The Partial Autocorrelation Function (PACF) plots show the partial correlation of each time series with its own lagged values, controlling for the values of the time series at all shorter lags. This is helpful in identifying the order of the autoregressive (AR) part of an ARIMA model. Here’s how to interpret these plots:
Logan Passengers: The PACF plot for ‘Logan Passengers’ might show significant partial autocorrelations at one or more lags. Significant spikes (those that cross the blue confidence interval) suggest that those lags have a predictive relationship with the current value, after accounting for the relationships at all shorter lags. If such spikes occur at the first few lags and then cut off, it indicates an AR process of that order.
Logan Intl Flights: Like ‘Logan Passengers’, look for significant spikes in the early lags. The number of significant lags can indicate the order of an AR process for ‘Logan Intl Flights’. If there are no significant spikes or they are sporadic, it might suggest that an AR process is not appropriate.
Hotel Occupancy Rate: If there are significant spikes at fixed intervals, it may suggest seasonality in the data. Otherwise, the number and position of significant spikes can help determine the order of the AR process.
Labor Force Participation Rate: This PACF plot would be analyzed in the same manner, identifying the number of significant lags to determine the potential order of an AR process.
Hotel Average Daily Rate: If significant partial autocorrelations are present, they indicate the potential order of the AR process. If they decay gradually, it might suggest a mixed ARMA process.
Total Jobs: Look for the point at which the partial autocorrelations become insignificant. This will give you the suggested order of the AR process for the ‘Total Jobs’ series.
Unemployment Rate: As with the others, the presence and position of significant partial autocorrelations will inform the choice of AR order for modeling the ‘Unemployment Rate’.