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This chapter extends the univariate forecasting method proposed by Wang, Luc, and Hsiao (2013) to forecast the multivariate long memory model subject to structural breaks. The approach does not need to estimate the parameters of this multivariate system nor need to detect the structural breaks. The only procedure is to employ a VAR(k) model to approximate the multivariate long memory model subject to structural breaks. Therefore, this approach reduces the computational burden substantially and also avoids estimation of the parameters of the multivariate long memory model, which can lead to poor forecasting performance. Moreover, when there are multiple breaks, when the breaks occur close to the end of the sample or when the breaks occur at different locations for the time series in the system, our VAR approximation approach solves the issue of spurious breaks in finite samples, even though the exact orders of the multivariate long memory process are unknown. Insights from our theoretical analysis are confirmed by a set of Monte Carlo experiments, through which we demonstrate that our approach provides a substantial improvement over existing multivariate prediction methods. Finally, an empirical application to the multivariate realized volatility illustrates the usefulness of our forecasting procedure.

The purpose of this paper is to explore whether stock index volatility series exhibit real long memory.

The authors employ sequential procedure to test structural break in volatility series, and use DFA and 2ELW to estimate long memory parameter for the whole samples and subsamples, and further apply adaptive FIGARCH (AFIGARCH) to describe long memory and structural break.

The empirical results show that stock index volatility series are characterized by long memory and structural break, and therefore it is appropriate to use AFIGARCH to model stock index volatility process.

This study empirically investigates the properties of long memory and structural break in stock index volatility series. The conclusion has a certain reference value for understanding the properties of long memory and structural break in volatility series for academic researchers, market participants and policy makers, and for modeling and forecasting future volatility, testing market efficiency, pricing financial assets, constructing quantitative investment strategy and measuring market risk.

The main goal of this paper is to investigate whether there is long-memory behavior in the CBOE Brazil ETF volatility index (named here VIXBR). As structural breaks may create a spurious long-range dependence, the presence of structural breaks is also gauged.

The study considers the period from October 2011 to March 2021, using daily data. To test the long-memory behavior, three empirical approaches are adopted: GPH, ELW and robust GPH (RGPH) estimator. To estimate the structural break points adopted to date the subsamples, the ICSS algorithm is used.

Results considering the total period (TP) and subsamples show that the breaks did not create a spurious long-memory behavior and together with the rolling estimation, reveal strong evidence of the long-range dependence in the CBOE Brazil ETF volatility index. The higher degree of persistent of the VIXBR series suggests an extended period of increased uncertainty that agents need consider when making their investment decision.

As possible extension of this study is to investigate the behavior of long memory and structural breaks for different frequencies (weekly, monthly, among others).

The presence of long-range dependence in the CBOE Brazil ETF volatility index reveals that the past information is important for the predictability of risks, and therefore, can help to protect against market risks, which has important implications regarding the future decisions of economic agents (for example, policy makers and investors).

Brazil is an emerging capital market (ECM) that has attracted a great deal of attention from investors and investment funds seeking to diversify its assets. This paper contributes to the empirical financial literature, by studying the long-memory behavior of the CBOE Brazil ETF volatility index, considering possible structural breaks. To the best of knowledge, this has not been done so far.

This study aims to examine the long memory as well as the effect of structural breaks in the US and the Chinese stock markets. More importantly, it further explores possible causes of the differences in long memory between these two stock markets.

The authors employ various methods to estimate the memory parameters, including the modified R/S, averaged periodogram, Lagrange multiplier, local Whittle and exact local Whittle estimations.

China's two stock markets exhibit long memory, whereas the two US markets do not. Furthermore, long memory is robust in Chinese markets even when we test break-adjusted data. The Chinese stock market does not meet the efficient market hypothesis (EMHs), including the efficiency of information disclosure, regulations and supervision, investors' behavior, and trading mechanisms. Therefore, its stock prices' sluggish response to information leads to momentum effects and long memory.

The authors elaborately illustrate how long memory develops by analyzing not only stock market indices but also typical individual stocks in both the emerging China and the developed US, which diversifies the EMH with wider international stylized facts and findings when compared with previous literature. A couple of tests conducted to analyze structural break effects and spurious long memory demonstrate the reliability of the results. The authors’ findings have significant implications for investors and policymakers worldwide.

This study aims to analyse the conditional volatility of the Vietnam Index (Ho Chi Minh City) and the Hanoi Exchange Index (Hanoi) with a specific focus on their application to risk management tools such as Expected Shortfall (ES).

First, the author tests both indices for long memory in their returns and squared returns. Second, the author applies several generalised autoregressive conditional heteroskedasticity (GARCH) models to account for asymmetry and long memory effects in conditional volatility. Finally, the author back tests the GARCH models’ forecasts for Value-at-Risk (VaR) and ES.

The author does not find long memory in returns, but does find long memory in the squared returns. The results suggest differences in both indices for the asymmetric impact of negative and positive news on volatility and the persistence of shocks (long memory). Long memory models perform best when estimating risk measures for both series.

Short-time horizons to estimate the variance should be avoided. A combination of long memory GARCH models with skewed Student’s t-distribution is recommended to forecast VaR and ES.

Up to now, no analysis has examined asymmetry and long memory effects jointly. Moreover, studies on Vietnamese stock market volatility do not take ES into consideration. This study attempts to overcome this gap. The author contributes by offering more insight into the Vietnamese stock market properties and shows the necessity of considering ES in risk management. The findings of this study are important to domestic and foreign practitioners, particularly for risk management, as well as banks and researchers investigating international markets.

Growth enterprise market (GEM) in Hong Kong is acknowledged as one of the world’s most successful examples of small and medium enterprise (SME) stock market. The purpose of this paper is to examine the evolving efficiency and dual long memory in the GEM. This paper also explores the joint impacts of thin trading, structural breaks and inflation on the dual long memory.

State-space GARCH-M model, Kalman filter estimation, factor-adjustment techniques and fractionally integrated models: ARFIMA–FIGARCH, ARFIMA–FIAPARCH and ARFIMA–HYGARCH are adopted for the empirical analysis.

The results indicate that the GEM is still weak-form inefficient but shows a tendency towards efficiency over time except during the global financial crisis. There also exists a stationary long-memory property in the market return and volatility; however, these long-memory properties weaken in magnitude and/or statistical significance when the joint impacts of the three aforementioned factors were taken into account.

A forecasts of the hedging model that capture dual long memory could provide investors further insights into risk management of investments in the GEM.

The findings of this study are relevant to market authorities in improving the GEM market efficiency and investors in modelling hedging strategies for the GEM.

This study is the first to investigate the evolving efficiency and dual long memory in an SME stock market, and the joint impacts of thin trading, structural breaks and inflation on the dual long memory.

In order to assess the informational efficiency of African equity markets (AEMs), the purpose of this paper is to examine long memory in both equity returns and volatility using auto‐regressive fractionally integrated moving average (ARFIMA)‐FIGARCH/hyperbolic GARCH (HYGARCH) models.

In order to test for long memory, the behaviour of the auto‐correlation function for 11 AEMs is examined. Following the graphical analysis, the authors proceed to estimate ARFIMA‐FIGARCH and ARFIMA‐HYGARCH models, specifically designed to capture long‐memory dynamics.

The results show that these markets (largely) display a predictable component in returns; while evidence of long memory in volatility is very mixed. In comparison, results from the control of the UK and USA show short memory in returns while evidence of long memory in volatility is mixed. These results show that the behaviour of equity market returns and risks are dissimilar across markets and this may have implications for portfolio diversification and risk management strategies.

The results of the analysis may have important implications for portfolio diversification and risk management strategies.

The importance of this paper lies in it being the first to systematically analyse long‐memory dynamics for a range of AEMs. African markets are becoming increasingly important as a source of international portfolio diversification and risk management. Hence, the results here have implication for the conduct of international portfolio building, asset pricing and hedging.

The main purpose of this paper is to examine the asymmetry and long memory properties in the volatility of the stock indices of the PIIGS economies (Portugal, Ireland, Italy, Greece and Spain).

The paper utilizes the wavelets approach (based on Haar, Daubechies‐4, Daubechies‐12 and Daubechies‐20 wavelets) and the GARCH class of models (namely, ARFIMA (p,d′,q)‐GARCH (1,1), IGARCH (1,1), FIGARCH (1,d,0), FIGARCH (1,d,1), EGARCH (1,1) and FIEGARCH (1,d,1)) to accomplish the desired goals.

The findings provide evidence in support of the presence of long range dependence in the various proxies of volatility of the PIIGS economies. The results from the wavelet approach also support the Taylor effect in the volatility proxies. The results show that ARFIMA (p,d′,q)‐FIGARCH (1,d,0) model specification is better able to capture the long memory property of conditional volatility than the conventional GARCH and IGARCH models. In addition, the ARFIMA (p,d′,q)‐FIEGARCH (1,d,1) model is better able to capture the asymmetric long memory feature in the conditional volatility.

This paper has both methodological and empirical originality. On the methodological side, the study applies the wavelet technique on the major proxies of volatility (squared returns, absolute returns, logarithm squared returns and the range) because the wavelet‐based estimator exhibits superior properties in modeling the behavior of the volatility of stock returns. On the empirical side, the paper finds asymmetry and long range dependence in the conditional volatility of the stock returns in PIIGS economies using the GARCH family of models.

The purpose of this paper is to assess to what extent intraday data can explain and predict long-term memory.

This article analysed the presence of long-memory volatility in five Asian equity indices, namely, SENSEX, CNIA, NIKKEI225, KO11 and FTSTI, using five-min intraday return series from 05 January 2015 to 06 August 2015 using two approaches, i.e. conditional volatility and realized volatility, for forecasting long-term memory. It employs conditional-generalized autoregressive conditional heteroscedasticity (GARCH), i.e. autoregressive fractionally integrated moving average (ARFIMA)-FIGARCH model and ARFIMA-asymmetric power autoregressive conditional heteroscedasticity (APARCH) models, and unconditional volatility realized volatility using autoregressive integrated moving average (ARIMA) and ARFIMA in-sample forecasting models to estimate the persistence of the long-term memory.

Given the GARCH framework, the ARFIMA-APARCH long-memory model gave the better forecast results signifying the importance of accounting for asymmetric information when modelling volatility in a financial market. Using the unconditional realized volatility results from the Singapore and Indian markets, the ARIMA model outperforms the ARFIMA model in terms of forecast performance and provides reasonable forecasts.

The issue of long memory has important implications for the theory and practice of finance. It is well-known that accurate volatility forecasts are important in a variety of settings including option and other derivatives pricing, portfolio and risk management.

It could be said that using long-memory augmented models would give better results to investors so that they could analyse the market trends in returns and volatility in a more accurate manner and reach at an informed decision. This is useful to minimize the risks.

This research enhances the literature by estimating the influence of intraday variables on daily volatility. This is one of very few studies that uses conditional GARCH framework models and unconditional realized volatility estimates for forecasting long-term memory. The authors find that the methods complement each other.

There is evidence that a stationary short memory process that encounters occasional structural break can show the properties of long memory processes or persistence behaviour which may lead to extreme weather condition. In this chapter, we applied three techniques for testing the long memory for six daily rainfall datasets in Kelantan area. The results explained that all the datasets exhibit long memory. An empirical fluctuation process was employed to test for structural changes using the ordinary least square (OLS)-based cumulative sum (CUSUM) test. The result also shows that structural change was spotted in all datasets. A long memory testing was then engaged to the datasets that were subdivided into their respective break and the results displayed that the subseries follows the same pattern as the original series. Hence, this indicated that there exists a true long memory in the data generating process (DGP) although structural break occurs within the data series.