The main objective of this study is to propose a method of analysing the volatility of a seemingly random walk time series with correlated errors without transforming the series as performed traditionally. The proposed method involves the computation of moving volatilities based on sliding and cumulative data matrices. Our method rests on the assumption that the number of subperiods for which the series is available is the same for all periods and on the assumption that the series observations in each subperiod for all the periods under consideration are a random sample from a particular distribution. The method was successfully implemented on a simulated dataset. A paired sample
t
-test, Wilcoxon signed rank test, repeated measures (ANOVA), and Friedman tests were used to compare the volatilities of the traditional method and the proposed method under both sliding and cumulative data matrices. It was found that the differences among the average volatilities of the traditional method and sliding and cumulative matrix methods were insignificant for the simulated series that follow the random walk theorem. The implementation of the method on exchange rates for Canada, China, South Africa, and Switzerland resulted in adjudging South Africa to have the highest fluctuating exchange rates and hence the most unstable economy.
In this paper, we apply Markov chain techniques to select the best financial stocks listed on the Ghana Stock Exchange based on the mean recurrent times and steady-state distribution for investment and portfolio construction. Weekly stock prices from Ghana Stock Exchange spanning January 2017 to December 2020 was used for the study. A three-state Markov chain was used to estimate the transition matrix, long-run probabilities, and mean recurrent times for stock price movements from one state to another. Generally, the results revealed that the long-run distribution of the stock prices showed that the constant state recorded the highest probabilities as compared to the point loss and point gain states. However, the results showed that the mean recurrent time to the point gain state ranges from three weeks to thirty-five weeks approximately. Finally, Standard Chartered Bank, GCB, Ecobank, and Cal Bank emerged as the top best performing stocks with respect to the mean recurrent times and steady-state distribution, and therefore, these equities should be considered when constructing asset portfolios for higher returns.
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