- Autocorrelation:
- Lets consider a series 1,2,3,4,5,6
- There is a correlation between every consecutive elements:
- second number = first number + 1 (correlation between first and second number)
- third number = second number + 1 (correlation between second and third number)
- This consecutive correlation goes on for every n-th element with its previous element and evaluates the same correlation value
- We can say this is kind of an echo that is embedded within every n-th element of the sequence
- We call this autocorrelation.
- So we say, Autocorrelation is the Correlation of a series with a lagged copy of itself
- We need it while working with time series.
- Negative autocorrelation : Mean Reversion
- Positive autocorrelation : Momentum, or Trend Following
- Partial Autocorrelation:
- Shows incremental benefit of adding nth lag when n-1 lags are already present
- Removes the effects of previous lags (cumulative nth - cumulative n-1th)
- eg: a partial autocorrelation function of order 3 returns the correlation between our time series t1 and lagged values of itself by 3 time points t4 but only after removing all effects attributing to lags 1 and 2