Bayesian statistical analysis of daily returns runs in Brazilian stock exchange


Abstract


In the financial market analysis, it is usual that the random variations in price movements share non-trivial statistical properties as return distributions, absence of autocorrelations in asset returns, volatility clustering and asymmetry between rises and falls. Most of fluctuations in asset prices have been deeply investigated using time series models to get inferences of interest and forecasting. In this paper, the main goal is, instead of using time series models in the data analysis it is considered the use of distributions for the run lengths and absolute run returns of historical price stated in NYSE stock exchange for three private banks located in Brazil in the period ranging from July,19 2013 to July, 19 2018 using discrete Weibull distributions as an alternative for the exponential law commonly used in this kind of analysis. Under this modeling approach it is possible to get information on the market structure as the probability of the stock-market is equally likely to go up and down everyday and the magnitude of returns, for example.

DOI Code: 10.1285/i20705948v16n2p192

Keywords: Discrete models, financial market, private banks, stock exchange, Weibull distributions.

References


Adrian, T. and Rosenberg, J. (2008). Stock returns and volatility: Pricing the short-run and long-run components of market risk. The

Journal of Finance, 63(6):2997–3030.

Akgiray, V. and Booth, G. G. (1987). Compound distribution models of stock returns: An empirical comparison. Journal of Financial Research, 10(3):269–280.

Almalki, S. J. and Nadarajah, S. (2014). A new discrete modified Weibull distribution. Reliability, IEEE Transactions on, 63(1):68–80.

Andersen, T. G., Bollerslev, T., Diebold, F. X., and Ebens, H. (2001). The distribution of realized stock return volatility. Journal of financial economics, 61(1):43–76.

Bartels, R. (1982). The rank version of von Neumann’s ratio test for randomness. Journal of the American Statistical Association, 77(377):40–46.

Brunello, G. and Nakano, E. (2015). Inferência Bayesiana no modelo Weibull discreto em dados com presença de censura. TEMA (São Carlos), 16(2):97–110.

Chib, S. and Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. The american statistician, 49(4):327–335.

Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues.

Easley, D., Kiefer, N. M., and O’Hara, M. (1997). One day in the life of a very common stock. Review of Financial Studies, 10(3):805–835.

Englehardt, J. D. and Li, R. (2011). The discrete Weibull distribution: An alternative for correlated counts with confirmation for microbial counts in water. Risk Analysis, 31(3):370–381.

Fama, E. F. (1965). The behavior of stock-market prices. The journal of Business, 38(1):34–105.

Gelfand, A. E. and Smith, A. F. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American statistical association, 85(410):398–409.

Good, P. I. (2006). Permutation, parametric, and bootstrap tests of hypotheses. Springer Science & Business Media.

Grafton, R. (1981). Algorithm AS 157: The runs-up and runs-down tests. Journal of the Royal Statistical Society. Series C (Applied Statistics), 30(1):81–85.

Khan, M. A., Khalique, A., and Abouammoh, A. (1989). On estimating parameters in a discrete Weibull distribution. Reliability, IEEE Transactions on, 38(3):348–350.

Kulasekera, K. (1994). Approximate MLE’s of the parameters of a discrete Weibull distribution with type I censored data. Microelectronics Reliability, 34(7):1185–1188.

Li, H. and Gao, Y. (2006). Statistical distribution of stock returns runs. In Econophysics of Stock and other Markets, pages 59–66. Springer.

Longin, F. M. (1996). The asymptotic distribution of extreme stock market returns. Journal of business, pages 383–408.

Mandelbrot, B. B. (1997). The variation of certain speculative prices. Springer.

Mann, H. B. (1945). Nonparametric tests against trend. Econometrica: Journal of the Econometric Society, pages 245–259.

Murthy, D. N. P., Bulmer, M., and Eccleston, J. A. (2004). Weibull model selection for reliability modelling. Reliability Engineering & System Safety, 86(3):257–267.

Nakagawa, T. and Osaki, S. (1975). The discrete Weibull distribution. IEEE Transactions on Reliability, 5:300–301.

Ohira, T., Sazuka, N., Marumo, K., Shimizu, T., Takayasu, M., and Takayasu, H. (2002). Predictability of currency market exchange. Physica A: Statistical Mechanics and its Applications, 308(1):368–374.

R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.

Roy, D. (2002). Discretization of continuous distributions with an application to stress-strength reliability. Bulletin of the Calcutta Statistical Association, 52(205-208):295–314.

Roy, D. (2004). Discrete Rayleigh distribution. Reliability, IEEE Transactions on, 53(2):255–260.

Sensoy, A. (2012). Analysis on runs of daily returns in Istanbul stock exchange. Journal of Advanced Studies in Finance (JASF), (2 (III):151–161.

Stockbridge, R. (2008). The discrete binomial model for option pricing. Program in Applied Mathematics.

Su, Y.-S. and Yajima, M. (2012). R2jags: A package for running jags from r. R package version 0.03-08, URL http://CRAN. R-project. org/package=R2jags.

Tucker, A. L. and Pond, L. (1988). The probability distribution of foreign exchange price changes: tests of candidate processes. The Review of Economics and Statistics, pages 638–647.


Full Text: pdf
کاغذ a4
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.