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This paper's aim is to test for the presence of fractional integration, or long memory, in the daily returns of the Portuguese stock market using autoregressive fractionally integrated moving average (ARFIMA), generalised autoregressive conditional heteroskedasticity (GARCH) and ARFIMA‐FIGARCH models.

The data cover two periods: 4 January 1993‐13 January 2006 (full sample), and 1 February 2002‐13 January 2006 (that is, data are considered after the merger of the Portuguese Stock Exchange with Euronext).

The results from the full sample show strong evidence of long memory in stock returns. When data after the merger are considered, weaker evidence of long memory is found. It is concluded that the Portuguese stock market is more efficient after the merger with Euronext.

The findings of this paper are helpful to financial managers and investors dealing with Portuguese stock indices.

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.

This study employs a new time series representation of persistence in conditional mean and variance to test for the existence of the long memory property in the currency futures market. Empirical results indicate that there exists a fractional exponent in the differencing process for foreign currency futures prices. The series of returns for these currencies displays long-term positive dependence. A hedging strategy for long memory in volatility is also discussed in this article to help the investors hedge for the exchange rate risk by using currency futures.

This paper aims to propose a framework based on the unbiased extreme value volatility estimator (namely, the AddRS estimator) to compute and predict the long position and the short position value-at-risk (VaR) and stressed expected shortfall (ES). The precise prediction of VaR and ES measures has important implications toward financial institutions, fund managers, portfolio managers, regulators and business practitioners.

The proposed framework is based on the Giot and Laurent (2004) approach and incorporates characteristics like long memory, fat tails and skewness. The authors evaluate its VaR and ES forecasting performance using various backtesting approaches for both long and short positions on four global indices (S&P 500, CAC 40, Indice BOVESPA [IBOVESPA] and S&P CNX Nifty) and compare the results with that of various alternative models.

The findings indicate that the proposed framework outperforms the alternative models in predicting the long and the short position VaR and stressed ES. The findings also indicate that the VaR forecasts based on the proposed framework provide the least total loss for various long and short position VaR, and this supports the superior properties of the proposed framework in forecasting VaR more accurately.

The study contributes by providing a framework to predict more accurate VaR and stressed ES measures based on the unbiased extreme value volatility estimator.

The purpose of this paper is to compare different models’ performance in modelling and forecasting the Finnish house price returns and volatility.

The competing models are the autoregressive moving average (ARMA) model and autoregressive fractional integrated moving average (ARFIMA) model for house price returns. For house price volatility, the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model is competing with the fractional integrated GARCH (FIGARCH) and component GARCH (CGARCH) models.

Results reveal that, for modelling Finnish house price returns, the data set under study drives the performance of ARMA or ARFIMA model. The EGARCH model stands as the leading model for Finnish house price volatility modelling. The long memory models (ARFIMA, CGARCH and FIGARCH) provide superior out-of-sample forecasts for house price returns and volatility; they outperform their short memory counterparts in most regions. Additionally, the models’ in-sample fit performances vary from region to region, while in some areas, the models manifest a geographical pattern in their out-of-sample forecasting performances.

The research results have vital implications, namely, portfolio allocation, investment risk assessment and decision-making.

To the best of the author’s knowledge, for Finland, there has yet to be empirical forecasting of either house price returns or/and volatility. Therefore, this study aims to bridge that gap by comparing different models’ performance in modelling, as well as forecasting the house price returns and volatility of the studied market.

Investment in Australia’s property market, whether directly or indirectly through Australian real estate investment trusts (A-REITs), grew remarkably since the 1990s. The degree of segregation between the property market and other financial assets, such as shares and bonds, can influence the diversification benefits within multi-asset portfolios. This raises the question of whether direct and indirect property investments are substitutable. Establishing how information transmits between asset classes and impacts the predictability of returns is of interest to investors. The paper aims to discuss these issues.

The authors study the linkages between direct and indirect Australian property sectors from 1985 to 2013, with shares and bonds. This paper employs an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process to de-smooth a valuation-based direct property index. The authors establish directional lead-lag relationships between markets using bi-variate Granger causality tests. Johansen cointegration tests are carried out to examine how direct and indirect property markets adjust to an equilibrium long-term relationship and short-term deviations from such a relationship with other asset classes.

The authors find the use of appraisal-based property data creates a smoothing bias which masks the extent of how information is transmitted between the indirect property sector, stock and bond markets, and influences returns. The authors demonstrate that an ARFIMA process accounting for a smoothing bias up to lags of four quarters can overcome the overstatement of the smoothing bias from traditional AR models, after individually appraised constituent properties are aggregated into an overall index. The results show that direct property adjusts to information transmitted from market-traded A-REITs and stocks.

The study shows direct property investments and A-REITs are substitutible in a multi-asset portfolio in the long and short term.

The authors apply an ARFIMA(p,d,q) model to de-smooth Australian property returns, as proposed by Bond and Hwang (2007). The authors expect the findings will contribute to the discussion on whether direct property and REITs are substitutes in a multi-asset portfolio.

Since the seminal works by Granger and Joyeux (1980) and Hosking (1981), estimations of long-memory time series models have been receiving considerable attention and a number of parameter estimation procedures have been proposed. This paper gives an overview of this plethora of methodologies with special focus on likelihood-based techniques. Broadly speaking, likelihood-based techniques can be classified into the following categories: the exact maximum likelihood (ML) estimation (Sowell, 1992; Dahlhaus, 1989), ML estimates based on autoregressive approximations (Granger & Joyeux, 1980; Li & McLeod, 1986), Whittle estimates (Fox & Taqqu, 1986; Giraitis & Surgailis, 1990), Whittle estimates with autoregressive truncation (Beran, 1994a), approximate estimates based on the Durbin–Levinson algorithm (Haslett & Raftery, 1989), state-space-based maximum likelihood estimates for ARFIMA models (Chan & Palma, 1998), and estimation of stochastic volatility models (Ghysels, Harvey, & Renault, 1996; Breidt, Crato, & de Lima, 1998; Chan & Petris, 2000) among others. Given the diversified applications of these techniques in different areas, this review aims at providing a succinct survey of these methodologies as well as an overview of important related problems such as the ML estimation with missing data (Palma & Chan, 1997), influence of subsets of observations on estimates and the estimation of seasonal long-memory models (Palma & Chan, 2005). Performances and asymptotic properties of these techniques are compared and examined. Inter-connections and finite sample performances among these procedures are studied. Finally, applications to financial time series of these methodologies are discussed.

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.

Using the ARFIMA-FIGARCH model, this paper studies the efficiency of the Japanese equity market by examining the statistical properties of the returns and volatility of the Nikkei 225. It shows that both follow a long-range dependence, which stands against the applicability of the efficient market hypothesis. The result is valid for all sample periods, suggesting that the Japanese market remains inefficient despite the recent equity market reform.