Autocorrelation function (ACF)

Computes the sample autocorrelation function of a one-dimensional signal at lags 0, 1, ..., lag_max using the biased estimator (dividing each autocovariance by \(N\)), with the mean removed by default – the same definition as stats::acf() and statsmodels.tsa.acf(adjusted = FALSE). The autocorrelation measures how similar a signal is to a time-shifted copy of itself, and is the basic tool for detecting periodicity, rhythmicity, and the decorrelation time of a physiological signal.

Usage

autocorrelation(x, lag_max = 30L, demean = TRUE)

Arguments

x

A numeric vector (the time series).

lag_max

Maximum lag (default 30); the returned vector has lag_max + 1 values (lags 0 through lag_max).

demean

If TRUE (default), subtract the mean before computing the autocovariance (the standard definition).

Value

A numeric vector of autocorrelation coefficients at lags 0:lag_max; the lag-0 value is always 1.

References

Box, G.E.P., Jenkins, G.M. (1976). Time Series Analysis: Forecasting and Control. Holden-Day.

See also

acf

Examples

set.seed(1)
autocorrelation(sin(seq(0, 20 * pi, length.out = 500)), lag_max = 20)
#>  [1]  1.00000000  0.99208311  0.96852099  0.92974895  0.87644110  0.80949880
#>  [7]  0.73003544  0.63935797  0.53894543  0.43042487  0.31554498  0.19614791
#> [13]  0.07413976 -0.04853987 -0.16994869 -0.28817248 -0.40135531 -0.50772859
#> [19] -0.60563878 -0.69357304 -0.77018262