Long memory in stock returns: evidence from the major emerging Central European stock markets

Abstract

This article analyses the long-memory properties of the daily stock market returns of four major emerging Central European countries, the Czech Republic, Hungary, Poland and the Slovak Republic. We use the semi-parametric method of Geweke and Porter-Hudak (1983) and parametric method of Sowell (1992). The results indicate a significant long memory in the return series of the Slovak Republic. The evidence of long memory in Hungary and the Czech Republic is, however weak. Poland is the only market exhibiting short memory. Since long-memory property is inconsistent with the market efficiency, there is still room for the investors to receive unexploited profits in the stock market of the Slovak Republic.

Notes

¹ Lo (1991), Crato (1994), Cheung and Lai (1995), Barkoulas and Baum (1996), Jacobsen (1996) and Tolvi (2003) provide no or little evidence on long memory in developed stock markets, whereas Sadique and Silvapulle (2001), Henry (2002) and Gil-Alana (2006) found long memory property in these markets.

² Barkoulas et al. (2000) for the Greek stock market; Sourial (2002) for the Egyptian stock market; Limam (2003) for the stock markets in eight Arab countries and Assaf (2006) for the stock markets in Egypt and Morocco. There are few studies, however in the literature which found little or no evidence for long memory in emerging stock returns [see for example, Wright (2001) and Kilic (2004)].

³ The Prague Stock Exchange has started trading on 5 April 1994; the Budapest Stock Exchange on 2 January 1991; the Warsaw Stock Exchange on 16 April 1991; the Bratislava Stock Exchange on 14 September 1993.

⁴ The number of listed companies in the Prague and Bratislava Stock Exchanges is relatively high at the beginning since most of the mass privatization program companies, often illiquid, experienced mandatory listing. Once the markets became more established, the illiquid companies were de-listed due to stronger regulatory environment.

⁵ Despite the significant growth, market capitalizations for the four CE countries are well under those of the Western European Exchanges. For example, market capitalization is 1 635 909 million US$ for Germany and 3 789 571 million US$ for the UK in 2006. The picture is similar regarding the market capitalization/GDP ratio, indicating the importance of the stock market for the economy. It is under 50% for four CE stock exchanges, whereas it is 53.9 for Germany and 152.1 for UK in 2006.

⁶ The Bratislava Stock Exchange has an insignificant capitalization due to the poor economic development and weak regulatory environment (Pajuste, 2001).

⁷ For market efficiency see for example, Filer and Hanousek (1996); Dockery and Vergari (1997); Zalewska-Mitura and Hall (1999); Gilmore and McManus (2003); Smith and Ryoo (2003); Worthington and Higgs (2004); Tsukuda et al. (2006). For long memory property see for example, Pajuste et al. (2000); Rockinger and Urga (2000, 2001); Mateus (2004), Cajueiro and Tabak (2006).

⁸ The integer values of d lead to the traditional ARIMA process.

⁹ Baillie (1996) provides an extensive review on the ARFIMA models and the estimation methods.

¹⁰  g(T) should satisfy the following conditions: lim _{T →∞}  g(T) and lim _{T →∞} g(T)/T = 0.

¹¹ The OLS variance of the error term can also be used to test for d = 0, however Geweke and Porter-Hudak (1983) propose to use the asymptotic variance to increase efficiency.

¹² The likelihood function in logarithmic form can be written as follows: where μ is the mean and σ² is the variance of the process, x is the T-dimensional vector of x_t , and Σ is the T × T autocovariance matrix.

¹³ We also used the traditional R/S statistic of Mandelbrot (1972) and the modified R/S statistic of Lo (1991) to test for long memory in the series. The findings are consistent with those of the GPH and ML methods. The detailed results are available from the authors upon request.

¹⁴ Geweke and Porter-Hudak (1983) suggest 0.50 and claim that as more number of ordinates is included in the spectral regression the reliability of the confidence intervals deteriorates. Diebold and Rudebusch (1989) also select the value of λ as 0.50 while Sowell (1992) claims that number of ordinates should be based on the shortest cycle associated with the long memory.