# Infinite autocorrelation - Unit root?

I have a time series of gold prices, on which I want to build an ARIMA model. The series is autocorrelated and if I can difference as often as I want, it always is.

First: data: d1gold Dickey-Fuller = -18.5829, Lag order = 19, p-value = 0.01 alternative hypothesis: stationary

Second: data: d2gold Dickey-Fuller = -32.6297, Lag order = 19, p-value = 0.01 alternative hypothesis: stationary .. and so on.

What can I do to fit the data in an ARIMA model? Data: https://drive.google.com/file/d/0B7cBu_0IHA17a1lQUlpsS1BJXzg/edit?usp=sharing

Best Regards Erik

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Please clarify the titel of your question. What does "infinite" autocorrelation mean? ;) –  Richard Jun 23 '14 at 6:53

Check your calculations, gold prices are indeed auto-correlated. acf(diff(log(OilGold\$price_gold))) will yield no auto-correlation in gold log-returns.

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You are probably computing autocorrelation in the prices. If you compute autocorrelation between the returns or log returns then you will not see the results you are getting.

This is because:

1. Tomorrow's price will always be influenced by lagged prices and the series will not look weak stationary if you plot it. The direct differencing doesn't help either because you don't have a normalized value and weak stationarity doesn't hold.

2. Returns are normalized to last closing price so you get meaningful results. Also returns can exhibit weak stationarity which you can try to model using ARIMA.

Cheers!

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