Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model

We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to returns, we consider a filtered FIEGARCH-in-mean (FIEGARCH-M) effect in the return equation. The filtering of the volatility-in-mean component thus allows the co-existence of long memory in volatility and short memory in returns. We present an application to the daily CRSP value-weighted cum-dividend stock index return series from 1926 through 2006 which documents the empirical relevance of our model. The volatility-in-mean effect is significant, and the FIEGARCH-M model outperforms the original FIEGARCH model and alternative GARCH-type specifications according to standard criteria.     

Long memory and level shifts in REITs returns and volatility

This paper provides an empirical investigation of the long memory in the returns and volatility of REITs markets of the USA, the UK, Hong Kong, Australia, and Japan. Initially, we subject the series to unit root tests proposed by Saikkonen and Lütkepohl (2002) and Lanne et al. (2002), which allow for a level shift in the data generating process. We confirm the stationarity of the REITs returns in the presence of structural breaks, with the breaks happening during the 2008 and 2009 periods. Second, by employing long memory tests and estimators, a weak long memory is demonstrated in the return series, but a strong evidence is provided in the volatility measures. Then using Smith (2005)'s modified GPH estimator, we find that a short-memory model with a level shift is a viable alternative to a long memory model for the USA, Hong Kong and Japan and not for the UK nor for Australia. Finally, we confirm that the long memory in volatility is real and not caused by shifts in variance for all markets. Our results should be useful to market participants in the REITs markets, whose success depends on the ability to forecast and model REITs price movements.     

Another look at long memory in common stock returns

We apply the modified rescaled range test to the return series of 1,952 common stocks. The results indicate that long memory is not a widespread characteristic of these stocks. But logit models of the event of a test rejection reveal that rejections are linked to firms with large risk-adjusted average returns. The maximal moment of a return distribution is also found to influence the event of a rejection, but not in a way suggestive of moment-condition failure. Evidence suggestive of survivorship bias is also uncovered. We conclude that there is some evidence consistent with persistent long memory in the returns of a small proportion of stocks.     

MENA stock market volatility persistence: Evidence before and after the financial crisis of 2008

The global financial crisis began with a financial meltdown in the United States in early 2008 and then it had spread to the rest of the world. In this paper we test whether the MENA equity market volatility presents a different behavior before and after the financial crisis of 2008. Using long range dependence techniques we test for long memory in the returns, absolute and squared returns of the MENA equity markets. We subject the series to unit root tests that allow for structural breaks and use the Bai and Perron (1998, Econometrica, 66, 47; 2003a, J. Appl. Econometrics, 6, 72; 2003b, Econometrics J., 18, 1) to test for multiple breaks in the mean returns. The results indicate that the volatility measures represented by absolute and squared returns show evidence of long memory for the full and subsample periods, while the returns show a weak evidence of long memory. Considering the shift dates and corresponding to the 2008 financial crisis, the returns and volatility measures display less evidence of long memory in the after crisis period as opposed to the before crisis period. The change in the returns and volatility dynamics of these markets was due to financial and economic conditions that took place in the MENA region after the crisis.     

STOCK RETURNS AND VOLATILITY ON CHINA'S STOCK MARKETS

We examine time‐series features of stock returns and volatility, as well as the relation between return and volatility in four of China's stock exchanges. Variance ratio tests reject the hypothesis that stock returns follow a random walk. We find evidence of long memory of returns. Application of GARCH and EGARCH models provides strong evidence of time‐varying volatility and shows volatility is highly persistent and predictable. The results of GARCH‐M do not show any relation between expected returns and expected risk. Daily trading volume used as a proxy for information arrival time has no significant explanatory power for the conditional volatility of daily returns. JEL classification: G15     

Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.     

The Impact of Inflation Measures on the Real Returns and Risk of U.S. Stocks

Using different inflation measures produces economically significant differences in both the inflation record and inflation‐adjusted stock returns. We introduce a more consistent measure of the monthly Consumer Price Index (CPI) inflation rate to better measure real returns over 1913–2004, for which the official CPI exists. We also extend the series backward to 1871 on a monthly basis, an important addition to the data series. We analyze the impact of inflation on the real standard deviation of stock returns and find that, in contrast to the results for geometric mean returns, inflation adjustments have little impact on estimates of return variability.     

The volatility dynamics of spot and futures gold prices: Evidence from Russia

We examine the long memory property and structural break in the spot and futures gold volatility in Russia from 2008 through 2013. We find strong evidence of long memory in the volatility of both spot and futures gold series. The break dates are associated with the recent global financial crisis. Moreover, we investigate the volatility spillover effect between the Russian spot and futures gold markets using the corrected Dynamic Conditional Correlation model (cDCC). The findings show relatively high level of conditional correlation between spot and futures gold returns. This outcome decreases the portfolio diversification benefits for gold investors.     

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

This paper provides empirical evidence on the long memory behavior of the stock markets of Egypt, Jordan, Morocco, and Turkey. To test for long memory in the returns and volatility, we employ the modified rescaled range statistic R/S proposed by Lo [Lo, A.W., 1991. Long-term memory in stock market prices. Econometrica 59, 1279–1313] and the recently proposed rescaled variance V/S statistic developed by Giraitis et al. [Giraitis, L., Kokoszka, P.S. Leipus, R., Teyssiere, G., 2003. Rescaled variance and related tests for long memory in volatility and levels. J. Econ. 112, 265–294]. Further analysis is conducted by employing the ARFIMA (p, d, q) model to estimate the long memory parameters. Egypt and Morocco show evidence of long memory in the return series, while Jordan and Turkey display negative persistence. For the volatility series, long memory is conclusively demonstrated for all markets. Then, we compare the forecasting performance of ARMA and ARFIMA models and find that the ARFIMA model outperforms in out-of-sample forecasting of the markets. Our results should be useful to regulators, practitioners and derivative market participants, whose success depends on the ability to forecast stock price movements in these markets.     

Detecting structural breaks and identifying risk factors in hedge fund returns: A Bayesian approach

Extending previous work on asset-based style factor models, this paper proposes a model that allows for the presence of structural breaks in hedge fund return series. We consider a Bayesian approach to detecting structural breaks occurring at unknown times and identifying relevant risk factors to explain the monthly return variation. Exact and efficient Bayesian inference for the unknown number and positions of the breaks is performed by using filtering recursions similar to those of the forward–backward algorithm. Existing methods of testing for structural breaks are also used for comparison. We investigate the presence of structural breaks in several hedge fund indices; our results are consistent with market events and episodes that caused substantial volatility in hedge fund returns during the last decade.     

Modelling changes in the unconditional variance of long stock return series

In this paper we develop a testing and modelling procedure for describing the long-term volatility movements over very long daily return series. For this purpose we assume that volatility is multiplicatively decomposed into a conditional and an unconditional component as in Amado and Teräsvirta (2012, 2013). The latter component is modelled such that the unconditional time-varying component evolves slowly over time. Statistical inference is used for specifying the parameterization of the time-varying component by applying a sequence of Lagrange multiplier tests. The model building procedure is illustrated with an application to 22,986 daily returns of the Dow Jones Industrial Average stock index covering a period of more than ninety years. The main conclusions are as follows. First, the LM tests strongly reject the assumption of constancy of the unconditional variance. Second, the results show that the apparent long memory property in volatility may be interpreted as changes in the unconditional variance of the long series. Finally, based on a formal statistical test we find evidence of the superiority of volatility forecasting accuracy of the new model over the GJR-GARCH model at all horizons for eight subsets of the long return series.     

How long memory in volatility affects true dependence structure

Long memory in volatility is a stylized fact found in most financial return series. This paper empirically investigates the extent to which interdependence in emerging markets may be driven by conditional short and long range dependence in volatility. We fit copulas to pairs of raw and filtered returns, analyse the observed changes in the dependence structure may be driven by volatility, and discuss whether or not asymmetries on propagation of crisis may be interpreted as intrinsic characteristics of the markets. We also use the findings to construct portfolios possessing desirable expected behavior such as dependence at extreme positive levels.     

Forecasting daily variability of the S&P 100 stock index using historical,realised and implied volatility measurements

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper, we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First, we consider unobserved components (UC-RV) and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility (SV) models and generalised autoregressive conditional heteroskedasticity (GARCH) models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 (S&P 100) stock index series for which trading data (tick by tick) of almost 7 years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.     

Long-term asset tail risks in developed and emerging markets

A power law typically governs the tail decay of financial returns but the constancy of the so-called tail index which dictates the tail decay remains relatively unexplored. We study the finite sample properties of some recently proposed endogenous tests for structural change in the tail index. Given that the finite sample critical values strongly depend on the tail parameters of the return distribution we propose a bootstrap-based version of the structural change test. Our empirical application spans developed and emerging financial asset returns. Somewhat surprisingly, emerging stock market tails are not more inclined to structural change than their developed counterparts. Emerging currency tails, on the contrary, do exhibit structural shifts in contrast to developed currencies. Our results suggest that extreme value theory (EVT) applications in hedging tail risks can assume stationary tail behavior over long time spans provided one considers portfolios that solely consist of stocks or bonds.     

Long Memory and Forecasting in Euroyen Deposit Rates

We test for long memory in 3- and 6-month daily returns series on Eurocurrency deposits denominated in Japanese yen (Euroyen). The fractional differencing parameter is estimated using the spectral regression method. The conflicting evidence obtained from the application of tests against a unit root as well as tests against stationarity provides the motivation for testing for fractional roots. Significant evidence of positive long-range dependence is found in the Euroyen returns series. The estimated fractional models result in dramatic out-of-sample forecasting improvements over longer horizons compared to benchmark linear models, thus providing strong evidence against the martingale model.     

How does electronic trading affect efficiency of stock market and conditional volatility? Evidence from Toronto Stock Exchange

The present paper investigates informational efficiency and changes in conditional volatility of the TSX before and after the implementation of an automated trading system on April 23, 1997. Using a battery of unit root, stationarity, as well as linear tests, we find that the introduction of electronic trading led to an increase in linearity dependence in TSX daily returns. In addition, when we examined the nonlinearity dependences using powerful econometric tests, we find that electronic trading has increased nonlinear dependencies in return series, which is the main cause of rejecting the Random Walk Hypothesis (RWH). Our results suggest that the automated trading system has negatively affected informational efficiency of the TSX. We also find evidence of long memory following automation which suggests that the introduction of electronic trading has increased the level of persistence of information and trading shocks.     

True or spurious long memory in European non-EMU currencies

We examine the Croatian Kuna, the Czech Koruna, the Hungarian Forint, the Polish Złoty, the Romanian Leu, and the Swedish Krona whether their Euro exchange rates volatility exhibits true or spurious long memory. Recent research reveals long memory in foreign exchange rate volatility and we confirm this finding for these currency pairs by examining the long memory behavior of squared residuals by means of the V/S test. However, by using the ICSS approach we also find structural breaks in the unconditional variance. Literature suggests that structural breaks might lead to spurious long memory behavior. In a refined test strategy, we distinguish true from spurious long memory for the six exchange rates. Our findings suggest that Czech Koruna and Hungarian Forint only feature spurious long memory, while the rest of the series have both structural breaks and true long memory. Lastly, we demonstrate how to extend existing models to jointly model both properties yielding superior fit and better Value-at-Risk forecasts. The results of our work help to avoid misspecification and provide a better understanding of the properties of the foreign exchange rate volatility.     

Robust estimation of intraweek periodicity in volatility and jump detection

Opening, lunch and closing of financial markets induce a periodic component in the volatility of high-frequency returns. We show that price jumps cause a large bias in the classical periodicity estimators and propose robust alternatives. We find that accounting for periodicity greatly improves the accuracy of intraday jump detection methods. It increases the power to detect the relatively small jumps occurring at times for which volatility is periodically low and reduces the number of spurious jump detections at times of periodically high volatility. We use the series of detected jumps to estimate robustly the long memory parameter of the squared EUR/USD, GBP/USD and YEN/USD returns.     

Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19

In this paper, we study the long memory behavior of the hourly cryptocurrency returns during the COVID-19 pandemic period. Initially, we apply different tests against the spurious long memory, with the results indicating the presence of true long memory for most cryptocurrencies. Yet, using the multivariate test, the series are found to be contaminated by level shifts or smooth trends. Then, we adopt the wavelet-based multivariate long memory approach suggested by Achard and Gannaz (2016) to model their long memory connectivity. The findings indicate a change in persistence for all series during the sample period. The fractal connectivity clustering indicates a similarity among Ethereum (ETH) and Litecoin (LTC), Monero (XMR), Bitcoin (BTC), and EOC token (EOS), while Stellar (XLM) is clustered away from the remaining series, indicating the absence of any interdependence with other crypto returns. Overall, shocks arising from COVID-19 crisis have led to changes in long-run correlation structure.     

Accurate minimum capital risk requirements: A comparison of several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of short and long memory stochastic volatility and GARCH-type models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns’ series. The results suggest that accurate modelling of extreme observations obtained for long and short trading investment positions is possible with an autoregressive stochastic volatility model. Moreover, modelling futures returns with a long memory stochastic volatility model produces, in general, excessive volatility persistence, and consequently, leads to large minimum capital risk requirement estimates. Finally, the models’ predictive ability is assessed with the help of out-of-sample conditional tests.