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The purpose of this research is to analyze the Bitcoin (BTC) and Ether (ETH) long memory and conditional volatility.

The empirical approach includes ARFIMA-HYGARCH and ARFIMA-FIGARCH, both models under Student‘s t-distribution, during the period (ETH: November 9, 2017 to November 25, 2021 and BTC: September 17, 2014 to November 25, 2021).

Findings suggest that ARFIMA-HYGARCH is the best model to analyze BTC volatility, and ARFIMA-FIGARCH is the best approach to model ETH volatility. Empirical evidence also confirms the existence of long memory on returns and on BTC volatility parameters. Results evidence that the models proposed are not as suitable for modeling ETH volatility as they are for the BTC.

Findings allow to confirm the fractal market hypothesis in BTC market. The data confirm that, despite the impact of the Covid-19 crisis, the dynamics of BTC returns, and volatility maintained their patterns, i.e. the way in which they evolve, in relation to the prepandemic era, did not change, but it is rather reaffirmed. Yet, ETH conditional volatility was more affected, as it is apparently higher during Covid-19. The originality of the research lies in the focus of the analysis, the proposed methodology and the variables and periods of study.

Introduction – The rapid flow of information between the markets eliminates the possibility of diversifying the portfolio by bringing the markets closer, and may cause the volatility in a market to spread to another market. In this context, revealing the relationships between conventional and participation markets or financial assets is important in terms of portfolio diversification and risk management.

Purpose – The major aim of this work is to analyse the existence of volatility spillover between conventional stock index and participation index based on the indexes in Turkish Capital Markets. BIST-30 and Katılım-30 indexes are used as the representatives of conventional stock index and participation index, respectively.

Methodology – Firstly, the univariate HYGARCH (1,d,1) parameters are calculated, and secondly, the dynamic equicorrelation (DECO) methodology is applied. DECO model is proposed to simplify structural assumptions by introducing a structure in which all twosomes of returns take the same correlation for a given time period. In this way, DECO model enables to have an optimal portfolio selection in comparison to an unrestricted time varying-dynamic correlation approaches and gives more advanced forecasting ability for the duration of the financial crisis periods compared to the various portfolios.

Findings – There is a strong correlation between BIST-30 and Katılım-30. They are affected by the same shocks. We expect to see different investor behaviours for Katılım-30 and BIST-30. However, they seem to have almost the same investor profile. In addition, there is a causality in both ways and volatility spillover between them.

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.

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.

This paper aims to analyze and give directions for advancing research in stock market volatility highlighting its features, structural breaks and emerging developments. This study offers a platform to research the benchmark studies to know the research gap and give directions for extending future research.

The author has performed the literature review, and, reference checking as per the snowballing approach. Firstly, the author has started with outlining and simplifying the significance of the subject area, the review illustrating the various elements along with the research gaps and emphasizing the finding.

This work summarizes the studies covering the volatility, its properties and structural breaks on various aspects such as techniques applied, subareas and the markets. From the review’s analysis, no study has clarified the supremacy of any model because of the different market conditions, nature of data and methodological aspects. The outcome of this research work has delivered further magnitude to research the benchmark studies for the upcoming work on stock market volatility. This paper has also proposed the hybrid volatility models combining artificial intelligence with econometric techniques to detect noise, sudden changes and chaotic information easily.

The author has taken the research papers from the scholarly journal published in the English language only and the author may also consider other nonscholarly or other language journals.

To the best of the author’s knowledge, this research work highlights an updated and more comprehensive framework examining the properties and demonstrating the contemporary developments in the field of stock market volatility.

This paper aims to focus on a better model to capture the trait of varying volatility in various financial time series, as well as to obtain reliable estimate of value at risk (VaR).

The typical methods in spectral analysis are used to obtain the sample of conditional mean, conditional variance and residual term. The generalized regression neural network is used to establish a time-varying non-linear model, and the non-parametric kernel density estimation method is applied for the estimation of VaR.

The proposed model is able to follow the heteroscedastic characteristic which is common in financial time series, and the estimated VaR is satisfactory.

The analysis method in this study allows the hedgers, bankers, financial analysts as well as economists to draw a better inference from financial time series. Also, relatively more precise estimate of the VaR value for a certain kind of financial asset is available. The model with its derived estimates would definitely help in developing other models.

Up-to-date, the study in literature which models financial time serial from the viewpoint of spectral analysis is rare to see. Thus, the proposed model, along with a comprehensive empirical study which reveals desirable result for the estimation of VaR would enrich the related researches at present.

In this paper, the authors seek to investigate the dynamics of Bitcoin, Litecoin, Ethereum and Ripple daily returns and volatilities.

In this paper, the authors apply the MS-ARMA model on daily returns of Bitcoin (19/04/2013-13/02/2018), Ripple (05/08/2013-14/02/2018), Litcoin (29/04/2013-14/02/2018) and Ethereum (08/02/2015-14/02/2018). This model allows capture of the nonlinear structure in both the conditional mean and the conditional variance of cryptocurrency returns.

All the cryptocurrency markets show regime switching in the return-generating process. Market dynamics seem to be governed by two different states which differ from one cryptocurrency market to another in terms of mean return, volatility and interstate dynamics. These findings can be explained by investors’ behavior, i.e. speculative trading and herding behavior. By choosing to participate (or imitating some investors) in some cryptocurrency markets (in particular Bitcoin market), they affect the price movements and therefore the market dynamics in the short run.

Identifying the different market states provides information for investors to make more accurate portfolio decisions in the virtual market and follow the market timing strategy.

This paper attempts to analyze potential nonlinear structure in cryptocurrencies returns and analyze if there is a difference between the cryptocurrencies market cycles. So, the search for congruent and adequate specification to reproduce the stock returns dynamics in the virtual market still remains the concern of several empirical studies. This research not only examines the behavior of stock returns in the cryptocurrencies’ market but also highlights the existence of nonlinearity propriety as a stylized fact.

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.