GARCH Research Articles

Stock Price Forecasting for Xiaomi Auto: Application of ARIMA and GARCH Models

Since Xiaomi Corporation entered the market for electric vehicles, the volatility of its stock price has attracted a lot of attention from investors. This study's objective is to foresee the stock price of Xiaomi Auto by constructing GARCH and ARIMA models in R. By conducting a stationarity test and differencing the previous stock price information of Xiaomi Auto, and then the stock price for the upcoming 30 days is predicted using an ARIMA (0,1,0) model. The findings demonstrate that while the ARIMA model predicts a short-term phase of relatively stable stock price, the widening prediction intervals suggest increasing uncertainty. The construction of a GARCH (1,1) model aims to more accurately represent the fluctuations in the stock price. Predictions from the GARCH model point to higher price volatility in coming 30 days. Based on these model outcomes, this paper proposes short-term and medium- to long-term investment strategies for investors and discusses the limitations of the models as well as potential improvement for future research. This research improves the understanding of stock price trends and volatility in the electric vehicle market. It provides practical insights for better investment decisions. The study also advances financial forecasting methods, making them more applicable to real-world market behavior.

Volatility and spillover analysis between cryptocurrencies and financial indices: a diagonal BEKK and DCC GARCH model approach in support of SDGs

Volatility and spillover analysis between cryptocurrencies and financial indices: a diagonal BEKK and DCC GARCH model approach in support of SDGs

Improving realised volatility forecast for emerging markets

AbstractAccurate forecasting of realised volatility is essential for financial risk management and investment decision-making in emerging markets, taking the South African financial market as a benchmark. This study examines the predictive performance of four prominent models: HAR (Heterogeneous AutoRegressive), realised GARCH (Generalized AutoRegressive Conditional Heteroscedasticity), Recurrent Conditional Heteroskedasticity (RECH), and the Rough Fractional Stochastic Volatility (RFSV) models. These models are specifically tailored to capture the complex dynamics and long-range dependence observed in financial time series. We illustrate the challenges and limitations of these models outside the context of established markets. Our empirical findings reveal unique strengths for each model. The HAR model excels in capturing long-term volatility patterns, while realised GARCH models effectively capture volatility clustering and persistence. RECH model showcases their ability to forecast Value-at-Risk, while the RFSV model successfully captures irregular and long-memory characteristics. We provide empirical evidence that the South African financial market is rough. Moreover, this study provides valuable insights into forecasting realised volatility in the South African market, and the findings can assist practitioners and investors in making informed decisions and developing robust risk management strategies.

Food Financialization: Impact of Derivatives and Index Funds on Agri-Food Market Volatility

This study explores the financialization of agricultural commodities, focusing on how financial derivatives and index funds impact the volatility of agro-food markets. Using a Dynamic Conditional Correlation (DCC) GARCH model, we analyze volatility spillovers among key agricultural commodities, particularly maize, and related financial assets over a sample period from 2007 to 2020. Our analysis includes major financial assets like Exchange-Traded Funds (ETFs), the S&P 500 index, and agribusiness corporations such as ADM and Bunge and the largest corn flour producer, GRUMA. The results indicate that financial speculation, especially via passive investments such as ETFs, has intensified price volatility in commodity futures, leading to a systemic risk increase within the sector. This study provides empirical evidence of increased market integration between the agro-food sector and financial markets, underscoring risks to food security and economic stability. We conclude with recommendations for regulatory actions to mitigate systemic risks posed by the growing financial influence in agricultural markets.

Comparative Analysis of Stochastics Approaches in Forecasting Nigeria’s Key Macroeconomic Indicators

The Nigerian economy faces significant volatility in key macroeconomic variables, posing challenges to economic stability and growth. This study compares the performance of ARIMA, GARCH, and VAR models in forecasting GDP, exchange rates, interest rates, inflation, and unemployment, using annual data from 1981-2024. Results show that while ARIMA and GARCH models capture certain dynamics, the VAR model consistently delivers the highest forecast accuracy across all variables. These findings offer valuable insights for policymakers seeking data-driven strategies to stabilize the economy and manage macroeconomic uncertainty.

Semi-parametric financial risk forecasting incorporating multiple realized measures

A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting framework employing multiple realized measures is developed. The proposed framework extends the realized exponential GARCH model to be semi-parametrically estimated, via a joint loss function, whilst extending existing quantile time series models to incorporate multiple realized measures. A quasi-likelihood is built, employing the asymmetric Laplace distribution that is directly linked to a joint loss function, which enables Bayesian inference for the proposed model. An adaptive Markov Chain Monte Carlo method is used for the model estimation. The empirical section evaluates the performance of the proposed framework with six stock markets from January 2000 to June 2022, covering the period of COVID-19. Three realized measures, including 5-minute realized variance, bi-power variation, and realized kernel, are incorporated and evaluated in the proposed framework. One-step-ahead 1% and 2.5% VaR and ES forecasting results of the proposed model are compared to a range of parametric and semi-parametric models, lending support to the effectiveness of the proposed framework.

Analysis of Foreign Exchange Rate Volatility Based on the GARCH Model

At present, the foreign exchange rate is still an important factor affecting international trade transactions. Since 1990, when the yen first broke through the 150 yen mark, the yen has been depreciating continuously. At the end of April 2024, the yen fell to 158 yen to a dollar. According to research, the Fed's interest rate hike policy has impacted the yen's plunge. This paper takes this event as the starting point. It uses the GARCH model to analyze the financial time series of the dollar-yen exchange rate, to explore its volatility law, to bring certain reference significance to China's monetary policymakers. According to the empirical analysis, this paper concludes that the GARCH (1,1) model can better capture the volatility characteristics of this sequence.

Networked control systems induced delay modeling and stability analysis using Markov-regime-switching GARCH model

This article focuses on the stability analysis of networked control systems (NCSs). It is well-known that network-induced delays pose many control challenges due to their non-uniform and multifractal nature. With the growing integration of communication networks in control systems, the impact of time-varying and random delays on system performance becomes critical. Hence, it is essential to study their impact on the system’s stability. There are several network-induced delay modeling methods, resulting in constant, random, and probabilistic random delays, which provide the most realistic representation according to recent studies. This article introduces a new network-induced delay modeling method based on the Markov-regime-switching generalized autoregressive conditional heteroskedasticity (MRS-GARCH) process, which captures the intricate temporal dependence of random network delays. The resulting model offers a more accurate depiction of delay volatility behavior, accommodating sudden shifts between volatility regimes. Simulation results demonstrate that MRS GARCH-type modeling enables a more realistic representation of delay dynamics. We also conduct a stability analysis of NCSs modeled with the proposed method using linear matrix inequalities LMIs criteria derived from the Lyapunov-Krasovskii theorem. The simulation results show less conservatism than conventional models and provide a larger maximum allowable upper delay bound MAUDB.

Trend Analysis on Prices of Sunflower in Andhra Pradesh- A Time Series Approach

The present study made an attempt to forecast the sunflower prices in Adoni, Kurnool and Yemmiganur markets of Andhra Pradesh by using the secondary time series data for a period of 147 months with an interval ranging from Jan 2011 to Apr 2023. For this study various Growth models (linear, Cubic, Quadratic, Exponential and power models) and time series models (ARIMA and GARCH) and Hybrid Times series models were applied. On consideration of the selected diagnostic criterion like R2, RMSE and MAPE, it resulted that Hybrid time series models outperformed among the selected models for all the three selected markets. Finally, the prices of sunflower in Adoni, Kurnool and Yemmiganur market were forecasted by ARIMA(1,1,1)-GARCH(1,1), ARIMA(2,1,1)-GARCH(1,1) and ARIMA(2,1,2)-GARCH(1,1) models respectively and prices of for the month of April 2024 were estimated as 5527.7 (Rs. /Q.), 5819.70(Rs. /Q.) and 5395.04 (Rs. /Q.).. KEYWORDS :Price, Model, Sunflower, Forecast.

Stochastic behavior of green bond premiums

This paper aims to examine the stochastic behavior of green bond premiums that can characterize the benefits of green bonds. We propose a novel affine model of green bond pricing with mean-reverting interest rates and green bond premiums and a new model parameter estimation method using conventional and green bond prices to capture the stochastic behavior. Then, the model parameter estimation results demonstrate mean-reverting stochastic behavior for conventional bond yield and green bond premium using the US and EU green bond indexes for Corporate and three corporate bond indexes for intermediate, total, and long-term periods of the Bloomberg Fixed Income Indices from November 3, 2014 to December 11, 2020. Comparative statics using simulated green bond premiums show that green bond premiums orient toward negative values in nature. Moreover, the stochastic behavior of green bond premiums demonstrates that the greenness of green bonds has a downward effect on interest rates in COVID-19 and has a mitigating impact on liquidity risk in corporate bond markets. These results confirm the benefits of green bonds. Finally, the discussions secure the validity of the green bond pricing model by conducting econometric analyses of regime switching, principal component ones, and the GARCH (1,1) model.

Analytical Solution of Terzaghi’s Ground Arch Model for Loads on Circular Tunnels

Analytical Solution of Terzaghi’s Ground Arch Model for Loads on Circular Tunnels

Application of a combined arching model in the load transfer platform of rigid inclusion system with raft through FEM evaluation

Application of a combined arching model in the load transfer platform of rigid inclusion system with raft through FEM evaluation

Application of GARCH Model in the Field of Finance

Application of GARCH Model in the Field of Finance

Analyzing Rupiah-USD Exchange Rate Dynamics: A Study with ARCH and GARCH Models

The study aims to analyze the volatility of the Rupiah-USD exchange rate and predict future fluctuations using the Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. The exchange rate data, spanning from January 2010 to December 2023, is sourced from Bank Indonesia (BI) and adheres to the Jakarta Interbank Spot Dollar Rate (JISDOR) regulations, focusing solely on business days. ARCH and GARCH models are widely applied in financial time series analysis because they capture and forecast time-varying volatility. This study analyzes historical exchange rate data to evaluate the persistence of volatility and detect any structural breaks that could impact future exchange rate behavior. The findings reveal that both models effectively capture the volatility of the Rupiah-USD exchange rate, but the GARCH (1,1) model demonstrates superior forecasting accuracy. This model's ability to account for long-term volatility clustering makes it particularly useful for predicting exchange rate dynamics. The research contributes to a deeper understanding of the factors driving exchange rate fluctuations, offering valuable insights for policymakers, investors, and businesses. These insights can help stakeholders manage exchange rate risks more effectively within Indonesia's open economy, where global financial conditions and external shocks significantly shape currency movements. The study emphasizes the importance of using advanced econometric models for accurate volatility predictions and informed decision-making.

Time-Varying Spillover Effects of Carbon Prices on China’s Financial Risks

As China’s financial markets become increasingly integrated and the carbon market undergoes financialization, the impact of carbon emission price fluctuations on financial markets has emerged as a key area of systemic risk research. This study employs the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model and the optimal Copula function to investigate the dynamic correlation between carbon prices and China’s financial markets. Building on this, the Monte Carlo simulation and Copula CoVaR models are used to explore the spillover effects of carbon price volatility on China’s financial markets. The findings reveal the following: (1) Carbon price fluctuations generate spillover effects on all financial markets, but the intensity varies across different markets. The foreign exchange market experiences the strongest spillover effect, followed by the bond market, while the stock and money markets are relatively less affected. (2) The optimal Copula functions differ between the carbon market and China’s financial markets, indicating heterogeneous characteristics across regional markets. (3) There is a degree of interdependence between the carbon market and various sub-markets in China’s financial system. The carbon market has the strongest positive correlation with the commodity market and a relatively high negative correlation with the real estate market. These findings underscore the importance of integrating carbon price volatility into financial risk management frameworks. For policymakers, it highlights the need to consider market stability measures when crafting carbon emission regulations. Market managers can leverage these insights to develop strategies that mitigate risk spillover effects, while investors can use this analysis to inform their portfolio diversification and risk assessment processes.

Trivariate-ARMA–GARCH type–Vine Copula model for time series forecasting

The present study proposes trivariate-autoregressive moving average-generalized autoregressive conditional heteroscedasticity (TV-ARMA–GARCH) type Vine Copula model. The algorithm for generating a one-step-ahead forecast has been developed based on simulation. Detailed analysis of price volatility for three major vegetable crops across three geographically diverse markets in India has been carried out. The dataset comprises monthly price data for Tomato, Onion and Potato from January 2010 to July 2024, which is employed to assess the model’s forecasting accuracy. Comparative assessments are made against traditional time series models, including the multivariate-GARCH (MV-GARCH)-dynamic conditional correlation (DCC) model and the univariate (UV)-ARMA–GARCH model. Empirically, the results indicate that the TV-ARMA–GARCH type–Vine Copula model significantly outperforms these conventional models, as evidenced by evaluation metrics such as MAE (mean absolute error), RMSE (root mean square error), and MAPE (mean absolute percentage error). Additionally, the Diebold–Mariano test is utilized to validate the superior forecasting accuracy of the proposed model. The integration of Vine Copulas with the ARMA–GARCH type model significantly enhances price forecasting accuracy. This approach provides valuable insights for managing India’s complex agricultural markets.

Application of VAR-GARCH for Modeling the Causal Relationship of Stock Prices in the Mining Sub-sector

Accurate modeling is expected to minimize risk and maximize profit in investment portfolios, one ofwhich is in stock price modeling. This research aims to model the causal relationship between stockprices using the Vector Autoregressive - Generalized Autoregressive Conditional Heteroskedasticity(VAR-GARCH) model. The VAR-GARCH model is used to overcome heteroscedasticity and modeldynamic volatility. The data used for the modeling consists of daily stock prices from July 2023 toMay 2024 for mining sub-sector companies listed on the Jakarta Islamic Index (JII), including ADMR,ADRO, and ANTM. The results showed that the VAR(1) model is stable, but this model indicates thepresence of heteroskedasticity or ARCH effects. Therefore, the VAR(1) model was combined with theGARCH model, and the results showed that the best model is VAR(1)-GARCH(1,1). The VAR(1)-GARCH(1,1) model is appropriate and meets the homoskedasticity assumptions for modeling the stockprices of the mining sub-sector in the Jakarta Islamic Index (JII). This indicates that the VAR-GARCHmodel could successfully handle the volatility of stock price data. In general, this research is in linewith previous research, i.e., the VAR-GARCH model showed a better model for capturing the volatilitypatterns in the data.

Crossproduct Effect and Volatility Forecasting

ABSTRACTThis paper explores if the crossproduct of return and realized volatility measure contributes to volatility forecasting. We find there is an asymmetric crossproduct effect in volatility and propose a realized asymmetric GARCH (henceforth RealAGARCH) model. The RealAGARCH model is a generalization to the absolute GARCH and the asymmetric GARCH. Moreover, the RealAGARCH model has a news impact surface instead of a news impact curve, which makes it different from other GARCH‐like models. Empirical performance of the RealAGARCH model is evaluated on a variety of stock indices, and the results show dominance of RealAGARCH over the benchmark RealGARCH judging by either in‐sample or out‐of‐sample forecasting performance. A battery of checks confirm the robustness of our findings and thus the importance of incorporating crossproduct effect into volatility forecasting.

Combining Volatility Forecasts of Duration‐Dependent Markov‐Switching Models

ABSTRACTDuration‐dependent Markov‐switching (DDMS) models require a user‐specified duration hyperparameter, for which there is currently no established procedure for estimation or testing. As a result, an ad‐hoc duration choice must be heuristically justified. This paper proposes a methodology for handling duration selection in DDMS models, with a focus on volatility forecasting. The main novelty lies in generating forecasts through model combination techniques. The idea is that the combined forecasts will be more robust to misspecification in selecting the duration structure, thus yielding more accurate forecasts. Additionally, the paper contributes to the literature by evaluating the out‐of‐sample volatility forecasting performance of DDMS models compared to benchmark conditional volatility models. Empirical analysis involves returns from three distinct asset classes: a cryptocurrency, a stock market index, and a foreign currency exchange rate. Various volatility proxies and robust loss functions are incorporated into our analysis. The results indicate that combined forecasts outperform individual models and, in some cases, are more accurate than GARCH and MS‐GARCH models. Furthermore, models with fixed duration typically underperform relative to the simple GARCH model, often resulting in test rejections.

Empirical likelihood for martingale differences

In this article, we consider an empirical likelihood with vector observations that are martingale differences and prove a Wilks' type theorem under a conditional Lindeberg condition. We then generalize this result to approximate martingale differences. As applications of the first result we discuss the construction of confidence regions for various time series models, including linear and nonlinear autoregressive models, an ARCH(1) model, and nonlinear autoregressive models with heteroskedasticity. The second result is used to derive a Wilks' type theorem for a blockwise empirical likelihood for Markov chains.