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Journal articles on the topic 'Random Walk Hypothesis'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 May 2022

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1

GRAMATOVICI, Sorina, and Corina-Mihaela MORTICI. "RANDOM WALK HYPOTHESIS ON BUCHAREST STOCK EXCHANGE." Review of the Air Force Academy 16, no. 2 (October 31, 2018): 59–74. http://dx.doi.org/10.19062/1842-9238.2018.16.2.7.

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2

Shiller, Robert J., and Pierre Perron. "Testing the random walk hypothesis." Economics Letters 18, no. 4 (January 1985): 381–86. http://dx.doi.org/10.1016/0165-1765(85)90058-8.

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3

Beckmann, Martin J. "Speculation Under the Random Walk Hypothesis." Pacific Economic Review 7, no. 2 (June 2002): 221–27. http://dx.doi.org/10.1111/1468-0106.00160.

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4

Reschenhofer, Erhard. "Robust tests of the random walk hypothesis." Quantitative Finance 4, no. 6 (December 1, 2004): 57–60. http://dx.doi.org/10.1080/14697680500040322.

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5

Chu, Chia-Shang J., and Hsin-Min Lu. "Random walk hypothesis in exchange rate reconsidered." Journal of Forecasting 25, no. 4 (2006): 275–90. http://dx.doi.org/10.1002/for.988.

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6

Handa, Jagdish, and Barry K. Ma. "Four tests for the random walk hypothesis." Economics Letters 29, no. 2 (January 1989): 141–45. http://dx.doi.org/10.1016/0165-1765(89)90264-4.

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7

Tas, Oktay, and Cigdem Guleroglu Atac. "Testing random walk hypothesis for Istanbul stock exchange." Pressacademia 9, no. 9 (July 30, 2019): 48–53. http://dx.doi.org/10.17261/pressacademia.2019.1063.

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8

Akahori, Jirô, and Nien-Lin Liu. "Around the Random Walk Hypothesis on Interest Rates." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2010 (May 5, 2010): 206–10. http://dx.doi.org/10.5687/sss.2010.206.

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9

Pikoulakis, Emmanuel, and Terence C. Mills. "The random walk hypothesis of the exchange rate." Economics Letters 45, no. 2 (June 1994): 203–5. http://dx.doi.org/10.1016/0165-1765(94)90135-x.

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10

Sami, Janesh. "Random Walk Hypothesis for Stock Prices in Fiji." Asian Journal of Finance & Accounting 13, no. 2 (September 20, 2021): 79–88. http://dx.doi.org/10.5296/ajfa.v13i2.14674.

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The main goal of this paper is to investigate the random walk hypothesis in Fiji using monthly data from January 2000 to October 2017. Applying augmented Dickey Fuller (ADF 1979, 1981) and Phillips-Perron (1988), Zivot-Andrews (1992), and Narayan and Popp (2010) unit root tests, this study finds that stock prices is best characterized as non-stationary. The estimated multiple structural break dates in the stock prices corresponds with devaluation of Fijian dollar by 20 percent in 2009 and General Elections in September 2014, which Fiji First Party won by majority votes. The empirical results indicate that stock prices are best characterized as a unit root (random walk) process, indicating that the weak-form efficient market hypothesis holds in Fiji’s stock market. Hence, it will be difficult to predict future returns based on historical movement of stock prices in Fiji’s stock market.

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11

Kuhe, DA, and J. Akor. "An Empirical Investigation of the Random Walk Hypothesis in the Nigerian Stock Market." NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES 4, no. 1 (August 21, 2021): 62–77. http://dx.doi.org/10.46912/napas.229.

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The Random Walk Hypothesis (RWH) states that stock prices move randomly in the stock market without following any regular or particular pattern and as such historical information contained in the past prices of stocks cannot be used to predict current or future stock prices. Hence, stock prices are unpredictable and that investors cannot usurp any available information in the market to manipulate the market and make abnormal profits. This study empirically examines the random walk hypothesis in the Nigerian stock market using the daily quotations of the Nigerian stock exchange from 2nd January, 1998 to 31st December, 2019. The study employs Augmented Dickey-Fuller unit root test, the random walk model, Ljung-Box Q-statistic test for serial dependence, runs test of randomness, and the robust variance ratio test as methods of analyses. The result of the study rejected the null hypotheses of a unit root and random walk in the stock returns. The null hypothesis of no serial correlation in the residuals of stock returns was also rejected indicating the presence of serial correlation/autocorrelation in the residual series. The result of the runs test rejected the null hypothesis of randomness in the Nigerian stock returns. The results of the variance ratio test under homoskedasticity and heteroskedasticity assumptions both strongly rejected the null hypothesis of a random walk for both joint tests and test of individual periods. Based on the results of the four tests applied in this study, it is concluded that the Nigerian daily stock returns under the period of investigation do not follow a random walk and hence the null hypothesis of a random walk is rejected. The results of the study further revealed that the Nigerian stock market is weak-form inefficient indicating that prices in the Nigerian stock market are predictable, dependable, consistently mispriced, inflated, liable to arbitraging and left unprotected to speculations and market manipulations. The study provided some policy recommendations

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12

Haug, Alfred A. "The random walk hypothesis of consumption and time aggregation." Journal of Macroeconomics 13, no. 4 (September 1991): 691–700. http://dx.doi.org/10.1016/s0164-0704(05)80020-5.

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13

Nakamura, Tomomichi, and Michael Small. "Tests of the random walk hypothesis for financial data." Physica A: Statistical Mechanics and its Applications 377, no. 2 (April 2007): 599–615. http://dx.doi.org/10.1016/j.physa.2006.10.073.

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14

Mishra, Ankita, Vinod Mishra, and Russell Smyth. "The Random-Walk Hypothesis on the Indian Stock Market." Emerging Markets Finance and Trade 51, no. 5 (August 25, 2015): 879–92. http://dx.doi.org/10.1080/1540496x.2015.1061380.

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15

Lifshits, Mikhail, and Michel Weber. "Sampling the Lindelöf Hypothesis with the Cauchy random walk." Proceedings of the London Mathematical Society 98, no. 1 (June 24, 2008): 241–70. http://dx.doi.org/10.1112/plms/pdn026.

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16

Choi, In. "Testing the random walk hypothesis for real exchange rates." Journal of Applied Econometrics 14, no. 3 (May 1999): 293–308. http://dx.doi.org/10.1002/(sici)1099-1255(199905/06)14:3<293::aid-jae503>3.0.co;2-5.

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17

MacDonald, R., and D. A. Peel. "The velocity of money and the random walk hypothesis." Economics Letters 20, no. 1 (January 1986): 63–66. http://dx.doi.org/10.1016/0165-1765(86)90082-0.

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18

Shlesinger, Michael F. "On the Riemann hypothesis: A fractal random walk approach." Physica A: Statistical Mechanics and its Applications 138, no. 1-2 (September 1986): 310–19. http://dx.doi.org/10.1016/0378-4371(86)90187-1.

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19

Roy, Subrata. "Testing Random Walk and Market Efficiency: A Cross-Stock Market Analysis." Foreign Trade Review 53, no. 4 (October 8, 2018): 225–38. http://dx.doi.org/10.1177/0015732518797183.

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The study seeks to examine the Random Walk Hypothesis (RWH) and market efficiency of the selected stock market indices particularly London Stock Exchange, EuroStoxx 50, Nihon Keizai Shimbum (NIKKI), Shanghai Composite Stock Exchange and Bombay Stock Exchange. Daily closing index value is considered and transformed into logarithm return. Various tests like serial independence test, unit root test and multiple variance tests are applied. It is observed that the null hypotheses (presence of random walks) of the daily returns of the indices are rejected and in few cases are accepted based on various test statistics. JEL Classification: G00, G01, G02

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20

Anam Hassan, Syeda. "Examination of Random Walk Hypothesis in Beverages Sector of Pakistan." Journal of Economic Info 1, no. 2 (April 30, 2014): 1–3. http://dx.doi.org/10.31580/jei.v1i2.107.

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The objective of the study is to examine the random walk hypothesis in three largest industries of Pakistan namely, Murree Brewery, Shezan International and Nirala MSR Foods limited. The results show that Bevarges sector do not follow the Random Walk Hypothesis. The results conclude that investors may predict the future outcome of stocks. The risk minimization strategy and profitable mode to purchase share of Shehzan International especially in the start of every month and sell them in end days of month.

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21

Bam, Nirajan, Rajesh Kumar Thagurathi, and Bipin Shrestha. "Stock Price Behavior of Nepalese Commercial Banks: Random Walk Hypothesis." Journal of Business and Management 5 (December 1, 2018): 42–52. http://dx.doi.org/10.3126/jbm.v5i0.27387.

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Using the data set on daily stock prices during the fiscal year 2015/16 (Sept 23, 2015 through Dec 22, 2015), this paper attempts to analyze the random behavior of stock price of Nepalese Commercial Banks by using run test, serial correlation and run tests and martingale random walk hypothesis under heteroscedasticity assumption of standard error. The results conclude that the proposition of Random Walk Hypothesis (RWH) in Nepalese stock markets does not hold true. This conclusion corroborates with the conclusions of the past studies carried out in Nepalese context.

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22

Bookstein, Fred L. "Random walk and the existence of evolutionary rates." Paleobiology 13, no. 4 (1987): 446–64. http://dx.doi.org/10.1017/s0094837300009039.

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Before one can study evolutionary rates one must reject the null model of symmetric random walk. for which the requisite quantity does not exist. As random walks reliably simulate all the features we find so compelling in the fossil record—jumps, trends, and irregular cycles—rejection of this irritating hypothesis is much more difficult than one might hope. This paper reviews principal theorems from the mathematical literature of random walk and shows how they may be applied to empirical data by scaling net changes according to the square root of elapsed time. The notorious pair of “opposite” findings, equilibrium and anagenesis, may be construed as deviations from random walk in opposite directions. Malmgren's data on Globorotalia tumida, previously interpreted as an example of punctuated anagenesis, are consistent with a random walk showing neither punctuation nor anagenesis, but instead varying in speed over four subsequences.

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23

Obayagbona, Joel, and Sunday Osaretin Igbinosa. "Test of Random Walk Hypothesis in the Nigerian Stock Market." Current Research Journal of Social Sciences 7, no. 2 (April 25, 2015): 27–36. http://dx.doi.org/10.19026/crjss.7.5220.

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24

Kim, Tae Yoon, Cheolyong Park, Seul Gee Kim, Chan Jin Kim, Hyun Kim, Ju Hyung Yu, Kyung Min Jang, and Young Seok Jang. "A sign test for random walk hypothesis based on slopes." Journal of the Korean Data and Information Science Society 25, no. 2 (March 31, 2014): 385–92. http://dx.doi.org/10.7465/jkdi.2014.25.2.385.

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25

Darrat, Ali F., and Maosen Zhong. "On Testing the Random-Walk Hypothesis: A Model-Comparison Approach." Financial Review 35, no. 3 (August 2000): 105–24. http://dx.doi.org/10.1111/j.1540-6288.2000.tb01423.x.

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26

Smith, Graham. "Tests of the random walk hypothesis for London gold prices." Applied Economics Letters 9, no. 10 (August 1, 2002): 671–74. http://dx.doi.org/10.1080/1350485021012458.

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27

Bahi, Sa�d, and Sa�d Bahi. "RANDOM WALK HYPOTHESIS: AN INVESTIGATION OF THE CASABLANCA STOCK RETURNS." International Journal of Business Research 15, no. 5 (December 20, 2015): 99–104. http://dx.doi.org/10.18374/ijbr-15-5.9.

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28

Poshakwale, Sunil. "The Random Walk Hypothesis in the Emerging Indian Stock Market." Journal of Business Finance Accounting 29, no. 9&10 (November 2002): 1275–99. http://dx.doi.org/10.1111/1468-5957.00469.

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29

Semenov, Andrei. "Testing the random walk hypothesis through robust estimation of correlation." Computational Statistics & Data Analysis 52, no. 5 (January 2008): 2504–13. http://dx.doi.org/10.1016/j.csda.2007.08.016.

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30

Chitenderu, Tafadzwa T., Andrew Maredza, and Kin Sibanda. "The Random Walk Theory And Stock Prices: Evidence From Johannesburg Stock Exchange." International Business & Economics Research Journal (IBER) 13, no. 6 (October 31, 2014): 1241. http://dx.doi.org/10.19030/iber.v13i6.8918.

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In this paper, we test the Johannesburg Stock Exchange market for the existence of the random walk hypothesis using monthly time series of the All Share Index (ALSI) covering the period 2000 2011. Traditional methods, such as unit root tests and autocorrelation test, were employed first and they all confirmed that during the period under consideration, the JSE price index followed the random walk process. In addition, the ARIMA model was constructed and it was found that the ARIMA (1, 1, 1) was the model that most excellently fitted the data in question. Furthermore, residual tests were performed to determine whether the residuals of the estimated equation followed a random walk process in the series. The authors found that the ALSI resembles a series that follow random walk hypothesis with strong evidence of a wide variance between forecasted and actual values, indicating little or no forecasting strength in the series. To further validate the findings in this research, the variance ratio test was conducted under heteroscedasticity and resulted in non-rejection of the random walk hypothesis. It was concluded that since the returns follow the random walk hypothesis, it can be said that JSE, in terms of efficiency, is on the weak form level and therefore opportunities of making excess returns based on out-performing the market is ruled out and is merely a game of chance.

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31

Boutabba, Islem. "Testing financial market efficiency." JOURNAL OF SOCIAL SCIENCE RESEARCH 4, no. 2 (June 4, 2014): 548–63. http://dx.doi.org/10.24297/jssr.v4i2.3151.

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Since the birth of the financial literature until the 1970s, the efficient market hypothesis has been regarded as a central hypothesis. In the mid-1970s, there were theoretical and empirical evidence stating that the EMH seems untouchable. However, recently there has been an emergence of arguments doubting the EMH. The EMH implicitly indicates that stock prices can follow a random walk. Currently, financial theory has shown that stock prices do not follow a random walk. In this regard, our empirical study rejected the hypothesis of a random walk for 27 indices out of 28 studied. We confirm that the studied indices time series do not follow a random walk, and therefore we reject the financial markets efficiency hypothesis in its weak form. This result corroborates those of Fama and French (1992.993), DeBondt and Thaler (1985), Lo and MacKinlay (1991), Jagadeesh and Titman (1993) and Shleifer and Vishny (1997). Therefore, financial markets efficiency hypothesis in its weak form is also rejected. This result is logical given the limited capacity of the classical theory in explaining abnormal returns such as bubbles, crashes and excess volatility.

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32

Thonse Hawaldar, Iqbal, Babitha Rohit, and Prakash Pinto. "Testing of weak form of efficient market hypothesis: evidence from the Bahrain Bourse." Investment Management and Financial Innovations 14, no. 2 (August 21, 2017): 376–85. http://dx.doi.org/10.21511/imfi.14(2-2).2017.09.

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Efficient market hypothesis (EMH) states that financial markets are “informationally efficient”, implying that current prices fully reflect all available information. The present study aims at testing the weak form of market efficiency of the individual stocks listed on the Bahrain Bourse for the period 2011 to 2015. Weak form of EMH is tested using the Kolmogorov-Smirnov goodness of fit test, run test and autocorrelation test. The K-S test result concludes that in general the stock price movement does not follow random walk. The results of the runs test reveals that share prices of seven companies do not follow random walk. Autocorrelation tests reveal that share prices exhibit low to moderate correlation varying from negative to positive values. As the study shows mixed results, it is difficult to conclude the weak form of efficiency of Bahrain Bourse.

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33

Boutabba, Islem Ahmed. "Testing financial market efficiency." JOURNAL OF SOCIAL SCIENCE RESEARCH 3, no. 3 (April 30, 2014): 351–72. http://dx.doi.org/10.24297/jssr.v3i3.3264.

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Since the birth of the financial literature until the 1970s, the efficient market hypothesis has been regarded as a central hypothesis. In the mid-1970s, there were theoretical and empirical evidence stating that the EMH seems untouchable. However, recently there has been an emergence of arguments doubting the EMH. The EMH implicitly indicates that stock prices can follow a random walk. Currently, financial theory has shown that stock prices do not follow a random walk.In this regard, our empirical study rejected the hypothesis of a random walk for 27 indices out of 28 studied. We confirm that the studied indices time series do not follow a random walk, and therefore we reject the financial markets efficiency hypothesis in its weak form. This result corroborates those of Fama and French (1992.993), DeBondt and Thaler (1985), Lo and MacKinlay (1991), Jagadeesh and Titman (1993) and Shleifer and Vishny (1997). Therefore, financial markets efficiency hypothesis in its weak form is also rejected. This result is logical given the limited capacity of the classical theory in explaining abnormal returns such as bubbles, crashes and excess volatility

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34

Roy, Subrata. "Testing Random Walk Hypothesis and Volatilities of SRI and Traditional Indices." IIMS Journal of Management Science 8, no. 3 (2017): 296. http://dx.doi.org/10.5958/0976-173x.2017.00022.7.

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35

Iancu, Alexie Ciprian Alupoaiei, and Ana-Maria Săndică. "Testing Random Walk Hypothesis for Romanian Consumption: A Continuous Time Approach." Procedia Economics and Finance 15 (2014): 228–37. http://dx.doi.org/10.1016/s2212-5671(14)00490-0.

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36

Kumbhakar, Manotosh, Koeli Ghoshal, and Vijay P. Singh. "Renyi Entropy and Random Walk Hypothesis to Study Suspended Sediment Concentration." Journal of Hydrologic Engineering 22, no. 8 (August 2017): 04017027. http://dx.doi.org/10.1061/(asce)he.1943-5584.0001546.

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37

Dockery, E., and F. Vergari. "Testing the random walk hypothesis: evidence for the Budapest stock exchange." Applied Economics Letters 4, no. 10 (October 1997): 627–29. http://dx.doi.org/10.1080/758533288.

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38

Fadda, Sadi. "Testing the random walk hypothesis of stock indexes through variance-ratio." Periodicals of Engineering and Natural Sciences (PEN) 7, no. 1 (February 13, 2019): 12. http://dx.doi.org/10.21533/pen.v7i1.212.

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39

SMITH, WILLIAM T. "BIRTH, DEATH, AND CONSUMPTION: OVERLAPPING GENERATIONS AND THE RANDOM WALK HYPOTHESIS." International Economic Journal 12, no. 4 (December 1, 1998): 105–16. http://dx.doi.org/10.1080/10168739800080032.

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40

Blasco, Natividad, Cristina Del Rio, and Rafael Santamaria. "The Random Walk Hypothesis in the Spanish Stock Market: 1980-1992." Journal of Business Finance Accounting 24, no. 5 (June 1997): 667–84. http://dx.doi.org/10.1111/1468-5957.00128.

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41

Frennberg, Per, and Björn Hansson. "Testing the random walk hypothesis on Swedish stock prices: 1919–1990." Journal of Banking & Finance 17, no. 1 (February 1993): 175–91. http://dx.doi.org/10.1016/0378-4266(93)90087-t.

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42

Urrutia, Jorge L. "Time Series Properties of four Latin American Equity Markets: Argentina, Brazil, Chile and Mexico." Estudios de Administración 1, no. 2 (March 4, 2020): 1. http://dx.doi.org/10.5354/0719-0816.1994.56689.

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Variance ratio tests indicate that the equity markets of Argentina, Brazil and Mexico follow random walks, but not those of Chile. The low correlations among the four markets suggest that investments in these countries can contribute to reduce portfolio risk. The research on the random walk hypothesis has been heavily concentrated on the large equity markets of the United States, Canada, Japan and Europe (summers 1986; Fama and French 1986a, 1986b; Lo and MacKinlay 1988, and Poterba and Summers 1988). Even though some studies have been conducted for stock markets of developing countries (Errunza 1983 and Errunza and Losq 1985), little research has been done in Latin American capital markets (Errunza and Losq 1987). This paper employs the variance-ratio test to investigate the random walk hypothesis for the following four Latin American equity markets: Argentina, Brazil, Chile and Mexico. Two versions of the variance-ratio tests are implemented : first, the variance-ratio under the maintained hypothesis of homocedasticity and, second, the heteroscedasticity-robust variance-ratio. The empirical results reported in the paper indicate that the random walk hypothesis is rejected for Chile but it is generally confirmed for Argentina, Brazil and Mexico. Therefore, American investors might not be able to develop investment strategies that can be generate abnormal returns in these three countries. However, the low correlation among these markets suggests that American investors can reduce the risk of their portfolios by diversifying in international stocks of these countries.

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43

HASAN, MOHAMMAD S. "ON THE VALIDITY OF THE RANDOM WALK HYPOTHESIS APPLIED TO THE DHAKA STOCK EXCHANGE." International Journal of Theoretical and Applied Finance 07, no. 08 (December 2004): 1069–85. http://dx.doi.org/10.1142/s0219024904002797.

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This paper employs a battery of statistical tests to examine the random walk variant of the weak-form efficient market hypothesis (EMH) using the daily data of the Dhaka Stock Exchange, the major equity market of Bangladesh, over a period of January 1990 to December 2000. The test results, however, are at variance across testing procedures and sub-periods. Results based on the random walk model and unit root tests show that the null hypothesis of randomness cannot be rejected and stock prices have a significant random walk or permanent component. Our analysis of autocorrelation functions indicates mean-reversion behavior of stock returns in most cases albeit with stock returns exhibiting some memory and predictable components during the bubble and post-speculation periods. The evaluation of the EGARCH-M model suggests significant asymmetric and leverage effects during the sub-period of speculative bubbles of 1996–1997. The BDS test indicates evidence of nonlinear long-term dependence during the pre-speculation period, while during the speculation and post-speculation periods the null hypothesis of nonlinear independence was not rejected. Overall, based on this evidence we do not categorically claim that the Dhaka Stock Exchange is weak-form efficient. However, these findings underscore the predictive significance and relevance of the random walk hypothesis as a generalized theory in explaining movements of share prices.

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44

LeClair, André. "Riemann Hypothesis and Random Walks: The Zeta Case." Symmetry 13, no. 11 (October 23, 2021): 2014. http://dx.doi.org/10.3390/sym13112014.

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In previous work, it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its L-function is valid to the right of the critical line ℜ(s)>12, and the Riemann hypothesis for this class of L-functions follows. Building on this work, here we propose how to extend this line of reasoning to the Riemann zeta function and other principal Dirichlet L-functions. We apply these results to the study of the argument of the zeta function. In another application, we define and study a one-point correlation function of the Riemann zeros, which leads to the construction of a probabilistic model for them. Based on these results we describe a new algorithm for computing very high Riemann zeros, and we calculate the googol-th zero, namely 10100-th zero to over 100 digits, far beyond what is currently known. Of course, use is made of the symmetry of the zeta function about the critical line.

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45

Nkemnole, Edesiri. "A Hidden Markov Model inference approach to testing the Random Walk Hypothesis: Empirical evidence from the Nigerian Stock Market." Journal of Economic and Financial Sciences 9, no. 3 (December 3, 2016): 696–713. http://dx.doi.org/10.4102/jef.v9i3.66.

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The movement of stock prices, in capital markets across the world, has been found to be both random and non-random. Basically, for a stock price to follow a random walk, its future price changes randomly based on all currently available information in the stock market, its price history inclusive. Some research findings have shown that the existing traditional unit root tests have low statistical power and hence cannot capture gradual changes over successive observations. Consequently, there is a need to revisit the random walk theory in stock prices using other tests. This study employs a Hidden Markov Model (HMM) with time-varying parameters to assess whether the stock price movements of the Nigerian Stock Exchange (NSE) follow a random walk process, or otherwise. Via hidden states, the HMM allows for periods with different volatility levels characterised by the hidden states. By simply accounting for the non-constant variance of the data with a two-state Hidden Markov Model and taking estimation into account via the Sequential Monte Carlo Expectation Maximisation (SMCEM) technique, this study finds no support of randomness. In conclusion, the stock price movements of the NSE do not follow the random walk process.

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46

MOLLAH, A. SABUR. "TESTING WEAK-FORM MARKET EFFICIENCY IN EMERGING MARKET: EVIDENCE FROM BOTSWANA STOCK EXCHANGE." International Journal of Theoretical and Applied Finance 10, no. 06 (September 2007): 1077–94. http://dx.doi.org/10.1142/s021902490700455x.

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Market efficiency is an area of enormous interest in financial literature. Numerous researchers conducted empirical studies in testing weak-form market efficiency in several stock markets and employed various techniques but the empirical evidence is controversial. Triangulation econometric approach is employed to assess the predictability of daily return series of Botswana Stock Exchange (BSE) and to test the null hypothesis of random walk model. The empirical results reject the null hypothesis of random walk model for the daily return series of BSE for the period of 1989–2005 and evidenced serial autocorrelation of return series, which clearly indicate predictability and volatility of security prices of Botswana market. However, the empirical evidence of both non-parametric (Kolmogrov–Smirnov: normality test and run test) and parametric test (Auto-correlation test, Auto-regressive model, ARIMA model) reject the hypothesis of random walk model and indeed violate the notion of weak-form market efficiency.

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47

Kim, Tae Yoon, Cheolyong Park, Seul Gee Kim, Min Seok Kim, Woo Jung Lee, and Yunji Kwon. "A Wilcoxon signed-rank test for random walk hypothesis based on slopes." Journal of the Korean Data and Information Science Society 25, no. 6 (November 30, 2014): 1499–506. http://dx.doi.org/10.7465/jkdi.2014.25.6.1499.

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48

Kitazawa, Shigeru. "Optimization of goal-directed movements in the cerebellum: a random walk hypothesis." Neuroscience Research 43, no. 4 (August 2002): 289–94. http://dx.doi.org/10.1016/s0168-0102(02)00058-5.

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Hall, Alastair. "JOINT HYPOTHESIS TESTS FOR A RANDOM WALK BASED ON INSTRUMENTAL VARIABLE ESTIMATORS." Journal of Time Series Analysis 13, no. 1 (January 1992): 29–45. http://dx.doi.org/10.1111/j.1467-9892.1992.tb00093.x.

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Yan, Rongguo, and Lingxiang Zhang. "Linearity tests under the null hypothesis of a random walk with drift." Statistical Papers 57, no. 2 (January 20, 2015): 407–18. http://dx.doi.org/10.1007/s00362-015-0659-1.

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