In section 10.4 of the Momentum Trading Strategies course, you state that the Null Hypothesis is "Past and future returns are not correlated". But the null hypothesis is defined as the hypothesis that there is no significant difference between specified populations, and any observed difference is due to sampling or experimental error. A significant p-value (say < 0.05) means you can reject the null hypothesis and infer that the two populations are different. In other words, a null hypothesis is a hypothesis that two things are the same but if the p-value is small, then differences are significant and we can infer that they are not the same. Statistics often comes down to testing the significance of the difference.
If the returns are correlated, they would come from the same population, and the null hypothesis would not be rejected. This is the opposite of what you are saying. Can anyone help me to understand this? Thank you!
We are using the pearsonr method of scipy library to calculate a correlation coefficient and the p-value for testing non-correlation. According to scipy documentation, the p-value roughly indicates the probability of an uncorrelated system.
Using the scipy document basis, our null hypothesis is past and future returns are not correlated, and alternate hypothesis is past, and future returns are correlated. If the p-value is below significance level (0.1 or 0.005 or 0.001…) then we can reject the null hypothesis 90% or 95% or 99% (depends on the significance level) confidence level that past and future returns are not correlated, or we can accept the alternate hypothesis with the same confidence level.