T-statistic of correlation coefficient Hi I am trying to calculate the t-statistic for a correlation coefficient between two vectors $x$ and $y$.
The individual vectors shows signs of autocorrelation. I have made use of the formula:
$\frac{r}{\sqrt{(1-r^2)(n-2)}}$
but I'm not sure this is the correct way of solving the problem.
The correlation between the two vectors has been calculated with the Excel formula for correlation.
 A: If you should view your individual vectors as time series (because of the signs of autocorrelation you mentioned), you should be more interested in a cross-correlation function (ccf) of the two time series. This functions is essentially the product-moment correlation as a function of lag, or time-offset, between the series. This link contains the relevant details, including statistical significance of the ccf. The example considered is as follows:
Consider the two time series of annual tree-ring index plotted in Figure 1. The plots
suggest the series are positively correlated, but the year-to-year variations are too
noisy to visually judge whether one series tends to lead or lag the other. Both series,
however, appear to be positively autocorrelated, as positive departures from the mean
tend to follow positive departures, and negative departures tend to follow negative
departures. 

The link above makes a reference to the 6th edition of Chatfield's  The Analysis of Time Series masterpiece (and the 5th edition will have that material in chapter 8 entitled Bivariate Processes) if you want to read more on this. In particular, if a test is required for a non-zero correlation between two time series, both series must first be converted to white noise (the book will tell you how) and then the usual theory applies. 
A: The degrees of freedom is n-2. this lets you test for whether rho (the correlation coefficient) is 0 or not. so calculate this value, find the p value using the degrees of freedom and decide if the null hypothesis of correlation coefficient being 0 is significant or not.
The autocorrelation of the variables do not have any effect on the correlation coefficient of the variables unless you want to check out if the lag of one variable has any affect on the other which the question does not indicate. So leave the autocorrelation part.
