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I am looking at finding correlations between house price time series and the time series of multiple indicators in an area. For example

enter image description here enter image description here

These two trends clearly show a sort of strong negative correlation.

Other indicators in this example could be income (expected positive correlation), crime (expected weak negative correlation), number of pizzas I've eaten that month (expected zero correlation).

I've read that cross-correlation if the method used to find a correlation between stationary time series but these are clearly non-stationary.

This is where I'm getting confused. Is it correct to detrend e.g. take the residual part of this plot:

enter image description here

and then perform cross-correlation on this, providing that it is stationary enough?

I'm struggling to believe this as I feel that if we do this, we're ignoring the key part of the information which is the overall trend of the two-series through time.

I feel that perhaps a better option is to take the trend and then perform e.g. first order differencing on it. And then hopefully providing that both of the differenced time series are stationary enough, performing cross correlation on that.

Which of these options, if either is correct?

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  • $\begingroup$ Differencing is definitely a good start! $\endgroup$ – ERT Aug 10 '18 at 16:30
  • $\begingroup$ Thanks @ERT and do you believe detrending is helpful or unhelpful? $\endgroup$ – DaveJay Aug 10 '18 at 16:40
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    $\begingroup$ The discussion in this post makes it doubtful that your objective is to find correlations among time series, because it looks like you're perfectly willing to modify those series. Could you articulate your ultimate objective explicitly? $\endgroup$ – whuber Aug 10 '18 at 16:43
  • $\begingroup$ hi @whuber the ultimate objective is to know, for each area, how each indicator correlates with house price (and present pretty table to the stakeholder who has employed me to do this work) so I would guess that the thing in my post that is actually doubtful is my knowledge of how to proceed rather than my objective! It is this unwillingness to modify these series that led me to question that detrending was the correct way to go. Any help / advice would be greatly appreciated $\endgroup$ – DaveJay Aug 10 '18 at 16:58
  • $\begingroup$ Related: stats.stackexchange.com/questions/313119/… $\endgroup$ – Alexis Aug 10 '18 at 17:11
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Find correlation between two time series. Theory and practice (R) is a good place to start your education. Note the discussion that points to the flaw of interpreting ( not computing ! ) correlation coefficients when you have auto-correlated data ...as you do .

This problem was recognized for time series as early as 1926 by Yule in his presidential address to the Royal Statistical Society and nearly 100 years later we have Google https://www.google.com/trends/correlate/tutorial and tons of others promoting the erroneous interpretation ( i.e. using standard significance testing !) of time series correlations.

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  • $\begingroup$ Thanks for the reference material, I'll study it properly when I'm back in work on Monday. From the rest of what you're saying, am I to interpret it as the calculated correlation coefficients will be useless to me? As this seems contradictory to the comments left by Whuber above who seems to imply that it's trivially easy to do so. $\endgroup$ – DaveJay Aug 10 '18 at 20:00
  • $\begingroup$ The distribution is affected by the autocorrelation in X and Y thus tests of statistical significance are affected. Ease of computation doesn't imply usability. $\endgroup$ – IrishStat Aug 10 '18 at 21:39
  • $\begingroup$ An important clarification ....The distribution is affected by the auto-correlation in X and Y thus "standard" tests of statistical significance are affected. Ease of computation doesn't imply usability. $\endgroup$ – IrishStat Aug 11 '18 at 12:13

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