Partial autocorrelation function (PACF)

Computes the sample partial autocorrelation function of a one-dimensional signal at lags 0, 1, ..., lag_max. The partial autocorrelation at lag \(k\) is the correlation between \(x_t\) and \(x_{t+k}\) with the linear effect of the intervening lags removed, obtained here by the Durbin-Levinson recursion on the biased, demeaned autocorrelation sequence (via autocorrelation) – the same definition as stats::pacf and statsmodels.tsa.pacf(method = "ldb"). Where the ACF decays, the PACF cuts off after the autoregressive order, so it is the standard tool for choosing AR model order.

Usage

partialAutocorrelation(x, lag_max = 20L)

Arguments

x

A numeric vector (the time series).

lag_max

Maximum lag (default 20); the returned vector has lag_max + 1 values (lags 0 through lag_max).

Value

A numeric vector of partial autocorrelation coefficients at lags 0:lag_max; the lag-0 value is 1 by convention and the lag-1 value equals the lag-1 autocorrelation.

References

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

See also

autocorrelation, pacf

Examples

set.seed(1)
partialAutocorrelation(as.numeric(arima.sim(list(ar = 0.6), 500)), lag_max = 10)
#>  [1]  1.000000000  0.570267215 -0.014477934 -0.032401946  0.004478176
#>  [6]  0.013318710 -0.056459201  0.027871328 -0.030965381  0.071692262
#> [11] -0.093560384