A novel time-varying FIGARCH model for improving volatility predictions

Due to the illiquidity of inventories pledged, the essential of price risk management of supply chain finance is to long-term price risk measure. Long memory in volatility, which attests a slower than exponential decay in the autocorrelation function of standard proxies of volatility, yields an additional improvement in specification of multi-period volatility models and further impact on the term structure of risk. Thus, long memory is indispensable to model and measure long-term risk. This paper sheds new light on the impact of the existence and persistence of long memory in volatility on inventory portfolio optimization. Firstly, we investigate the existence of long memory in volatility of the inventory returns, and examine the impact of long memory on the modeling and forecasting of multi-period volatility, the dependence structure between inventory returns and portfolio optimization. Secondly, we further explore the impact of the persistence of long memory in volatility on the efficient frontier of inventory portfolio via a data generation process with different long memory parameter in the FIGARCH model. The extensive Monte Carlo evidence reveals that both GARCH and IGARCH models without accounting for long memory will misestimate the actual long-term risk of the inventory portfolio and further bias the efficient frontier; besides, through A sensitive analysis of long memory parameter d, it is proved that the portfolio with higher long memory parameter possesses higher expected return and lower risk level. In conclusion, banks and other participants will benefit from the long memory taken into the long-term price risk measure and portfolio optimization in supply chain finance.

This research applied closing price return for ASEAN ETFs. Comparing the long memory in volatility and asymmetric volatility of ASEAN ETFs, this research used four models, fractional autoregressive integrated moving average (ARFIMA), a hybrid of ARFIMA and fractionally integrated generalized autoregressive conditional heteroscedasticity (ARFIMA-FIGARCH), ARFIMA with fractionally integrated asymmetric power autoregressive conditional heteroscedasticity (ARFIMA-FIAPARCH) and ARFIMA with hyperbolic generalized autoregressive conditional heteroscedasticity (ARFIMA-HYGARCH) models. The results show that by using closing price return data samples ASEAN ETF have a long memory in volatility and negative asymmetric volatility. ARFIMA-FIAPARCH model perform better to investigate long memory in volatility and asymmetric volatility for ASEAN ETF. This findings can be evaluated by academicians, financial risk managers, investors, and regulators.

Long memory in variance or volatility refers to a slow hyperbolic decay in autocorrelation functions of the squared or log-squared returns. The conventional volatility models extensively used in empirical analysis do not account for long memory in volatility. This chapter revisits the Indian stock market by using the fractionally integrated generalized autoregressive conditional heteroscedasticity (FIGARCH) model. For empirical modeling, daily values of 14 indices from the National stock exchange (NSE) and Bombay Stock Exchange (BSE) from June 1997 to March 2010 are used. The results of the study confirm the presence of long memory in volatility of index returns. This shows that FIGARCH model better describes the persistence in volatility than the conventional GARCH models. Against the evidence of fractional behavior of volatility in Indian stock market, it is essential to factor the long memory in derivative pricing and value at risk models.

This article attempts to verify the presence of long memory in volatility in the Indian foreign exchange market using daily bilateral returns of the Indian Rupee against the US dollar from 17/02/1994 to 08/11/2013. In the first part of the analysis the presence of long-term dependence is confirmed in the return series as well as in two measures of unconditional volatility (absolute returns and squared returns) by employing three measures of long memory. Next, the presence of long memory in conditional volatility is tested using ARMA-FIGARCH and ARMA-FIAPARCH models under various distributional assumptions. The results confirm the presence of long memory in conditional variance for two models. In the last part, the presence of long memory in conditional mean and conditional variance is verified using ARFIMA-FIGARCH and ARFIMA-FIAPARCH models. It is also found that long-memory models fare well compared to short-memory models in sample forecast performance.

A partir de uma base de dados de ações da Telemar S.A. para o período de 21/09/1998 a 21/10/2002 e de opções desta mesma empresa para o período de 02/10/2000 a 21/10/2002 foi avaliada a precisão na previsão da volatilidade futura usando-se as volatilidades implícita e estatística. A volatilidade implícita foi obtida por indução retroativa da fórmula de Black-Scholes. As previsões estatísticas da volatilidade foram obtidas pelos modelos de média móvel ponderada igualmente, GARCH, EGARCH e FIGARCH. A estatística de Wald revela que os modelos EGARCH e FIGARCH são previsores eficientes e não viesados da variação absoluta dos retornos da Telemar S.A. entre t e t+1. Na avaliação da volatilidade ao longo do tempo de vida da opção, os resultados rejeitam a hipótese de volatilidade implícita ser um melhor previsor da volatilidade futura, e a estatística Wald mostra que o modelo FIGARCH é um previsor eficiente e não viesado.

The Effect of Long Memory in Volatility on Stock Market Fluctuations

This paper tests for long memory in volatility of fixed‐income returns; specifically, South Africa's local currency 10‐year government bond, given that the characterisation of stochastic long‐memory volatility is of interest and importance in portfolio and risk management. The long‐memory parameter is estimated using methods based on wavelets, which have gained prominence in recent years. Evidence of long memory in fixed‐income return volatility is conclusively demonstrated across a variety of volatility measures and wavelet forms. This finding suggests a pattern of time dependence, which may potentially be exploited to generate improved volatility forecasting performance especially over long horizons. This paper further extends the extant literature by comparing the predictive power of long‐memory forecasts with those obtained from a standard (short‐memory) generalised autoregressive conditional heteroskedasticity (GARCH) process. The results of this exercise suggest that the information content of long‐memory models does not lead to improved forecast accuracy. The GARCH(1,1) model is shown to provide the best forecasts across most horizons (i.e.daily, weekly and monthly). Forecast performance is further revealed to be sensitive to the choice of volatility proxy used. Finally, the derived volatility forecasts are generally very close, and in some cases, almost indistinguishable.

This paper introduces the new FITVGARCH model to describe both long memory and structural change behaviour in the volatility process by allowing for time varying dynamic structure in the conditional variance. The parameters of the conditional variance in the FIGARCH model are allowed to change smoothly over time. We derive an LM-type test for parameter constancy of the FIGARCH model against the alternative of time dependent parameters. Simulation analysis shows that both empirical size and power of the constancy test are quite good. An empirical application to the stock market volatility indicates that this new class of model seems to outperform the FIGARCH model in the description of the daily NASDAQ composite index returns.

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.

A Component Markov Regime-Switching Autoregressive Conditional Range Model

In their study on the applicability of volatility forecasting for risk management applications, [2] stress the importance of long-term volatility dependencies under longer forecast horizons. The present contribution addresses multiple-period value-at-risk (VaR) prediction for equity markets under long memory in return volatilities. We account for long memory in the τ-step ahead volatility forecast of GJR-GARCH(1,1) by using a novel estimator considering the slowly declining influence of past volatility shocks. Our empirical study of established equity markets covers daily index returns during the period 1975 to 2007. We study the out-of-sample accuracy of VaR predictions for five, ten, 20 and 60 trading days. As a benchmark model we use the parametric GARCH setting of Drost and Nijman (1993) and the Cornish-Fisher expansion as an approximation to innovation quan-tiles. The backtesting results document that our novel approach improves forecasts remarkably. This outperformance is only in part due to higher levels of risk forecasts. Even after controlling for the unconditional VaR levels of the competing approaches, the long memory GJR-GARCH(1,1) approach delivers results which are not dominated by the benchmark approach.

When market returns follow a long memory volatility process, standard approaches to estimating dynamic minimum variance hedge ratios (MVHRs) are misspecified. Simulation results and an application to the S&P 500 index document the magnitude of the misspecification that results from failure to account for basis convergence and long memory in volatility. These results have important implications for the estimation of MVHRs in the S&P 500 example and other markets as well.

This work is devoted to the study of long correlations, memory effects and other statistical properties of a sample of high-frequency (tick) data. The high-frequency data sample consists of high-frequency (minute) data for several stocks over a seven-day period which we know is relevant for market crush behaviour in the US market; 10–18 March 2008. The Hurst exponent estimation, the detrended fluctuation analysis and the fractional difference parameter are the tools used for this analysis. It also investigates the underlying volatility processes in high-frequency (tick) data using range of GARCH specifications. The GARCH variants considered include the basic GARCH, IGARCH, ARFIMA (0,,0)-GARCH and FIGARCH models. In all the applications, the methodology provides insight into features of these series volatility.

Inference for Nonlinear State Space Models: A Comparison of Different Methods applied to Markov-Switching Multifractal Models

Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero