# [R] How to measure the significant difference between two time series

Gerard M. Keogh GMKeogh at justice.ie
Wed Nov 26 11:59:11 CET 2008

```Q1: Quick answer

a) you need to remove the seasonality - there s/b a tool in the time series
package to do this - though I'm not familar enough with R to know this.
b) check the resulting series  to see if it is stationary  - acf decays
quickly i.e. within a couple of lags.
c) if two series are stationary then overlay the acf plots and if second
plot lies within the CI of the first they are the same.
d) on the seasonal parts of the two series do regression on year vs b1*q1+
b2*q2 + b3*q3 + b4*q4 and if the coefficients of the second are within the
2 Se band of the first - seasonality is similar.

if c) and d) are not signif - the two series are similar.

Also, standardise all your series so that they have mean 0 (or 1) and
variance 1 before you start - it'll make the numerics and comparisons
better.
Also, before starting you may need to take logs if the series oscillations
increase with time.

Q2 - don't know what you mean by interannual variation - within year
possibly.

Hope this helps.

Gerard

"Bin Zhao"
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Subject
[R] How to measure the significant
24/11/2008 04:13          difference between two time
series

Please respond to
zhaobin1969 at gmail
.com

Dear R experts and statisticians,

I have some time series datasets, they are several years vegetation indices
(about 50 data points per year) sampled from different station. These
indices have similar dynamics with seasonal change.

My questions are,
1) How can I compare the difference among the indices, and how can I say
there is significant differnce between two time series. They don't have the
same values in the same date, but they may have the similar tendency and
change curves?

2) I also want to compare the interannual variation of the vegetation index
in the same station. Of course, the index can be separated into several
sub-series, i.e., one year one sub-series. Now I have the same question as
1), how can I compare the significant differnce between different year?

If there are mature theoretical framework can resolve my questions, is
there any package in R can do this?

Any further advice is highly appreciated.

Regards,

Bin Zhao

2008-11-24 , 10:53:58

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