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catch22 Features

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Linear Autocorrelation Function

These features capture properties of the linear autocorrelation function

`CO_f1ecac`

derives from an earlier version of `first1e_acf_tau`

).The *catch22* computes the first 1/*e* crossing of the autocorrelation function of the time series. In *hctsa*, this can be computed as

`first1e_acf_tau`

feature in `CO_FirstCrossing(x_z,'ac',1/exp(1),'discrete')`

.This feature measures the first time lag at which the autocorrelation function drops below 1/*e *(= 0.3679).

`first1e_acf_tau`

captures 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/- 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 *catch22* and matches the *hctsa* feature named

`CO_FirstMin_ac`

in `firstMin_acf`

.Similar to the 1/*e* crossing feature above,

`firstMin_acf`

computes the first minimum of the autocorrelation function. It exhibits similar behavior.Last modified 6mo ago

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CO_f1ecac (first1e_acf_tau)

What it does

What it measures

CO_FirstMin_ac (firstMin_acf)