Autocorrelation function (ACF) plot and the partial autocorrelation function (PACF) plot
Time series forecasting is a common task in data science, as it involves predicting future values of a time-dependent variable based on past observations. One of the tools that is commonly used to analyze and forecast time series data is the autocorrelation function (ACF) plot and the partial autocorrelation function (PACF) plot.
The ACF plot is a graphical representation of the autocorrelation between different lags of a time series. Autocorrelation is a measure of the correlation between a time series and a lagged version of itself. For example, if a time series exhibits strong autocorrelation at a lag of 1, this means that the current value of the time series is strongly correlated with the value from one time period ago.
The relation between PACF and ACF
The PACF plot is similar to the ACF plot, but it measures the partial correlation between a time series and a lagged version of itself, controlling for the effects of intermediate lags. In other words, the PACF plot helps to identify the direct relationship between a time series and its lags, without the influence of other intermediate lags.
Both the ACF and PACF plots are useful tools for identifying the appropriate lag structure for a time series model. For example, if a time series exhibits strong autocorrelation at a lag of 1 and a weaker autocorrelation at higher lags, this might suggest that an autoregressive model with a lag of 1 would be appropriate. On the other hand, if a time series exhibits strong autocorrelation at all lags, this might suggest that a moving average model would be more appropriate.
It’s important to note that ACF and PACF plots should be interpreted in conjunction with other tools and techniques, such as stationarity tests and model selection criteria, in order to identify the most appropriate time series model. By carefully interpreting ACF and PACF plots, data scientists can gain valuable insights into the underlying structure of a time series and choose an appropriate model for forecasting.