Linear Autocorrelation Function
These features capture properties of the linear autocorrelation function
NB: The name
CO_f1ecacderives from an earlier version of hctsa (the current version of hctsa names this feature as
first1e_acf_taufeature in catch22 computes the first 1/e crossing of the autocorrelation function of the time series. In hctsa, this can be computed as
This feature measures the first time lag at which the autocorrelation function drops below 1/e (= 0.3679).
first1e_acf_taucaptures the approximate scale of autocorrelation in a time series. This can be thought of as the number of steps into the future at which a value of the time series at the current point and that future point remain substantially (>1/e) correlated. For a continuous-time system, this statistic is high when the sampling rate is high relative to the timescale of the dynamics.
- For uncorrelated noise, like the Poisson-distributed series shown below, the autocorrelation function drops to ~0 immediately, and we obtain the minimum value of this statistic:
first1e_acf_tau = 1.
- For processes with a greater level of autocorrelation, the autocorrelation function decays more slowly, and we can obtain a larger value of this feature. Take this series simulated from a Chirikov map, which has
first1e_acf_tau = 6:
- We obtain even larger values for even more slowly varying time series, like this ODE, measured at a very high sampling rate, yielding
first1e_acf_tau = 17
- Financial series (and many non-stationary stochastic processes) are highly autocorrelated, like this series for which
first1e_acf_tau = 176
This feature is named
CO_FirstMin_acin catch22 and matches the hctsa feature named
Similar to the 1/e crossing feature above,
firstMin_acfcomputes the first minimum of the autocorrelation function. It exhibits similar behavior.