The ARIMA (Autoregressive Integrated Moving Average) model is a popular statistical method for time series forecasting that captures the dynamics of the series through three main parameters: AR (p), I (d), and MA (q).
AR (Autoregression): Refers to the use of previous values in the time series to predict future values.
I (Integrated): Represents the differencing of raw observations to make the time series stationary, which means that the series has constant mean and variance over time.
MA (Moving Average): Incorporates the dependency between an observation and a residual error from a moving average model applied to lagged observations.
The lines in each graph represent:
Blue Line (Actual): The actual observed values from the dataset.
Orange Line (Fitted): The values predicted by the ARIMA model.
Logan Passengers: The ARIMA model appears to track the seasonal pattern and general trend of the passenger data quite closely.
Logan International Flights: The model captures the seasonality and fluctuations in the number of flights well.
Hotel Occupancy Rate: The ARIMA model follows the actual occupancy rates, including the seasonal peaks and troughs.
Hotel Average Daily Rate: The model fits the average daily rate with some accuracy, again reflecting the seasonality in the data.
Total Jobs: The ARIMA model fits the data tightly, suggesting that the model is capturing the underlying trend effectively.
Unemployment Rate: The model seems to follow the actual rate closely, including the downward trend over time.
Labor Force Participation Rate: The ARIMA model provides a reasonable fit to the data, capturing the stability of the participation rate over time.