Statistical significance

[Cheezdoodles]

Gah, been a long time since i had a statistics course.

I need to check if a return series is significantly better than a market benchmarks return series. (The return series have different results, and different variance, all factors are known)

Anybody here know how i can do this?

Supposedly i need to do a t-test but i really dont remember which one etc.

 

[Mintmaster]

I know a reasonable amount of statistics and a few t-tests, but can you give me an example of what a "return series" and a "market benchmarks return series" are?

 

[Cheezdoodles]

Return series is basically just a time series of in this case monthly returns.

 

[Mintmaster]

Sorry, forgot about the thread. Did you figure it out already?

In any case, I'm not sure how valid it is to use monthly returns as a set of statistical data as opposed to a single data point due to the time value of money. IMO it makes sense to just calculate the present value of each series and compare the two numbers you get. Statistical significance would only come into play if you have a number of return series.

However, if you're set on using each monthly return as a data point, then you want to use a two sample t-test. I assume that both series are taken at the same time points, so you want the dependent t-test. Subtract the two series, multiply the mean by sqrt(N) and divide by standard deviation, and you have t. Now find a table with the CDF of the t-test for N-1 degrees of freedom, and find out what percentage you lie in.

Basically, this will tell you the probability that the mean monthly difference is greater than zero (under the assumption that the difference is normally distribuited), and "statistically significant" usually means that this needs to be >0.95.