Correlation between two sets of time series data

Question

I have an assignment to forecast snow depth at a certain location at a specific date. My approach to forecast this is to basically take previous years snowfall data and compare it to this years data so far. I need to figure out which snowfall pattern over the last 50 years is most correlated with this years pattern so far. I have matlab at my disposal and I have all the time series data but I don't know the best way to measure correlation between a certain years data and the current years data statistically.

I have thought about doing an absolute value difference between this years daily data and a given previous years, then averaging it to find the average difference. Whichever one has the smallest average difference will be the year I choose to base the prediction off of. I don't think this is the most accurate method though.

I am not very knowledgeable in statistics and want to be able to show that I used a statistically accurate method to measure correlation when I turn in my report.

Answer 1

Situations like yours are often treated using Exponential Smoothing. However, this works better if you have monthly data; if your data are daily, you may want to look through some of Rob Hyndman's work for extensions.

I strongly recommend this free online forecasting textbook, also by Hyndman.

Answer 2

Although beguiling the idea of "correlating" last years data with a particular year in the past to determine a good predictor is flawed at a number of levels. The correlation statistic , although contunued to be applied, is flawed when trying to characterize time series data http://www.math.mcgill.ca/~dstephens/OldCourses/204-2008/Handouts/Yule1926.pdf. Time Series was once approached ( and still is today ) as a way to use the history of the series as a predictor "ARIMA models". Others have attempted to force a specification of one trend and a set of seasonal coefficients, perhaps adapting in a presumed way and have employed Holt-Winters approaches. Modern time series suggests that there may be an ARIMA structure ( and it may have changed over time) AND there may have been 1 or more trends , 1 or more levels(intercepts), 1 or more points of change of the seasonal dummies and some 1 time anomalies http://www.unc.edu/~jbhill/tsay.pdf. Additionally the variance of the errors may have changed over time or there may be a relationship between the dispersion in the errors and the level of the series(Box-Cox). Packages like SAS, STATA, AUTOBOX ( which I am involved with as a developer ) to name a few provide implementations of some of the ideas I have laid out here.

Answer 3

A cross-correlation will be a better approach than your average absolute difference although there are some obvious problems to be wary of - if the current year has exactly twice the snow every day of some reference year it is perfectly correlated for example (this could still be useful info of course).

Your general approach is not a common one for forecasting in this situation, although it will not deliver insane results. Better ways would use the information in all 50 years efficiently, rather than just finding the "best" year and using that as a model. You may wish to do some more reading on forecast methods - there is plenty of Matlab-specific material on this on the web - although it quickly gets very complex.