Estimation of long memory in volatility using wavelets

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.

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 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.

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.

The Effect of Long Memory in Volatility on Stock Market Fluctuations

Speech spectral modeling and enhancement based on autoregressive conditional heteroscedasticity models

PurposeThe purpose of this study is to examine the spatial fluctuation spillover effect of green total factor productivity (GTFP) under the influence of Internet development.Design/methodology/approachUsing panel data from 283 cities in China for the period 2003–2016, this paper explores the spatial fluctuation spillover effect of internet development on GTFP by applying the spatial autoregressive with autoregressive conditional heteroscedasticity model (SARspARCH).FindingsThe results of Moran's I test of the residual term and the Bayesian information criterion (BIC) value indicate that the GTFP has a spatial fluctuation spillover effect, and the estimated results of the SARspARCH model are more accurate than the spatial autoregressive (SAR) model and the spatial autoregressive conditional heteroscedasticity (spARCH) model. Specifically, the internet development had a positive spatial fluctuation spillover effect on GTFP in 2003, 2011, 2012 and 2014, and the volatility spillover effect weakens the positive spillover effect of internet development on GTFP. Moreover, Internet development has a significant positive spatial fluctuation spillover effect on GTFP averagely in eastern China and internet-based cities.Research limitations/implicationsThe results of this study provide digital solutions for policymakers in improving the level of GTFP in China, with more emphasis on regional synergistic governance to ensure growth.Originality/valueThis paper expands the research ideas for spatial econometric models and provides a more valuable reference for China to achieve green development.

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.

PurposeThe purpose of this paper is to estimate volatility in African stock markets (ASMs), taking account of periodic level shifts in the mean level of volatility, where the regime shifts are determined endogenously.Design/methodology/approachVolatility estimates are incorporated into standard volatility models to assess the impact of structural breaks on volatility persistence, long memory and forecasting performance for ASMs.FindingsThe results presented here indeed suggest that persistence and long memory in volatility are overestimated when regime shifts are not accounted for. In particular, application of breakpoint tests and a moving average procedure suggest that unconditional volatility displays substantial time variation.Practical implicationsA modification of the standard generalised autoregressive conditional heteroscedasticity model to allow for time variation in the unconditional variance generates improved volatility forecasting performance for some African markets.Originality/valueThis paper describes one of the first studies to incorporate endogenously determined regime shifts into volatility estimates and assess the impact of structural breaks on volatility persistence, long memory and forecasting performance for ASMs.

The purpose of this study is to address the inference problem of the parameters of autoregressive conditional heteroscedasticity (ARCH) models. Specifically, we present a comparison of the two approaches — Bayesian and Maximum Likelihood (ML) for ARCH models, and the specific mathematical and algorithmic formulations of these approaches. In the ML, estimation we obtain confidence intervals by using the Bootstrap simulation technique. In the Bayesian estimation, we present a reparametrization of the model which allows us to apply prior normal densities to the transformed parameters. The posterior estimates are obtained using Monte Carlo Markov Chain (MCMC) methods. The methodology is exemplified by considering two Brazilian financial time series: the Bovespa Stock Index — IBovespa and the Telebrás series. The order of each ARCH model is selected by using the Bayesian Information Criterion (BIC).

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.

An empirical analysis of copper and a selection of currencies and indices of the countries that produce the largest amount of copper is done in the study to evaluate co-movement, volatility effects and static hedge ratios. The countries that are included are Chile, Peru, China, Australia, Congo, Zambia, Mexico, Indonesia, Canada, Russia, Poland, Kazakhstan, Brazil, South Africa and India. An index for Congo was not available, but the currency was included. To evaluate the overall effect on copper to emerging markets, the MSCI Emerging Market 50 Index was also included as part of the variables. The data will be evaluated by means of number of financial econometric models. The methodology includes correlation, VAR, Johansen Cointegration, Granger Causality, the generalised autoregressive conditional heteroscedastic (GARCH) model, Glosten-Jagannathan-Runkle generalised autoregressive conditional heteroscedastic (GJR-GARCH) model, and the exponential GARCH (EGARCH) model. The final part of the analysis includes the graphical representation of dynamic conditional correlations and four static hedge ratios which are the OLS methodology, ECM methodology, VECM methodology and finally the ECM-GARCH methodology. The models will be based on daily data from 1 August 2011 to 9 April 2018. The Granger Causality results suggest that relationships exist between all the variables except for seven currencies and one index, namely, the currencies for Australia, Brazil, Canada, Kazakhstan, Peru, Poland and Congo. The Index that does not show any relationship is the Zambian Lusaka All share Index. Volatility is present in the data and therefore the models mentioned will be compared in order to identify which model is the best fitting model for the selected commodities, currencies and index. Overall, GJR-GARCH was the best fitting model for copper spot and future, in addition, leverage effects exist which imply that negative shocks have a greater effect than positive shocks. The static hedge ratio analysis showed that Russian RPS Index and copper future provided the largest value, followed by the Brazilian Bovespa Index and the Peruvian S&P/BVL General Index. On the negative values, the largest negative value was obtained for the South African FTSE/JSE All Share Index.

A novel time-varying FIGARCH model for improving volatility predictions