GARCH Variance Research Articles

Calculation of Temperature Action of Flat Steel Box Girder of Long-Span Bridges Using a Joint Model of ARMA Mean and GARCH Variance

Using the monitoring temperature field data from the flat steel box girder, the time histories of temperature data and temperature difference data are investigated using the extreme value analysis method. Because the calculation of standard values of temperature action needs massive temperature field data, the simulation of daily extreme values of temperature data and temperature difference data is carried out by virtual of Probability Statistical Method. The seasonal and nonstationary trend terms are described using the weighted sum of a series of basic elementary functions. The random fluctuation term is represented by a joint model of ARMA mean and GARCH variance. Moreover, the yearly extreme values of temperature data and temperature difference data are considered as statistical variables, and their standard values of temperature action with 50-year return period are calculated by means of the general extreme value (GEV) distributive function. The research results can supply references for temperature action of flat steel box girder.

Does inclusion of GARCH variance in deep learning models improve financial contagion prediction?

Financial contagions have traditionally been studied using GARCH models to explain the volatility, whereas regression models have been used to predict the stock index values based on different underlying assets. Past research has shown that deep learning regression models have demonstrated superiority over traditional statistical models. This paper creates a hybrid prediction model by using the outputs of GARCH models as an input variable in deep learning regression models. It has been observed that hybrid models provide better results as compared to deep learning models. Such improved prediction shall provide portfolio managers an additional tool to determine the investment strategy.

Empirical investigation of relationship between equity ETF and stock index: Study of Indian market

The synergy between the index volatility and equity ETFs have attracted the analysts due to their increase in utility as investment vehicle. The current study aims to investigate the association between the equity ETF and index volatility. The daily data from 1st January 2021 to 31st December 2022 has been taken for the current study. The percentage change in volume traded of ETF has been calculated. The volatility of Sensex has been calculated by generating GARCH variance series in E-views. Before applying GARCH, the condition of ARCH has been estimated. Pearson correlation coefficient has been performed on SPSS. The result of the study indicates a positive correlation between he understudy variables. The results have been supported by previous studies. It signifies that with increase in volatility in Stock index, the fluctuation in ETF trade volume is also increased.

Testing an Algorithm with Asymmetric Markov-Switching GARCH Models in US Stock Trading

In the present paper, we extend the current literature in algorithmic trading with Markov-switching models with generalized autoregressive conditional heteroskedastic (MS-GARCH) models. We performed this by using asymmetric log-likelihood functions (LLF) and variance models. From 2 January 2004 to 19 March 2021, we simulated 36 institutional investor’s portfolios. These used homogenous (either symmetric or asymmetric) Gaussian, Student’s t-distribution, or generalized error distribution (GED) and (symmetric or asymmetric) GARCH variance models. By including the impact of stock trading fees and taxes, we found that an institutional investor could outperform the S&P 500 stock index (SP500) if they used the suggested trading algorithm with symmetric homogeneous GED LLF and an asymmetric E-GARCH variance model. The trading algorithm had a simple rule, that is, to invest in the SP500 if the forecast probability of being in a calm or normal regime at t + 1 is higher than 50%. With this configuration in the MS-GARCH model, the simulated portfolios achieved a 324.43% accumulated return, of which the algorithm generated 168.48%. Our results contribute to the discussion on using MS-GARCH models in algorithmic trading with a combination of either symmetric or asymmetric pdfs and variance models.

A Test of Using Markov-Switching GARCH Models in Oil and Natural Gas Trading

In this paper, we test the use of Markov-switching (MS) GARCH (MSGARCH) models for trading either oil or natural gas futures. Using weekly data from 7 January 1994 to 31 May 2019, we tested the next trading rule: to invest in the simulated commodity if the investor expects to be in the low-volatility regime at t + 1 or to otherwise hold the risk-free asset. Assumptions for our simulations included the following: (1) we assumed that the investors trade in a homogeneous (Gaussian or t-Student) two regime context and (2) the investor used a time-fixed, ARCH, or GARCH variance in each regime. Our results suggest that the use of the MS Gaussian model, with time-fixed variance, leads to the best performance in the oil market. For the case of natural gas, we found no benefit of using our trading rule against a buy-and-hold strategy in the three-month U.S. Treasury bills.

Financial Time Series Modelling of Trends and Patterns in the Energy Markets

Precise recognition of a time series path is important to policy makers, statisticians, economists, traders, hedgers and speculators alike. The correct time series path is also a key ingredient in pricing models. This study uses daily futures prices of crude oil and other distillate fuels. This paper considers the statistical properties of energy futures and spot prices and investigates the trends that underlie the price dynamics in order to gain further insights into possible nuances of price discovery and energy market dynamics. The family of ARMA-GARCH models was explored. The trends depict time varying variability and persistence of oil price shocks. The return series conform to a constant mean model with GARCH variance.

Pricing S&P 500 Index Options: A Conditional Semi‐Nonparametric Approach

AbstractWe price S&P 500 index options under the assumption that the conditional risk‐neutral density function of the index follows a Semi‐Nonparametric (SNP) process with GARCH variance. The model is estimated combining a set of option contracts written on the index and the daily index return time series in the period 1996–2011. The in‐sample and out‐sample performance of the model is compared with several benchmark models, beating most of them. We conclude that a pricing model dealing simultaneously with non‐normalities and time‐varying volatility helps to mitigate the observed S&P 500 index option biases. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:217–239, 2016

International Portfolio Diversification Benefits in Periods of Crises

This paper studies the benefits of international portfolio diversification in a context of growing market correlation and crises occurrence. Different investment strategies employing different risk measures (standard variance, GARCH variance, CVaR, LPM (2,3,4,5)) are used to assess the robustness of international diversification benefits. Equity returns from 41 countries, are used including both developed and emerging markets, over the period 1988-2009 which has been characterized by increasing market correlations. Our empirical results show that international diversification benefits can still be substantial despite the growing market correlations even in crises periods. We find similar results using both restricted and unrestricted portfolio optimization techniques. We conclude that emerging markets are an important source of diversification benefits only when combined with developed markets. Our results highlight the importance of the USA, Jordan and Nigeria indexes in efficient portfolios. Furthermore, we find no evidence that the use of a specific risk measure dominates all the times when it comes to portfolio selection. In particular, unlike previous evidence, our results do not support the dominance of “survival risk” measures during crises periods.

ARCH, GARCH, and ARMAX Models for Forecasting Pathogen Indicators and Advisories at Marine Recreational Sites

Despite the wide ranging applications of time series methodologies for stochastic processes, they have not been used for environmental economics (except climate change). To fill this gap, we introduce time series methodology for the environmental econometrics, presenting autoregressive, moving average, ARCH, GARCH, and ARMAX models. These models are applied to establish a functional relationship between pathogen indicator and meteorological and environmental variables using time series data associated with Huntington Beach, Ohio. According to ARCH, turbidity, dew point, flow, and rainfall are statistically significant variables. Other models produced roughly similar results because of the short lag order. Models confirm the lag order of one using Akaike, Schwartz, and Hannan-Quinn selection criteria, reflecting very short memory of the pathogen indicator series. However, the time series did not support GARCH variance structure. These models not only under forecasted observations at both ends of the distribution of the data, but also simultaneously underforecasted advisories.

How Big is Nuclear News? Views from the South Asian Stock Markets

This paper analyzes the differential impact of on the Pakistani and Indian stock markets using a GARCH (1,1) model. In May 1998, India carried out a series of nuclear tests; Pakistan reacted like wise in the very same month. Although it was not the first series of tests for India, it was for Pakistan. In December 2001, after the Indian parliament was attacked by a group of alleged militants, missiles capable of carrying nuclear warheads were deployed along the international border by both countries. This event made the threat of a nuclear war very real, as has been agreed upon by different analysts. The econometric results show that Karachi Stock Exchange (KSE-100 index) reacted negatively based on mean level effects to nuclear in 1998 and in 2001; whereas the Bombay Stock Exchange (BSE-100 index) reacted negatively only to the Indian nuclear tests in 1998. The GARCH variance analysis shows that the level effects are followed with high uncertainty for both the markets. Moreover, the differential immediate variance of the two markets suggests that Pakistan economy is more likely to face hardships of any nuclear fallout than the Indians. Thus not only does the nuclear news have non-symmetric effects on the two markets, Pakistan is more likely to be negatively effected than India as viewed by the stock market investors.

The Monthly Effect in Stock Returns and Conditional Heteroscedasticity

This paper analyzes the end-of-month (or monthly) effect in stock returns using a conditional GARCH variance model. Many researchers who have studied seasonal anomalies in stock returns have tried to explain these phenomena by looking at the stock market in isolation. In this paper, we relate the end-of-month effect to macroeconomic variables. Furthermore, we improve the efficiency of our statistical tests by including heteroscedasticity in the model. As a result, we present evidence that there is indeed an end-of-month effect distinct from the Mondays in the end-of-month effect documented by previous researchers. We show a link between this end-of-month effect and the economic business cycle, and present evidence that the end-of-month anomaly exists only during business cycle expansions; this anomaly disappears during business cycle contractions.

International Market Volatility Indexes: A Study on VX1, VDAX and VIX

It is well known that finding an accurate forecast of future volatility turns out to be very useful for pricing derivatives, hedging strategies or for the calculation of the Value at Risk. The market's assessment of the underlying asset's volatility as reflected in the option price is known as the implied volatility of the option. Based on teaching derived from these recent papers written on the forecasting ability of implied volatility, this paper deals with the accuracy of international volatility indexes (VX1, VDAX and VIX). First, we find that VX1, VIX and VDAX are good tools for predicting future realized volatility and we also show that past implied volatility informs more about future implied volatility than past realized volatility. We, also, embed each of the implied volatility indexes as an exogenous term in the GARCH variance equation and find that all of them dominates the GARCH terms. Second, We also compute parameters of a stochastic volatility model using implied volatility indexes. Third, we study the transmission mechanisms of implied volatility indexes.

Sensitivity Analysis of Volatility: A New Tool for Risk Management

The extension of GARCH models to the multivariate setting has been fraught with difficulties. In this paper, we suggest to work with univariate portfolio GARCH models. We show how the multivariate dimension of the portfolio allocation problem may be recovered from the univariate approach. The main tool we use is the sensitivity analysis, which measures the change in the portfolio variance as a consequence of an infinitesimal change in the portfolio allocation. We derive the sensitivity of the univariate portfolio GARCH variance to the portfolio weights, by analytically computing the derivatives of the estimated GARCH variance with respect to these weights. We suggest a new and simple method to estimate full variance-covariance matrices of portfolio assets. An application to real data portfolios shows how to implement our methodology and compares its performance against that of selected popular alternatives. JEL Classification: C32, C53, G15