to mankind. The fluctuation of crude oil prices has affected many related sectors and stock market indices. Hence, forecasting the crude oil prices is essential to avoid the future prices of the non-renewable natural resources to raise sky-rocket. In this study, daily West Texas Intermediate (WTI) crude oil prices data is obtained from Energy Information Administration (EIA) from 2nd January 1986 to 30th September 2009. This study uses the Box-Jenkins methodology and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) approach in analyzing the crude oil prices. ARIMA(1,2,1) and GARCH(1,1) are found to be the appropriate models under model identification, parameter estimation, diagnostic checking and forecasting future prices. In this study, the analyses are done with the aid of EViews software where the potential of this software in forecasting daily crude oil prices time series data is explored. Finally, using several measures, comparison performances between ARIMA(1, 2, 1) and GARCH(1,1) models are made. GARCH(1,1) is found to be a better model than ARIMA(1, 2, 1) model. Based on the study, it is concluded that ARIMA(1,2,1) model is able to produce good forecast based on a description of history patterns in crude oil prices. However, the GARCH(1,1) is the better model for daily crude oil prices due to its ability to capture the volatility by the non-constant of conditional variance.

The study proposes and a family of regime switching GARCH neural network models to model volatility. The proposed MS-ARMA-GARCH-NN models allow MS type regime switching in both the conditional mean and conditional variance for time series and further augmented with artificial neural networks to achieve improvement in forecasting capabilities. Gray (1996) RS-GARCH model allows within regime heteroskedasticity with markov switching of Hamilton (1989). Firstly, models are extended to fractional integration and asymmetric power GARCH and MS-ARMA-FIGARCH, MS-ARMA-APGARCH, MS-ARMA-FIAPGARCH models are evaluated and discussed. Secondly, in addition to regime swiching type nonlinearity, neural networks based augmentated models are evaluated and discussed. In this respect, MS-ARMA-GARCH models are augmented with Multi Layer Perceptron (MLP), Radial Basis Function (RBF), Elman type Recurrent NN (Elman RNN), Time lag (delay) Recurrent NN (RNN) and Hybrid MLP models. Therefore, the second model group includes MS-ARMA-GARCH-MLP, MS-ARMA-GARCH-RBF, MS-ARMA-GARCH-ElmanRNN, MS-ARMA-GARCH-RNN and MS-ARMA-GARCH-HybridMLP. Thirdly, fractional integrated versions are augmented with neural networks and denoted as MS-ARMA-FIGARCH-MLP, MS-ARMA-FIGARCH-RBF, MS-ARMA-FIGARCH-ElmanRNN, MS-ARMA-FIGARCH-RNN and MS-ARMA-FIGARCH-HybridMLP. Fourth, by allowing asymmetric power transformations, models are further extended to GARCH models. These models are MS-ARMA-APGARCH-RBF, MS-ARMA-APGARCH-ElmanRNN, MS-ARMA-APGARCH-RNN and MS-ARMA-FIGARCH-HybridMLP. Therefore, a total of four group of GARCH models are proposed and evaluated in the study. In the empirical application section, daily stock returns in ISE100 Istanbul Stock Index are modeled and forecasted. Forecast success is evaluated with MAE, MSE and RMSE criteria. Equal forecast accuracy is tested with modified Diebold-Mariano tests. Accordingly, fractional integration and asymmetric power transformation perform better in modeling the daily returns in IMKB100 stock index compared to the simple GARCH and RS-GARCH model of Gray. Hybrid MLP and time lag recurrent architectures (MS-ARMA-FIAPGARCH-HybridMLP and MS-ARMA-FIAPGARCH-RNN) provided the best forecast and modeling performance. In conclusion, the newly proposed GARCH models have significant forecasting improvement and therefore are promising in various economic applications.