[Question] How to apply the rules of correlation and linear regression to a data set constituting a discrete time series?
In other words, given a data set such as the following: 2002/1/1, 4500.63 2002/1/2, 10255.36 2002/1/8, 6530.63 2002/1/9, 5230.36 ... ... ... How to determine the regression line describing the overall trend of the time series? [Difficulty] Correlation coefficient, slope, intercept and standard deviation of the residuals are easy to calculate when both variables (X and Y) are numerical values from a continuous interval. Yet, how should I handle dates such as "2002/1/9"? How should I convert them to numerical values without altering the fundamental information they contain and represent? If I have 2 time series resulting from the observation of a same phenomenon, how should I build their respective regression line so that I may compare them? (granted that scales of measurements could be different and that dates at which those measurements are taken could be different) [Thoughts] I am trying to solve this problem programmatically. So, in a first attempt, I converted all dates to their number of millisecond since the epoch (January 1, 1970). I guess this should work. Yet, I came to doubt that solution because it seems arbitrary to pick an origin in such a fashion. So, I did a search on that topic and I was told to be able to compare 2 resulting regression lines I would have to standardize my data by using Z-scores instead of the raw values '2002/1/9' and '5230.36'. Is that true? (Yet, this advice does not tell me how to obtain a valid numerical representation of '2002/1/9' I could use to compute the Z- score of that date.) Brief, I am confused. PS: I am not interested in inferential statistics or forecasting. I am only interested in *describing* past data. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
