ARCH-type Models Research Articles

Corporate ESG indices and stability during periods of deep concerns in financial markets

This study analyzes the dynamics of the high ESG-score companies' returns reflected in socially responsible indices selected from the FTSE4Good family across the European market during the COVID-19 Pandemic and war in Ukraine. The dynamics of these changes were assessed through the conditional variance derived from Markov Switching ARCH-type models with two regimes. The findings indicate that the effect of market disturbances on the high ESG-score companies from the FTSE4Good Europe index was slightly less persistent than the broad market. Meanwhile, the high ESG-score companies from the FTSE4Good UK index demonstrated similar behavior to their conventional peer, which may be attributed to the composition of the respective index.

The effects of free trade agreements on the stock market: Evidence from Vietnam.

This study examines the effects of news events related to the European Union-Vietnam Free Trade Agreement (EVFTA) on the Vietnam stock market from 2010 to 2020. We calculate sectoral abnormal returns prior to, during, and after announcements and find that the Vietnamese stock market is susceptible to these events. We discovered that the announcement had a negative impact on the market, which might diminish the effectiveness of the Agreement. The findings show that more than half of Vietnam's sectors had an immediate reaction to EVFTA announcements, with fourteen reacting negatively and six responding positively. Two of the ten events did not have any immediate impact on these industries but all events resulted in either early or delayed reactions. We also find market scepticism and major changes in the deal led to the emergence of a diamond risk structure. We run multiple robustness tests to account for market integration and other factors that may affect stock returns. In addition, we explore potential sectoral systematic risk changes following these occurrences using different ARCH-type models. These additional tests confirm the robustness of our findings.

Portmanteau Test for ARCH-Type Models by Using High-Frequency Data

The portmanteau test is an effective tool for testing the goodness of fit of models. Motivated by the fact that high-frequency data can improve the estimation accuracy of models, a modified portmanteau test using high-frequency data is proposed for ARCH-type models in this paper. Simulation results show that the empirical size and power of the modified test statistics of the model using high-frequency data are better than those of the daily model. Three stock indices (CSI 300, SSE 50, CSI 500) are taken as an example to illustrate the practical application of the test.

Asymmetric Volatility Relevance in Risk Management: An Empirical Analysis using Stock Index Futures

The objective of this research work is to show the relevance of asymmetries in estimating volatility. The methodology consists in the application of ARCH-type models and implied volatilities of options (IV) to estimate Value-at-Risk (VaR). These for a portfolio of stock index futures for various time horizons. The empirical analysis is carried out for the futures contracts for the Standard and Poors 500 and Mexican Stock Exchange Indices. According to the results, the IV model is superior in terms of precision compared to the ARCH-type models. It is recommended to use the relevant statistical gains when asymmetries are included with respect to when asymmetries are not used. The referred gains range from 4 to 150 basis points of minimum capital risk requirements. The originality of the present work consists of showing the importance of considering the asymmetric effects with IV and ARCH-type models in volatility forecasts within risk management analysis. It is concluded that the methodology means gains in monetary terms.

Functional central limit theorem for ARCH(∞) models with weakly dependent innovations

Since the seminal work of Engle (1982) and Bollerslev (1986), many ARCH-type models have been suggested and examined to explain a variety of stylized facts of financial and economic time series. Various popular ARCH-type models can be expressed as ARCH(∞) models. In this paper, we study the stationarity and functional central limit theorem (FCLT) for ARCH(∞) models, because statistical inferences for ARCH(∞) sequences require the study of asymptotics of various statistics concerned. Most previous results are obtained under independent and identically distributed (i.i.d.) innovation processes. But the i.i.d. assumption on innovations substantially restricts the flexibility of the models. In addition, many authors have shown that the i.i.d. assumption can be weakened to mild conditions. We consider the ARCH(∞) model where the innovation processes are strictly stationary and λ-weakly dependent instead of independent and identically distributed. We provide sufficient conditions for the existence of a unique stationary and λ-weakly dependent Volterra series type solution to the given ARCH(∞) process. The FCLT for the stationary and λ-weakly dependent solution is also obtained by adding weak dependence coefficients condition on innovations and condition on ARCH(∞) parameters. The FCLT for GARCH(p; q) model with λ-weakly dependent innovations is considered as an example.

Archmodels.Jl: Estimating Arch Models in Julia

This paper introduces ARCHModels.jl, a package for the Julia programming language that implements a number of univariate and multivariate ARCH-type models. This model class is the workhorse tool for modelling the conditional volatility of financial assets. Their distinguishing feature is that they model the latent volatility as a (deterministic) function of past returns and volatilities. This recursive structure results in loop-heavy code which, due to its just-in-time compiler, Julia is well-equipped to handle. As such, the entire package is written in Julia, without any binary dependencies. We benchmark the performance of ARCHModels.jl against popular implementations in MATLAB, R, and Python, and illustrate its use in a detailed case study.

Hybrid quantile estimation for asymmetric power GARCH models

Asymmetric power GARCH models have been widely used to study the higher order moments of financial returns, while their quantile estimation has been rarely investigated. This paper introduces a simple monotonic transformation on its conditional quantile function to make the quantile regression tractable. The asymptotic normality of the resulting quantile estimators is established under either stationarity or non-stationarity. Moreover, based on the estimation procedure, new tests for strict stationarity and asymmetry are also constructed. This is the first try of the quantile estimation for non-stationary ARCH-type models in the literature. The usefulness of the proposed methodology is illustrated by simulation results and real data analysis.

A Study on Price Fluctuation in Chinese Grain Markets : Based on ARCH-type models

A Study on Price Fluctuation in Chinese Grain Markets : Based on ARCH-type models

Predicting the VIX and the volatility risk premium: The role of short-run funding spreads Volatility Factors

This paper presents an innovative approach to extract Volatility Factors which predict the VIX, the S&P500 Realized Volatility (RV) and the Variance Risk Premium (VRP). The approach is innovative along two different dimensions, namely: (1) we extract Volatility Factors from panels of filtered volatilities — in particular large panels of univariate ARCH-type models and propose methods to estimate common Volatility Factors in the presence of estimation error and (2) we price equity volatility risk using factors which go beyond the equity class namely Volatility Factors extracted from panels of volatilities of short-run funding spreads. The role of these Volatility Factors is compared with the corresponding factors extracted from the panels of the above spreads as well as related factors proposed in the literature. Our monthly short-run funding spreads Volatility Factors provide both in- and out-of-sample predictive gains for forecasting the monthly VIX, RV as well as the equity premium, while the corresponding daily volatility factors via Mixed Data Sampling (MIDAS) models provide further improvements.

The Modelling of Exchange Rate Volatility Using Arch-Garch Models: The Case of Turkey

This study investigates the most appropriate method for modelling the volatility for nominal exchange rate by using the ARCH type models. The research covers the period of 2002-2017 of nominal exchange rate using daily data. It is observed that the volatility of nominal exchange rate has the ARCH effect and the most appropriate model for forecasting the volatility of nominal exchange rate is GARCH(1,2) because it has the lowest Akaike Information Criterion. Furthermore, during the crises and uncertain periods, the volatility of nominal exchange rate series increases and volatility clustering is observed, meaning high volatility tends to follow high volatility and it is true for vice versa.

Monthly streamflow prediction using a hybrid stochastic-deterministic approach for parsimonious non-linear time series modeling

Accurate streamflow prediction is essential in reservoir management, flood control, and operation of irrigation networks. In this study, the deterministic and stochastic components of modeling are considered simultaneously. Two nonlinear time series models are developed based on autoregressive conditional heteroscedasticity and self-exciting threshold autoregressive methods integrated with the gene expression programming. The data of four stations from four different rivers from 1971 to 2010 are investigated. For examining the reliability and accuracy of the proposed hybrid models, three evaluation criteria, namely the R2, RMSE, and MAE, and several visual plots were used. Performance comparison of the hybrid models revealed that the accuracy of the SETAR-type models in terms of R2 performed better than the ARCH-type models for Daryan (0.99), Germezigol (0.99), Ligvan (0.97), and Saeedabad (0.98) at the validation stage. Overall, prediction results showed that a combination of the SETAR with the GEP model performs better than ARCH-based GEP models for the prediction of the monthly streamflow. Abbreviations: ADF = Augmented Dickey-Fuller; AIC = Akaike Information Criterion; ANFIS = Adaptive Neuro-Fuzzy Inference System; ANNs = Artificial Neural Networks; AR = Autoregressive Models; ARIMA = Autoregressive Integrated Moving Average; ARCH = Autoregressive Conditional Heteroscedasticity; ATAR = Aggregation Operator Based TAR; BL = Bilinear Models; BNN = Bayesian Neural Network; CEEMD = Complete Ensemble Empirical Mode Decomposition; DDM =Data-Driven Model; GA = Genetic Algorithm; GARCH = Generalized Autoregressive Conditional Heteroscedasticity; GEP = Gene Expression Programming; KNN = K-Nearest Neighbors; KPSS = Kwiatkowski–Phillips–Schmidt–Shin; LMR = Linear and Multilinear Regressions; LR = Likelihood Ratio; LSTAR = Logistic STAR; MAE = Mean Absolute Error; PACF = Partial Autocorrelation Function; PARCH = Partial Autoregressive Conditional Heteroscedasticity; R 2 = Coefficient of Determination; RMSE = Root Mean Square Error; RNNs = Recurrent Neural Networks; SETARMA = Self-Exciting Threshold Autoregressive Moving Average; SETAR = Self-Exciting Threshold Autoregressive; STAR = Smooth Transition AR; SVR = Support Vector Regression; TAR = Threshold Autoregressive; TARMA = Threshold Autoregressive Moving Average; ULB = Urmia Lake Basin; VMD = Variational Mode Decomposition; WT = Wavelet Transforms

A dynamic model of budget competition allocation on craft industry: evidence from Indonesia

This research aims to create a sustainable dynamic model concept towards the craft industry, which competes with each other in order to get the government budget allocation. The object of this research is superior industry (IU) from regional work unit. The regional work unit allocates its fund’s proportion of wood craft industry (IKA) by 51 percent and leather craft industry (IKU) by 49 percent. With almost equal portion, it turns out that the development result of IU has unequal proportion, which is 34 percent for IKA and 66 percent for IKU. This inequality indicates that there is a budgeting allocation, which is not based on performance. System dynamic simulation approach (SD) is conducted to predict the development of performance of both observation objects. In the phase of SD model development, Balanced Scoreboard (BSC) framework is used as a frame of development. The approach of ARCH-type model Success to Successful (StoS) is used as a concept of problem-solving. Several scenarios are formed in this research and needed as symbiosis redesign policy towards IKA product to increase the absorption of IKU product. Practical implications on sustainability of IKA and IKU are discussed in this research. The problem-solving can be applicable and replicable in Indonesia’s craft industry.

SpGARCH: An R-Package for Spatial and Spatiotemporal ARCH and GARCH models

In this paper, a general overview on spatial and spatiotemporal ARCH models is provided. In particular, we distinguish between three different spatial ARCH-type models. In addition to the original definition of Otto et al. (2016), we introduce an exponential spatial ARCH model in this paper. For this new model, maximum-likelihood estimators for the parameters are proposed. In addition, we consider a new complex-valued definition of the spatial ARCH process. From a practical point of view, the use of the R-package spGARCH is demonstrated. To be precise, we show how the proposed spatial ARCH models can be simulated and summarize the variety of spatial models, which can be estimated by the estimation functions provided in the package. Eventually, we apply all procedures to a real-data example.

Estimating and Testing Nonlinear Local Dependence Between Two Time Series

ABSTRACT The most common measure of dependence between two time series is the cross-correlation function. This measure gives a complete characterization of dependence for two linear and jointly Gaussian time series, but it often fails for nonlinear and non-Gaussian time series models, such as the ARCH-type models used in finance. The cross-correlation function is a global measure of dependence. In this article, we apply to bivariate time series the nonlinear local measure of dependence called local Gaussian correlation. It generally works well also for nonlinear models, and it can distinguish between positive and negative local dependence. We construct confidence intervals for the local Gaussian correlation and develop a test based on this measure of dependence. Asymptotic properties are derived for the parameter estimates, for the test functional and for a block bootstrap procedure. For both simulated and financial index data, we construct confidence intervals and we compare the proposed test with one based on the ordinary correlation and with one based on the Brownian distance correlation. Financial indexes are examined over a long time period and their local joint behavior, including tail behavior, is analyzed prior to, during and after the financial crisis. Supplementary material for this article is available online.

Risk management of time varying floors for dynamic portfolio insurance

We propose several important extensions of the standard Constant Proportion Portfolio Insurance (CPPI), which are based on the introduction of various conditional floors. In this framework, we examine in particular both the margin and the ratchet based strategies. The first method prevents the portfolio from being monetized, known as the cash-lock risk; the second one allows to keep part of the past gains whatever the future significant drawdowns of the financial market, which corresponds to ratchet effects. However, as for the standard CPPI method, the investor can benefit from potential market rises. To control the risk of such strategies, we introduce risk measures based both on quantile conditions and on the Expected Shortfall (ES). For each of these criteria, we prove that the conditional floor must be higher than a lower bound. We illustrate the advantages provided by such strategies, using a quite general ARCH type model. Our empirical analysis is mainly conducted on S&P 500 and Euro Stoxx 50. Using parameter estimation, we provide portfolio simulations and measure their respective performances using both the Sharpe and the Omega ratios. We also backtest the strategies, using a sliding window method to dynamically estimate the parameters of the models based on the last two years of weekly returns. Our results emphazise the advantages of introducing time varying floors from both the theoretical and operational points of view.

Rational GARCH model: An empirical test for stock returns

We propose a new ARCH-type model that uses a rational function to capture the asymmetric response of volatility to returns, known as the “leverage effect”. Using 10 individual stocks on the Tokyo Stock Exchange and two stock indices, we compare the new model with several other asymmetric ARCH-type models. We find that according to the deviance information criterion, the new model ranks first for several stocks. Results show that the proposed new model can be used as an alternative asymmetric ARCH-type model in empirical applications.

Parameter Stability and Semiparametric Inference in Time Varying Auto-Regressive Conditional Heteroscedasticity Models

Summary We develop a complete methodology for detecting time varying or non-time-varying parameters in auto-regressive conditional heteroscedasticity (ARCH) processes. For this, we estimate and test various semiparametric versions of time varying ARCH models which include two well-known non-stationary ARCH-type models introduced in the econometrics literature. Using kernel estimation, we show that non-time-varying parameters can be estimated at the usual parametric rate of convergence and, for Gaussian noise, we construct estimates that are asymptotically efficient in a semiparametric sense. Then we introduce two statistical tests which can be used for detecting non-time-varying parameters or for testing the second-order dynamics. An information criterion for selecting the number of lags is also provided. We illustrate our methodology with several real data sets.

Risk forecasting in (T)GARCH models with uncorrelated dependent innovations

(G)ARCH-type models are frequently used for the dynamic modelling and forecasting of risk attached to speculative asset returns. While the symmetric and conditionally Gaussian GARCH model has been generalized in a manifold of directions, model innovations are mostly presumed to stem from an underlying IID distribution. For a cross section of 18 stock market indices, we notice that (threshold) (T)GARCH-implied model innovations are likely at odds with the commonly held IID assumption. Two complementary strategies are pursued to evaluate the conditional distributions of consecutive TGARCH innovations, a non-parametric approach and a class of standardized copula distributions. Modelling higher order dependence patterns is found to improve standard TGARCH-implied conditional value-at-risk and expected shortfall out-of-sample forecasts that rely on the notion of IID innovations.

Modelling and Forecasting Exchange-rate Volatility with ARCHtype Models

This paper uses the Generalized Autoregressive Conditional Heteroskedasticity models to estimate volatility (conditional variance) in the monthly returns of the principal stock exchange of Sudan. over the period from January 1999 to December 2013. The models include both symmetric and asymmetric models that capture the most common stylized facts about index returns such as volatility clustering and leverage effect. The empirical results show that the conditional variance process is highly persistent (explosive process), and provide evidence on the existence of risk premium for the return series which support the positive correlation hypothesis between volatility and the expected stock returns. Our findings also show that the asymmetric models provide better fit than the symmetric models, which confirms the presence of leverage effect. These results, in general, explain that high volatility of return series is present in the Sudanese stock market over the period.

Robust and efficient estimation with weighted composite quantile regression

Abstract In this paper we introduce a weighted composite quantile regression (CQR) estimation approach and study its application in nonlinear models such as exponential models and ARCH-type models. The weighted CQR is augmented by using a data-driven weighting scheme. With the error distribution unspecified, the proposed estimators share robustness from quantile regression and achieve nearly the same efficiency as the oracle maximum likelihood estimator (MLE) for a variety of error distributions including the normal, mixed-normal, Student’s t , Cauchy distributions, etc. We also suggest an algorithm for the fast implementation of the proposed methodology. Simulations are carried out to compare the performance of different estimators, and the proposed approach is used to analyze the daily S&P 500 Composite index, which verifies the effectiveness and efficiency of our theoretical results.