For my project, I want to determine if the yearly returns of some decile portfolios (calculated with the monthly returns over the last 50 years) are not significantly different from my predicted returns (based on my mathematical model). Initially, I had two ideas:
(1) My first thought was to assume all monthly returns are IID. Then I could easily argue with the CLT that the portfolio return will be approximately t-distributed and could calculate a confidence interval as well as a hypothesis test. However, this assumption is too strong for my purpose, especially while dealing with time series.
(2) My second thought was to use the Newey and West (1987) t-statistics which is well-used in papers with the emphasis on determining the predictive power of some factors on stock returns. Since the Newy-West procedure is used in regressions to obtain HAC standard errors, there would be the option to regress the monthly stock returns on a vector only consisting of ones (1,...,1) to obtain the intercept, which will equal to the sample mean. However, most papers refer to some lags (normally between 4 and 6), which I don't understand with my basic statistical knowledge. Also, I don't know how I can compute whether the sample mean is significantly different from my prediction based on the HAC standard errors in R.
I would greatly appreciate it if somebody could help me with the commands I should use in R. Or maybe, there would be even a better test to determine if my prediction is valid instead of simply computing if the sample mean is not significantly different from my prediction.
Any help would be desperately needed :D