Testing for long memory in volatility in the Indian Forex market

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 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.

Rescaled variance and related tests for long memory in volatility and levels

The Effect of Long Memory in Volatility on Stock Market Fluctuations

Dependence and mean reversion in stock prices: The case of the MENA region

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.

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.

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 volatility of the Scandinavian international future energy market is examined based on a well known intra-day range-based measure of volatility. The main purpose of the paper is to identify determinants of the energy market's intra-day volatility. Firstly, the investigation is a contract-by-contract, range-based volatility measure. The findings are (1) long memory in volatility the longest contracts (year), but not for the shortest (month), (2) the first difference contemporaneous and one-day lagged trading volume measures influences daily volatility positively and consistently over all contracts, (3) trading volume seems to dominate the Samuelson (maturity) and the open-interest hypotheses thus manifesting earlier findings of future markets. Secondly, the paper applies a relatively new methodology to cope with dynamic panel data models, where every contract in the market is organized as a panel. The GMM-type estimator for dynamic panel-data of Arellano [1] is therefore implemented. The results show appropriate specification residual tests and demonstrate firstly the importance of volatility serial correlation. This estimator also shows that the change in daily trading volume is the major determinant of intra-day volatility. In contrast to the segmented analyses, time to maturity shows increased intra-day volatility influence while the measures of bid-ask spread and open interest show decreased significance. The main GMM findings are therefore that the change in trading volume (including lags) and time to maturity are major determinants of intra-day volatility.

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.

This work studies wavelet-based Whittle estimator of the fractionally integrated exponential generalized autoregressive conditional heteroscedasticity (FIEGARCH) model often used for modeling long memory in volatility of financial assets. The newly proposed estimator approximates the spectral density using wavelet transform, which makes it more robust to certain types of irregularities in data. Based on an extensive Monte Carlo study, both behavior of the proposed estimator and its relative performance with respect to traditional estimators are assessed. In addition, we study properties of the estimators in presence of jumps, which brings interesting discussion. We find that wavelet-based estimator may become an attractive robust and fast alternative to the traditional methods of estimation. In particular, a localized version of our estimator becomes attractive in small samples.

Chapter 9 A Source of Long Memory in Volatility

Bitcoin volatility was investigated with various symmetric and asymmetric models in the study. In addition, value at risk (VaR) was calculated by using the Kupiec LR test and the error prediction performances of the models were compared. As a result of the work, the long memory of volatility in Bitcoin returns was found. It means the cryptocurrency market is not efficient. According to the FIAPARCH asymmetric model, it was determined that positive information shocks reaching the Bitcoin market increased volatility more than negative information shocks. Comparing the error prediction performance of the models by calculating VaR, the HYGARCH model prediction results were found to be superior to other models included in the study. Thus, it was determined that the most suitable model in predicting the volatility, namely the risk of Bitcoin in short and long positions for those who consider investing in Bitcoin, is the asymmetric model HYGARCH.