Fractional integration in the equity markets of MENA region

Abstract

A major issue in financial economics is the behaviour of stock market returns over long horizons. This article provides an empirical investigation of the long-range dependence in the emerging stock markets of Egypt, Jordan, Morocco and Turkey. We use the modified rescaled range statistic (R/S) proposed by Lo (1991) and the rescaled variance statistic (V/S) developed by Giraitis et al . (2003) to investigate the long memory in the returns and volatility. Significant long memory is demonstrated in the series and implies a fractal market structure in the Middle East and North African (MENA) equity markets. We further investigate whether the long memory is caused by a shift in variance. Interestingly, our findings indicate that the presence of long memory in volatility due to shifts in variance cannot be confirmed for these markets and are consistent with those results obtained by Lobato and Savin (1998) on other markets. Thus, our results should be useful to regulators, practitioners and derivative market participants in the MENA region, whose success depends on the ability to forecast stock price movements over long horizons.

Notes

¹ For further results on the evidence of long memory in international equity markets (including emerging markets) see Kiliç (2004), Vougas (2004), Gil-Alana and Caporale (2004), Tolvi (2003), Olan (2002), Byers and Peel (2001) and So (2000).

² Emerging markets have been studied by Moosa and Al-Saad (2005), Galariotis (2004), Fifield et al . (2002) and Kumar and Tsetsekos (1999). Studies related to the emerging markets of the Mediterranean include Harvey (1995), Bekaert and Harvey (1995, 1997), Errunza (1983, 1994) and Choudhry (1996). For an overview of the state of equity markets in some Middle Eastern countries, see El Erian and Kumar (1995).

³ Two other studies examine the efficiency of the Kuwaiti stock market: Al-Loughani (1995) and Al-Loughani and Moosa (1997).

⁴ This could be due to several factors such as poor-quality (low precision) information, high trading costs and/or less competition due to international investment barriers.

⁵ For issues related to market efficiency and organizational structure, look at Claessens et al . (1995) and Karemera et al . (1999) for Jordan and Turkey; Ghysels and Cherkaoui (2003) for Morocco and Appiah-Kusi and Menyah (2003) for Egypt and Morocco.

⁶ The IFC attributed a weight of 0.4% to the Morrocan index in the computation of the global emerging market index. This weight exceeds that of Egypt (0.1%) and some of the previously incorporated emerging markets such as Jordan (0.2%).

⁷ We provide a brief description of the estimator and the reader is referred to Robinson (1995a, b) for further explanation.

⁸ In other words, the 95% confidence interval with equal probabilities in both tails is [0.809, 1.862]. The fractiles are given in Lo (1991).

⁹ Having long memory (d > 0) in the series implies that the market would return to its long-term trend sometime in the future, but it may not get all the way back there. Having no long memory (d = 0) in the series implies that the market would not return to its long-term trend ever and if it did, it is by chance.

¹⁰ Another reason behind spurious long memory effect is aggregation. For example, Andersen and Bollerslev (1997) provide a justification for the result of long memory in index return volatility, even though conditional volatility of individual stocks exhibits short memory property. They assume that the underlying volatility process reflects the aggregate impact of N distinct information arrival processes and therefore the aggregate volatility process might behave like the long memory volatility process. Thus, even if the volatility of an individual stock displays the short memory property, the long memory property in the stock index can be observed because of aggregation.

¹¹ For R/S and V/S analysis, we only provide the results related to absolute returns. The results of applying the two tests to squared returns are available from the author upon request.

¹² Random walks help identify the kinds of shocks that drive stock prices and have an important bearing on the associated potential trading strategies, as is amply suggested by Poterba and Summers (1988) and Lo and Mackinlay (1989). If a given equity price series is, for instance, a random walk, the generating process is dominated by permanent components and hence has no mean-reversion tendency. A shock to the series from an initial equilibrium will lead to increasing deviations from its long-run equilibrium.