I understand statistical significance in the general sense: we take a sample from a population and compute some parameter from the sample to infer what is the propulsion parameter to some degree of confidence, usually 95%. So if I want to find the p-value for a slope between two financial datasets, say interest rates each quarter, then I’d compute the slope between the two sample datasets and find the p-value. Less than 5%, we conclude the slope arrived at is very unlikely to have occurred by random chance. Otherwise, we fail to reject the hypothesis that the population slope is 0.
Here’s my question… if we are dealing with 200 quarters of data, what exactly is our “population?” In the commonly used example of IQs, the population is easily defined as the IQs of ALL the people. With financial data, considering quarterly data, it isn’t clear to me what is the population. Is it all historical data dating back to as long as our interest rates, in our example, existed? So if there were actually 500 quarters where our interest rates existed, that’s the population of data? Is it all of the data measured more granularly? Our interest rate measured at every second, millisecond, etc.?
I’m asking because I’m a bit perplexed how a p-value can be interpreted if we find the p-value for a slope between two datasets of interest rates, both 200 quarters worth of data. The sampling distribution which is assumed to be normal makes sense when thinking of pulling a sample of IQs from the population of all IQs.. how does it work for pulling sample last from the population of our interest rate data?
Additionally and most importantly, the reason I’m interested in this is because I am calculating the rolling slopes 24 quarters at a time, moving by one quarter at a time. If I run a t test on each slope, most are highly insignificant. If I think of these slopes as not trying to ascertain the population slope, but as simply representing the sample slope, then I think the idea of significance goes out the window here. Right? Confusing!
Sorry for the long winded question… I want to be as clear as possible where I’m confused. As always thank you all.