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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.

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 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 examine the evidence of long-range dependence behaviour in both house price returns and volatility for fifteen main regions in Finland over the period of 1988:Q1 to 2018:Q4. These regions are divided geographically into 45 cities and sub-areas according to their postcode numbers. The studied type of dwellings is apartments (block of flats) divided into one-room, two-rooms, and more than three rooms apartments types.

For each house price return series, both parametric and semiparametric long memory approaches are used to estimate the fractional differencing parameter d in an autoregressive fractional integrated moving average [ARFIMA (p, d, q)] process. Moreover, for cities and sub-areas with significant clustering effects (autoregressive conditional heteroscedasticity [ARCH] effects), the semiparametric long memory method is used to analyse the degree of persistence in the volatility by estimating the fractional differencing parameter d in both squared and absolute price returns.

A higher degree of predictability was found in all three apartments types price returns with the estimates of the long memory parameter constrained in the stationary and invertible interval, implying that the returns of the studied types of dwellings are long-term dependent. This high level of persistence in the house price indices differs from other assets, such as stocks and commodities. Furthermore, the evidence of long-range dependence was discovered in the house price volatility with more than half of the studied samples exhibiting long memory behaviour.

Investigating the long memory behaviour in both returns and volatility of the house prices is crucial for investment, risk and portfolio management. One reason is that the evidence of long-range dependence in the housing market returns suggests a high degree of predictability of the asset. The other reason is that the presence of long memory in the housing market volatility aids in the development of appropriate time series volatility forecasting models in this market. The study outcomes will be used in modelling and forecasting the volatility dynamics of the studied types of dwellings. The quality of the data limits the analysis and the results of the study.

To the best of the authors’ knowledge, this is the first research that assesses the long memory behaviour in the Finnish housing market. Also, it is the first study that evaluates the volatility of the Finnish housing market using data on both municipal and geographical level.

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.

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 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).

The 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.

The 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.

The 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.

This 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.

The 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.

Volatility estimates are incorporated into standard volatility models to assess the impact of structural breaks on volatility persistence, long memory and forecasting performance for ASMs.

The 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.

A 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.

This 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.

In this chapter, we investigate the effect of long memory in volatility on the accuracy of emerging stock markets risk estimation during the period of the recent global financial crisis. For this purpose, we use a short (GJR-GARCH) and long (FIAPARCH) memory volatility models to compute in-sample and out-of-sample one-day-ahead VaR. Using six emerging stock markets index, we show that taking into account the long memory property in volatility modelling generally provides a more accurate VaR estimation and prediction. Therefore, conservative risk managers may adopt long memory models using GARCH-type models to assess the emerging market risks, especially when incorporating crisis periods.