Modeling Gold Returns Instead of Persistent Prices with ARIMA

Summary

The document addresses a common time-series modeling problem: gold prices appear autocorrelated, and repeated differencing seems not to remove the effect. The responses suggest that the issue may be the choice of series. Price levels are persistent and generally do not behave like a weakly stationary series, so their autocorrelation is not by itself evidence that an ARIMA model should be fitted directly to those levels after arbitrary differencing.

Instead, the answers recommend examining changes scaled by the previous price, such as returns or log returns. These series can have more stable statistical properties and may be more suitable for ARIMA analysis. One response reports that an autocorrelation check on gold log returns showed no autocorrelation, while another explains the distinction between price dependence and return behavior. This is a diagnostic suggestion rather than a full modeling recipe: the document gives no broader test results, model selection, forecast evaluation, or evidence that gold returns are stationary across all periods.

Key ideas

• Autocorrelation in price levels does not establish that price levels are suitable for a stationary ARIMA model.
• Repeated differencing of prices may not address the underlying scale and persistence issue.
• Returns or log returns normalize price changes by the prior price and may be more appropriate modeling inputs.
• The responses suggest checking return autocorrelation, but provide no comprehensive stationarity or forecast evaluation.
• Model suitability should be assessed for the specific sample and period being analyzed.

Tags

# Infinite autocorrelation - Unit root?


# 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

## Answer by not.so.quanty (score 1)

https://quant.stackexchange.com/a/12753

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

## Answer by Taran (score 1)

https://quant.stackexchange.com/a/14120

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:

- 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.

- 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!

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.