# How do I calculate a p-value for a strongly autocorrelated time series mean?

I have 522 observations of a time series that shows autocorrelation until about 150 lags. How do I test if the mean is significantly different from zero?

My idea was to fit an intercept-only regression model and then use the Newey-West adjusted variance to calculate a t-statistic, however I don't know what cutoff to use for say 95% confidence. It just doesn't seem right to use the standard normal cutoffs.

The series is a rolling compound return of financial returns. So for instance the first entry is returns from weeks 1 through 252.The second entry is 2 through 253, and so on, until there are 522 such entries. I am looking to test whether the mean of such a series is zero or not.

• This may help. – GeoMatt22 Apr 28 '17 at 17:22
• There is to little information here. What is the marginal distribution of the series? Could it be normal? If there are stretches of almost constant values (say, stretches of zeros) that could artificially increase the autocorrelations? Is the seroes stationary? Can you show us aplot of the series? – kjetil b halvorsen Apr 29 '17 at 8:47
• Thanks for the heads up. I added some details. There are stretches of near-constant values by construction since it's essentially a very slow moving average. – badmax May 1 '17 at 20:16