I'd like to approximate the covariance between goals in football dataset assuming they come from bivariate Poisson distribution. In previous works, which model the distribution of goals by bivariate Poisson process (i.e. http://tolstoy.newcastle.edu.au/R/e8/help/att-6544/karlisntzuofras03.pdf by Karlis and Ntzoufras or https://pdfs.semanticscholar.org/fca7/0c6bd99b082759c08c035a8ecc6a2cac15de.pdf by Koopman and Lit) the authors state, that the covariance is positive and equal approximately 0.1.
However, when I use the sample covariance estimator function on goal counts, I obtain negative values (-0.05 to -0.18, depending on the football league and time period). I am using the same dataset as Koopman and Lit in above paper.
I'm using the following formula for sample covariance:
$cov(X,Y)= \frac{1}{n-1}\sum (X_i-\overline{X})(Y_i-\overline{Y})$
Where do the differences come from?