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You can't do a linear fit of the observed variable to the time. Among other things because the successive values of the observed variable are not uncorrelated.

To a first approximation you can assume the succesive differences are uncorrelated, and then you could try to do a linear fit. Which in this case means an average of the 3rd column. And then you remove the outlier because it has a large Mahalanobis distance.

What you should try to do is filter (e.g., taking successive differences is a filter) the original series untill you get something that presumably is stationary and then fit some sort of ad-hoc model. ARIMA models are ways to reduce the model to some linear regression or other, and you always have the issue of outlier rejection.

A man of words and not of deeds is like a garden full of weeds; a man of deeds and not of words is like a garden full of turds — Anonymous

by Migeru (migeru at eurotrib dot com) on Fri Jul 3rd, 2009 at 06:02:51 AM EST
[ Parent ]
You're right, of course.

But then again, GDP growth isn't uncorrelated either...

- Jake

If you only spend 20 minutes of the rest of your life on economics, go spend them here.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Fri Jul 3rd, 2009 at 12:26:16 PM EST
[ Parent ]

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