What’s The Difference Between Autocorrelation & Partial Autocorrelation For Time Series Analysis?

Photo by Tolga Ulkan on Unsplash
  • What’s Partial Autocorrelation?
  • What’s the difference between Autocorrelation and Partial Autocorrelation?
  • An example of ACF / PACF plotting for a time series created using Zillow housing data from 1996–2018

A Quick Word On The General Purpose Of Correlation In Data Analysis

It’s useful to mention here that statistical correlation in general helps us to identify the nature of the relationships between variables, and that this is where ACF and PACF come in with respect to Time Series data.

What’s Autocorrelation?

Autocorrelation is a calculation of the correlation of the time series observations with values of the same series, but at previous times.

What’s Partial Autocorrelation?

Partial Autocorrelation, on the other hand, summarizes the relationship between an observation in a time series with observations at previous time steps, but with the relationships of intervening observations removed.

This is the critical difference between Autocorrelation and Partial Autocorrelation — the inclusion or exclusion of indirect correlations in the calculation.

Examples: an ACF and PACF of time series for Real Estate Housing prices

One thing to remember and mention here:

Issues with covariance and homoscedasticity suggest a lack of stationarity as well.
Seasonal decomposition removes seasonality and trend, leaving only the residuals of the series.

Interpreting an ACF plot

The below graphic shows both ACF and PACF plots of the residuals from the above time series on which seasonal decomposition was applied.

Autocorrelation is a calculation of the correlation of the time series observations with values of the same series, but at previous times.

But also, we remember:

Partial Autocorrelation, on the other hand, summarizes the relationship between an observation in a time series with observations at previous time steps, but with the relationships of intervening observations removed.

Essentially, the indirect correlations are removed.

So, in the PACF plot above, we can see this happening. Because the indirect correlations are not calculated, the correlation “legs” dwindle completely to zero. There is much more to these calculations, of course, but a high-level understanding of PACF is rooted in its effort to remove indirect correlations.

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