(BLANK) is to a Simple Moving Average Line what R-squared is to a Linear Regression Line?

Question

In other words, where x=time in days in the linear regression equation, y=mx+b, and R-squared instructs us on the relationship of time and our values along our linear regression line, is there something similar to R-squared to measure the relationship of time and a simple moving average line?

Stated otherwise, I can do a simple R-squared analysis each day and find the linear regression trendline which is best explained by time (i.e., 125 days has a R-squared of .97 whereas a 27 day period has an R-squared value of .00). Is there a similar test I can perform, then, to determine which moving average model (time series) is best suited for my data each day?

Would the best moving average model actually be the converse of the best linear regression model? In other words, if a 27 day period has an R-squared value of 0, it's essentially a straight horizontal line. As a result, the prediction intervals at .05 etc., both above and below, also tend to be fixed horizontal lines.

What I meant by the last paragraph is that if there is essentially no linear relationship between x and y over 27 days, it's Simple Moving Average tends to be a straight horizontal line and, therefore, the Prediction and Confidence Intervals would also seem to be steady for prediction purposes. Thanks for your thoughts.

Answer 1

Wow, hope you get some help on this one, I've always been horrible at math - sorry!