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  • 1.
    Javed, Farrukh
    et al.
    Örebro University, Örebro University School of Business.
    Mazur, Stepan
    Örebro University, Örebro University School of Business.
    Ngailo, Edward
    Department of Mathematics, Linköping University, Linköping, Sweden.
    Higher order moments of the estimated tangency portfolio weights2020In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, , p. 18Article in journal (Other academic)
    Abstract [en]

    In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order non-central and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments.

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    Higher order moments of the estimated tangency portfolio weights
  • 2.
    Mantalos, Panagiotis
    et al.
    Department of Statistics, Lund University, Lund, Sweden.
    Shukur, Ghazi
    Department of Economics, Jönköping International Business School, Jönköping University, Jönköping, Sweden.
    The effect of spillover on the Granger causality test2010In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 37, no 9, p. 1473-1486Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate the properties of the Granger causality test in stationary and stable vector autoregressive models under the presence of spillover effects, that is, causality in variance. The Wald test and the WW test (the Wald test with White's proposed heteroskedasticity-consistent covariance matrix estimator imposed) are analyzed. The investigation is undertaken by using Monte Carlo simulation in which two different sample sizes and six different kinds of data-generating processes are used. The results show that the Wald test over-rejects the null hypothesis both with and without the spillover effect, and that the over-rejection in the latter case is more severe in larger samples. The size properties of the WW test are satisfactory when there is spillover between the variables. Only when there is feedback in the variance is the size of the WW test slightly affected. The Wald test is shown to have higher power than the WW test when the errors follow a GARCH(1,1) process without a spillover effect. When there is a spillover, the power of both tests deteriorates, which implies that the spillover has a negative effect on the causality tests.

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