# Determining the best correlated time series

I want to homogenize a climate time series of precipitation of the Dominican Republic over 64 years (1940-2003). For that, it is really important to select a reference series among a group of candidates.

Let's say sjo is the base series, for which I want to find a good reference series; bani, plc and ra are reference candidates, because they are close to sjo. In the following map, the red point is the base station, and the green ones are the reference candidates:

I performed three correlation analyses (done in R, function cor()), considering these monthly variables: raw precipitation value, normalized difference, and transformed values with Box-Cox. Those variables correspond, respectively, to fields that begin with p, dian and pnorm.

Normalized difference comes from the first difference series method (FDM), which was proposed by Peterson, consisting of: $[Pm_t - Pm_{t-1}] / [Pm_t + Pm_{t-1}]$, where $Pm_t$ is the precipitation value for the month $m$, and $Pm_{t-1}$ is the precipitation for the same month 1 year before. I followed Peterson and colleagues' (1998) remark, which says that FDM applied to precipitation might work better using normalized difference.

As can be seen in page 1 of this PDF file, correlation was calculated for the whole time series (1940-2003). For raw precipitation and Box-Cox transformed values, bani is the best correlated with sjo (yellow background cells shows the maximum correlation index). Notice that for raw precipitation, bani is significantly more correlated than others. For normalized difference, ra is only a bit more correlated than the rest. However, each candidate station has a statistically significant correlation index with sjo at the $\alpha=.05$ significance level, suggesting ANY of them could be used as a reference series.

This is a bit confusing, so I was unsatisfied and decided to make a more detailed analysis, splitting the series in 5-year period intervals, and evaluating correlation between series for the same 3 variables: raw precipitation, normalized difference and Box-Cox transformed.

Tables from page 2 to 8 in the PDF show the results of these partial correlations; the last page summarizes the times each station has had the maximum correlation value for each variable. As can be seen, bani is the most frequently correlated value for the 3 variables analyzed (in all cases, more than 7 times of the twelve 5-year periods analyzed).

With these results, I think that bani is the best candidate as a reference series of sjo, but I'm not sure about it. Is the five-year period analysis OK? Should I perform some other analysis?

• Thanks @Nick for corrections, I learned a lot from them. Sorry, English is not my mother tongue. – JoseRamon Mar 2 '14 at 14:08
• Glad to be of help :) Your work was already clearer than that of many native speakers! My changes were only cosmetic and technical, not essential. Welcome to CV BTW! – Nick Stauner Mar 2 '14 at 15:19
• the correlations are significant, but are the differences between these correlations different? if not, then you can't pick one reference station over another based on correlations – Aksakal Mar 2 '14 at 21:31
• Thanks @Aksakal for your comment. For the whole period analyzed, and exclusively for raw precipitation, 'sjo' (the base series) has this correlations indexes with reference candidates: 0.650 with 'bani', 0.536 with 'plc', and 0.557 with 'ra'. Is the largest index significantly greater than the next more correlated? Regarding to the other variables, normalized difference and Box-Cox transformed, difference are not large. Should I apply another analysis? What would you suggest me? – JoseRamon Mar 3 '14 at 1:04
• @JoseRamon, I can't answer these questions, you have the data. You can run the statistical tests to see whether the difference is significant – Aksakal Mar 3 '14 at 1:06