Use Returns, Not Prices, to Read Autocorrelation and Momentum
Summary
The document asks whether a long-lag autocorrelation pattern in an asset’s price series indicates momentum. The questioner reports examining a long price history, testing for trend stationarity, and seeing apparent continuation across many business-day lags in the price ACF. That pattern seems inconsistent with the visual price chart and the efficient market hypothesis.
The principal response says to calculate the autocorrelation function on log returns rather than price levels, since adjacent prices tend to be highly correlated by construction. Another response recommends differencing and then inspecting the return series’ ACF and partial ACF, while questioning whether the original series is stationary. A further answer discusses fractional differentiation and cautions that stationarity tests can be weak, suggesting comparison of mean and variance across chronological subperiods. These are forum suggestions, not a documented empirical resolution; the discussion does not show the return ACF or establish that any momentum exists.
Key ideas
- Price levels can show strong autocorrelation because successive prices differ by relatively small changes.
- Log returns are the suggested series for investigating return momentum with an ACF.
- Differencing a nonstationary price series produces returns for further autocorrelation analysis.
- The responses disagree about whether the original series is trend-stationary.
- Stationarity checks and fractional differentiation are mentioned, but no definitive diagnosis is demonstrated.
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Full text
# Interpreting ACF
# Interpreting ACF
I am currently struggling with the interpretation of a price chart and the corresponding ACF graph. The question is, if there is momentum in the price of this asset. This is the corresponding price chart for a period of 19 years (5000 business days):
It doesn't´t seem to have much of momentum when looking at the price development. After verifying that the time series is (trend)-stationary by means of the Zivot / Andrews Test (ur.za in R), i generated the ACF plot to get a further idea of potential Momentum. And there´s the problem. The ACF graph indicates a price continuation pattern of around 700-800 lags (business days as the data has business days as frequency) or 2.5 - 3 years of momentum. But this is in strong contrast to the price chart above and to the efficient market hypothesis. Is there any rationale mistake from my side?
## Answer by Chris Taylor (score 4)
https://quant.stackexchange.com/a/42570
You need to compute the autocorrelation of the log returns $r_t$, not of the prices, $p_t$. The relationship of the log return series to the price series is
$$ r_t = \log \frac{p_t}{p_{t-1}} $$
The price series is obviously very autocorrelated, since today's price is yesterday's price plus small delta.
## Answer by sukusi (score 1)
https://quant.stackexchange.com/a/42572
ACF plot suggests there is autocorrelation which lasts for long time. The series is clearly not stationary. You may try differencing once - return time series, then plot boathouse ACF and PACF.
## Answer by Andrew Beaven (score 0)
https://quant.stackexchange.com/a/42653
You should definitely look at Marcos Lopez De Prado, Advances in Financial Machine Learning (2018). In chapter 5 he lays out an innovative concept: Fractional Differentiation. This idea is to provide a continuum in which differencing time series is given to make time series stationary. Most formal tests for stationarity (i.e. Augmented Dickey-Fuller and other tests) are weak. The simple thing to do is to divide the time series (chronologically) in two: compute: [1] Mean and variance of the first period [2] Mean and variance of the second period Both periods should be approximately the same for both metrics to conclude one has stationarity. If you don't have an economic (theoretical) rationale for trend stationarity, then you probably should assume it is not.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.