![]() The use of this function was introduced as part of the Box–Jenkins approach to time series modelling, whereby plotting the partial autocorrelative functions one could determine the appropriate lags p in an AR ( p) model or in an extended ARIMA ( p, d, q) model. This function plays an important role in data analysis aimed at identifying the extent of the lag in an autoregressive (AR) model. It contrasts with the autocorrelation function, which does not control for other lags. In time series analysis, the partial autocorrelation function ( PACF) gives the partial correlation of a stationary time series with its own lagged values, regressed the values of the time series at all shorter lags. Partial autocorrelation function of Lake Huron's depth with confidence interval (in blue, plotted around 0)
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