1
$\begingroup$

I've got 36 months of timeseries data, and eyeballing it, it has a linear trend upward. I wanted to do a little more than just eyeball it though. So I put together a correlogram of autocorrelation values for lags 1 to 12 on my observations. They're all positive. Would you say that's good evidence that I've got a linear trend?

See a picture of my autocorrelations here.

And would that spike back up at the end there likely be due to some seasonality (that'd make total sense for my business's data...we do heavy sales at Xmas and Valentines day)?

$\endgroup$
1
$\begingroup$

Would you say that's good evidence that I've got a linear trend?

The autocorrelation on its own doesn't tell you that, because you could get similar patterns from other things that linear trend. You can get such patterns from linear trend, so you might say something like 'a pattern like that in the observed autocorrelations could be explained by a linear trend', but that doesn't tell you you have one.

$\endgroup$
2
$\begingroup$

Autocorrelation doesn't tell you anything about a trend - linear or otherwise. A high autocorrelation between time series values one period apart just tells you that the value in the previous period is highly related to the value in the current period. A random walk can have high first order autocorrelation but has no trend.

There are tests available: http://en.wikipedia.org/wiki/Cochran%E2%80%93Armitage_test_for_trend, but if there's a linear trend, a linear regression model should provide a "good" fit for the data. And of course, for a positive trend, the slope of the model should be positive.

$\endgroup$
  • $\begingroup$ I'm not sure your comment, "Autocorrelation doesn't tell you anything about a trend - linear or otherwise", is entirely correct. To cite Enders (Applied Economic Time Series, 2nd Ed., p 156): "Inspection of the autocorrelation function serves as a rough indicator of whether a trend is present in a series." Can you perhaps expand on your comment? $\endgroup$ – Jason Morgan Apr 2 '13 at 17:51
  • 1
    $\begingroup$ A sequence of positive autocorrelations from lag 1 occurs when there is a trend, but it occurs under other conditions as well as @wcampbell has pointed out. So on its own, autocorrelation does not tell you that a trend exists, although it can tell you that a trend does not exist. $\endgroup$ – Rob Hyndman Apr 3 '13 at 0:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.