Fractionally Integrated GARCH Research Articles

Effects of Crude Oil Price Shocks on Stock Markets and Currency Exchange Rates in the Context of Russia-Ukraine Conflict: Evidence from G7 Countries

The present study examines the effects of the steep surge in crude oil prices which has also been considered as an oil price shock on the stock price returns and currency exchange rates of G7 countries, namely Canada, France, Germany, Italy, Japan, the United Kingdom (UK) and the United States (US), in the context of the Russia–Ukraine conflict. Due to the outbreak of the war, the steep surge in Brent crude oil price returns is seen as an exogenous shock to stock price returns and exchange rates during the period from 2 January 2017 to 29 June 2022. The paper applies the Fractionally Integrated GARCH (FIGARCH) model to capture the effect of the crude oil price shock and the Breakpoint unit root test to examine the structural breaks in the dataset. Structural breakpoints in the dataset for the entire stock price returns and exchange rates are observed during the period commencing from the last week of February, 2022, to the last week of March, 2022. Except for TSX, NASDAQ and USD, noteworthy long memory effects running from Brent crude oil price to all the stock price returns along with the currency exchange rates for all G7 countries were also found.

Modelling COVID-19 Fluctuation in Nigeria Using Fractional Integrated Garch Model

This study applied a fractionally integrated GARCH (FIGARCH) process in modelling daily cases of COVID-19 in Nigeria from 28 February 2020 to 23 March 2022. The time plot of the series showed the constant fluctuation in the study variable. The daily COVID-19 data was tested for stationarity using Augmented Dickey-Fuller (ADF), the series was not stationary. The Geweke and Porter-Hudak (GPH) method was used to estimate the long memory parameter d of the FIGARCH model. The daily series was stationary at a fractional differencing of order (d=0.97). The presence of long memory was also detected using the autocorrelation function. The fractionally integrated GARCH model was used to detect the period of high and low crisis. The crisis period was identified by volatility clustering and the leverage effect process. However, four models were estimated for FIGARCH models. The best model was selected based on the information criteria. Finally, the most adequate model for estimating the volatility of COVID-19 in Nigeria was the FIGARCH (1,0.97, 1) model.

Modelling time-varying volatility using GARCH models: evidence from the Indian stock market.

Background: In this study, we examined the volatility of the Indian stock market from 2008 to 2021. Owing to the financial crisis, volatility forecasting of the Indian stock market has become crucial for economic and financial analysts. An empirical study of the returns of the NSE indices revealed an autoregressive conditional heteroskedastic trend in the Indian stock market. Methods: Using GARCH 1, 1 (generalized autoregressive conditional heteroskedasticity) and FIGARCH (fractionally integrated GARCH), we examine investor behaviour and the persistence of long-term volatility. Results: The empirical findings of the estimated models suggest that shocks persist for a long time in NSE returns. Furthermore, bad news has a greater impact on stock volatility than good news. The return on assets is stable but highly volatile, even though the Indian economy has experienced the global crash to some extent. Conclusions: Models of volatility derived from the GARCH equation provide accurate forecasts and are useful for portfolio allocation, performance measurement, and option valuation.

Modelling time-varying volatility using GARCH models: evidence from the Indian stock market.

Background: In this study, we examined the volatility of the Indian stock market from 2008 to 2021. Owing to the financial crisis, volatility forecasting of the Indian stock market has become crucial for economic and financial analysts. An empirical study of the returns of the NSE indices revealed an autoregressive conditional heteroskedastic trend in the Indian stock market. Methods: Using GARCH 1, 1 (generalized autoregressive conditional heteroskedasticity) and FIGARCH (fractionally integrated GARCH), we examine investor behaviour and the persistence of long-term volatility. Results: The empirical findings of the estimated models suggest that shocks persist for a long time in NSE returns. Furthermore, bad news has a greater impact on stock volatility than good news. The return on assets is stable but highly volatile, even though the Indian economy has experienced the global crash to some extent. Conclusions: Models of volatility derived from the GARCH equation provide accurate forecasts and are useful for portfolio allocation, performance measurement, and option valuation.

Is Bitcoin's Carbon Footprint Persistent? Multifractal Evidence and Policy Implications.

The Bitcoin mining process is energy intensive, which can hamper the much-desired ecological balance. Given that the persistence of high levels of energy consumption of Bitcoin could have permanent policy implications, we examine the presence of long memory in the daily data of the Bitcoin Energy Consumption Index (BECI) (BECI upper bound, BECI lower bound, and BECI average) covering the period 25 February 2017 to 25 January 2022. Employing fractionally integrated GARCH (FIGARCH) and multifractal detrended fluctuation analysis (MFDFA) models to estimate the order of fractional integrating parameter and compute the Hurst exponent, which measures long memory, this study shows that distant series observations are strongly autocorrelated and long memory exists in most cases, although mean-reversion is observed at the first difference of the data series. Such evidence for the profound presence of long memory suggests the suitability of applying permanent policies regarding the use of alternate energy for mining; otherwise, transitory policy would quickly become obsolete. We also suggest the replacement of ‘proof-of-work’ with ‘proof-of-space’ or ‘proof-of-stake’, although with a trade-off (possible security breach) to reduce the carbon footprint, the implementation of direct tax on mining volume, or the mandatory use of carbon credits to restrict the environmental damage.

Fractionally integrated GARCH model with tempered stable distribution: a simulation study

ABSTRACTWith the growing availability of high-frequency data, long memory has become a popular topic in finance research. Fractionally Integrated GARCH (FIGARCH) model is a standard approach to study the long memory of financial volatility. The original specification of FIGARCH model is developed using Normal distribution, which cannot accommodate fat-tailed properties commonly existing in financial time series. Traditionally, the Student-t distribution and General Error Distribution (GED) are used instead to solve that problem. However, a recent study points out that the Student-t lacks stability. Instead, the Stable distribution is introduced. The issue of this distribution is that its second moment does not exist. To overcome this new problem, the tempered stable distribution, which retains most attractive characteristics of the Stable distribution and has defined moments, is a natural candidate. In this paper, we describe the estimation procedure of the FIGARCH model with tempered stable distribution and conduct a series of simulation studies to demonstrate that it consistently outperforms FIGARCH models with the Normal, Student-t and GED distributions. An empirical evidence of the S&P 500 hourly return is also provided with robust results. Therefore, we argue that the tempered stable distribution could be a widely useful tool for modelling the high-frequency financial volatility in general contexts with a FIGARCH-type specification.

Modeling the risk-return characteristics of the SB1 Mexican private pension fund index

This paper analyzes the returns and variance behavior of the largest specialized private pension investment funds index in Mexico, the SIEFORE Básica 1 (or, SB1). The analysis was carried out with time series techniques to model the returns and volatility of the SB1, using publicly available historical data for SB1. Like many standard financial time series, the SB1 returns show non-normality, volatility clusters and excess kurtosis. The econometric characteristics of the series were initially modeled using three GARCH family models: GARCH (1,1), TGARCH and IGARCH. However, due to the presence of highly persistent volatility, the series modeling was extended using Fractionally Integrated GARCH (FIGARCH) methods. To that end, an extended specification: an ARFIMA (p,d,q) and a FIGARCH model were incorporated. The evidence obtained suggests the presence of long memory effects both in the returns and the volatility of the SB1. Our analysis results have important implications for the risk management of the SB1. Keywords: Private Pension Funds, Time Series modelling, GARCH models, Long Term memory series

ACTUARIAL IMPLICATIONS OF STRUCTURAL CHANGES IN EL NIÑO-SOUTHERN OSCILLATION INDEX DYNAMICS

The influence of climate variability on agricultural production and financial risks faced by an individual or an institution has been the center of the public discussion in the recent years. The changing weather patterns and environmental conditions could cause substantial unpredicted economic losses. Failure to capture such changes would underestimate the insurance contract's expected indemnity and further create a major obstacle for insurance sectors. In this paper, we undertake a case study of El Niño-Southern Oscillation (ENSO) Index insurance for coastal Peru proposed by Skees. We examined the behavior of El Niño index and uncovered the evidence that the conditional volatility of El Niño index has changed over time. A fractionally integrated GARCH (FIGARCH) process that captures long memory behavior for conditional variance and allows the disturbance variance to vary over time is used to design and rate the ENSO Index insurance contract. Our results show that, with the time-invariant AR(2) model serving as a benchmark, the AR(2)-FIGARCH(1, d, 1) model outperforms the AR(2) model in both in-sample fit and out-of-sample forecast for El Niño index. Moreover, the time-invariant model could underestimate the premium rates, exposing the insurer to undesired underwriting risk and ultimately causing the index insurance market to collapse.

The Tunisian stock market index volatility: Long memory vs. switching regime

This paper investigates the dilemma of long memory versus a switching regime for the Tunisian stock market index volatility. Precisely, different specifications of the Fractionally Integrated GARCH (FIGARCH) model of Baillie et al. (1996) and Switching ARCH (SWARCH) model of Hamilton and Susmel (1994) have been estimated under both Gaussian and Student error distributions.The empirical results show that the Student FIGARCH(1,d,1) specification outperforms the Markov switching ARCH model. In addition, the empirical results indicate that the long memory behavior observed in the Tunisian stock price (TUNINDEX) volatility is a true behavior and is not spuriously created by changes in regimes.

Long memory properties and asymmetric effects of emerging equity market

PurposeThe purpose of this paper is to examine the long memory property of equity returns and volatility of emerging equity market by focusing on the Malaysian equity market, namely the Kuala Lumpur Stock Exchange (KLSE).Design/methodology/approachThe study adopts the Fractionally Integrated GARCH (FIGARCH) model and Fractionally Integrated Asymmetric Power ARCH (FIAPARCH), focusing on the Malaysian data covering the period from April 15, 2004 to April 30, 2007.FindingsThe study finds evidence of long memory property as well as asymmetric effects in the volatility of the KLSE. The traditional ARCH/GARCH is shown to be insufficient in modeling the volatility persistence. The FIAPARCH specification outperforms the FIGARCH model by capturing both asymmetry effects and long memory in the conditional variance.Research limitations/implicationsThe results of this study have practical implications for the investors intending to invest in the emerging markets such as Malaysia. Understanding volatility and developing the appropriate models are important since volatility can be a measure of risk which is highly relevant in forecasting the conditional volatility of returns for portfolio selection, asset pricing, and value at risk, option pricing and hedging strategies.Originality/valueThis study contributes in providing the empirical evidence on the long memory property of equity returns and volatility of an emerging equity market with reliable estimation models, which is currently lacking, particularly for emerging markets.

Aplikace FIGARCH a EWMA modelů na burzovní indexy PX a BUX

Volatility of the financial time series belongs to the crucial estimated parameters in finance (e.g. in risk management, derivative pricing). It is well known, that volatility varies in time, so that new approaches of volatility modeling have appeared. In this paper two models of the conditional heteroskedasticity - fractionally integrated GARCH (FIGARCH) and EWMA are presented. These models are illustrated on the daily historical returns of stock index PX and index BUX. Standard tests of normality, autocorrelation and conditional heteroskedasticity are applied to these log-return time series and before estimating the models, which confirm a usability of the conditional heteroskedasticity models. Empirical results of the Rescale Range analysis (R/S) indicate a long memory in the volatility process of PX index and the first 40 autocorrelations of the square log-returns show their hyperbolic decay. The volatility models are estimated by quasi-maximum likelihood method with Student´s t-distribution and used to the calculation of the 1-day 95% and 99% Value at Risk values. Finally, the validity of the models is verified by Kupiec´s test, TUFF and Christoffersen´s test. These tests demonstrate, that the FIGARCH model is a suitable alternative to the EWMA model in the Value at Risk calculation.

Long memory in the volatility of China stock returns

In this paper, we empirically examine the volatility process of China's stock market returns using daily and weekly Shanghai and Shenzhen stock indices during January 1990 to August 2008. To investigate the property of the process, we used the FIGARCH (fractionally integrated GARCH) model including GARCH and IGARCH processes as special cases. Since the FIGARCH model allows fractional integration order, it can detect hyperbolically decaying volatility processes which cannot be explained by previous models with integer integration order. Our results show that the Shanghai and Shenzhen stock indices exhibit long-term dependencies. The long memory properties of the Shanghai and Shenzhen stock markets do not seem to be spuriously induced without exception.

Empirical wavelet analysis of tail and memory properties of LARCH and FIGARCH models

Using computationally efficient wavelet methods, we study two nonlinear models of financial returns {r t }: linear ARCH (LARCH) and fractionally integrated GARCH (FIGARCH). We estimate the tail index α and the long memory parameter d of the squared returns $${X_t= r_t^2}$$of LARCH, and of the powers X t = |r t |p of FIGARCH. We find that the X t have infinite variance and long memory, and show how the estimates of α and d depend on the model parameters. These relationships are determined empirically, as the setting is quite complex, and no suitable theory has been developed so far. In particular, we provide empirical relationships between the estimates $${\hat d}$$and the difference parameters in LARCH and FIGARCH. Our computational work uncovers tail and memory properties of LARCH and FIGARCH for practically relevant parameter ranges, and provides some guidance on modeling returns on speculative assets including FX rates, stocks and market indices.

Long Memory GARCH Processes: Empirical Evidence from the Tunisian Stock Exchange Market

This paper deals with statistics' and econometrics' properties of fractionally integrated GARCH (FIGARCH). We compare these characteristics with those of traditional models. We insist on the GARCH exponential/IGARCH infinite decrease of volatility impact. Then, we apply it on three Tunisian exchange rate series between 1994 and 2006. As Beine, Laurent and Lecourt (2002), the contributions of the FIGARCH model are extended by accounting for the observed kurtosis through a student-t based maximum likelihood estimation. This estimation improves the goodness of fit properties of this model and may lead to different interest parameters estimates.

Conditional Volatility and Distribution of Exchange Rates: GARCH and FIGARCH Models with NIG Distribution

This paper extends the Fractionally integrated GARCH (FIGARCH) model by incorporating Normal Inverse Gaussian Distribution (NIG). The proposed model is flexible and allows one to model time-variation, long memory, fat tails as well as asymmetry and skewness in the distribution of financial returns. GARCH and FIGARCH models for daily log exchange rate returns with Normal, Student's t and NIG error distributions as well as GARCH/FIGARCH-in-mean models with t errors are estimated and compared both in terms of sample fit as well as out-of-the-sample predictive ability in several dimensions. The FIGARCH model with symmetric and asymmetric NIG errors outperform alternatives both in-sample fit and 1-day and 5-day ahead predictions of the quartiles of the exchange rate return distributions.

Can GARCH Models Capture Long-Range Dependence?

This paper investigates if component GARCH models introduced by Engle and Lee(1999) and Ding and Granger(1996) can capture the long-range dependence observed in measures of time-series volatility. Long-range dependence is assessed through the sample autocorrelations, two popular semiparametric estimators of the long-memory parameter, and the parametric fractionally integrated GARCH (FIGARCH) model. Monte Carlo methods are used to characterize the finite sample distributions of these statistics when data are generated from GARCH(1,1), component GARCH and FIGARCH models. For several daily financial return series we find that a two-component GARCH model captures the shape of the autocorrelation function of volatility, and is consistent with long-memory based on semiparametric and parametric estimates. Therefore, GARCH models can in some circumstances account for the long-range dependence found in financial market volatility.

Long memory in the volatility of Korean stock returns

In this paper, we empirically examine the volatility process of Korean stock market returns using the KOSPI200. To investigate the property of the process, we use the FIGARCH (Fractionally Integrated GARCH) model that includes GARCH and 1GARCH processes as special cases. Since the FIGARCH model allows fractional integration order, it can detect hyperbolically decaying volatility processes with cannot be explained by existing models with integer integration order. The result shows that the KOSPI200 exhibits long-term dependencies. To investigate the robustness of the obtained result, we analyze the time and cross-sectional aggregation effect using weekly data and individual stock returns that the KOSPI200 is comprised of. The long memory property of the KOSPI200 does not seem to be spuriously induced by aggregation.