The persistence and asymmetric volatility in the Nigerian stock bull and bear markets OlaOluwa S. Yaya a,1 , Luis A. Gil-Alana b, ⁎ ,1 a Department of Statistics, University of Ibadan, Ibadan, Nigeria b Faculty of Economics and ICS, University of Navarra, Spain abstract article info Article history: Accepted 10 January 2014 Available online 22 February 2014 JEL classification: G1 C22 Keywords: Asymmetry Market phase Nigerian All Share Index: persistence This paper considers the persistence and asymmetric volatility at each market phase of the Nigerian All Share Index (ASI). The estimate of the fractional difference parameter is used as a stability measure of the degree of per- sistence in the level of the series and in the absolute/squared returns, which are used as proxies for the volatility. Both semi-parametric and parametric methods are applied. Forms of Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models, which include fractional integration and asymmetric variants are estimated at each market phase of the stock returns. The results show that the level of persistence differs between the two market phases in both level and squared/absolute return series. Apart from general asymmetry and persis- tence in Nigerian stocks, each market phase still presents significant persistence and asymmetry. © 2014 Elsevier B.V. All rights reserved. 1. Introduction This paper deals with the analysis of persistence and volatility in the bull and bear phases of the Nigerian stock index. The world is currently experiencing one of its worst bear markets since the Great Depression and thus there is an even greater need to study past bull and bear mar- kets in order to make long-term decisions about stock market invest- ment. We assume that financial markets are classified into bull and bear phases, and each market phase is a regime being driven by certain market forces. These market forces create bad news provoking panic and causing investors to hastily sell off stocks. When there is no more bad news, markets bounce back. Bull markets occur when a series of good news stories generate optimism in the mind of the investors who therefore retain stocks, whereas bear markets occur when a series of bad news generates pessimism and they rapidly sell off stocks. In stock markets, bull and bear markets correspond to periods of generally increasing and decreasing market prices respectively, and recent research has shown that bull markets persist longer than bear markets (Gil-Alana et al., 2014; Lunde and Timnermann, 2004; Pagan and Sossounov, 2003). Following Wiggins (1992), the market index gives a critical threshold value, which separates “up” (bull) markets from “down” (bear) markets. Granger and Silvapulle (2001) separate the market into bullish and bearish periods. Since bull markets last longer than bear markets, it is of interest to examine the extent of the persistence based on the estimates of the fractional difference parame- ter for both the level and the absolute and squared return series in each market phase. Due to the fact that the periods for the two market phases are not equal, the issue of the asymmetry in each of the market phases becomes relevant as well. Acemoglu and Scott (1993, 1994) claim that whenever there is internally increasing returns, both agents and the economy respond differently to the same shocks at different stages of the cycle, and thus leads to artificial asymmetries. These asymmetries imply that the summary statistics of the stochastic behaviour of any variable (e.g. mean, measure of persistence, and conditional variance), all need to be conditioned on the state of the business cycle. There are many papers in the literature identifying bull and bear phases, and these provide different definitions. Fabozzi and Francis (1977, 1979) use bull and bear market dates published later in Cohen et al. (1987) to classify their data into bull and bear categories, and Gooding and O'Malley (1977) applied that method in classifying the S&P425 index. Dukes et al. (1987) define the market phases as periods in which the index increased (decreased) by at least 20% from a trough (peak) to a peak (trough) for the bull and bear periods respectively. Pagan and Sossounov (2003) and Lunde and Timnermann (2004) de- veloped trend-based methodologies for the identification of market phases, and an algorithm to detect the market phases is given specifical- ly in Pagan and Sossounov (2003). Gil-Alana et al. (2014) identified bull and bear market phases in Asian, American and European markets using the algorithm of Pagan and Sossounov (2003) and the 20% definition given in Dukes et al. (1987). In the three markets, one peak and two troughs were detected meaning two bull and two bear phases. Volatility modelling has been Economic Modelling 38 (2014) 463–469 ⁎ Corresponding author at: University of Navarra, Edificio Amigos, E-31080 Pamplona, Spain. E-mail addresses: os.yaya@ui.edu.ng (O.S. Yaya), alana@unav.es (L.A. Gil-Alana). 1 Comments from the Editor and two anonymous referees are gratefully acknowledged. 0264-9993/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.econmod.2014.01.004 Contents lists available at ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/ecmod