ARIMA Control Charts with Predictors

An Individuals control chart is created using the residuals of the ARIMA with Predictors forecast model.

The ARIMA with Predictors model supports continuous or categorical predictors. See ARIMA Forecast with Predictors for more information.

The Moving Limits chart uses the one step prediction as the center line, so the control limits will move with the center line. If a Box-Cox transformation is used then an inverse transformation is applied to calculate the control limits.

The popular “Show Last 30” and “Scroll” features in SigmaXL Chart Tools are available for these control charts. Currently, the “Add Data” feature is not supported in ARIMA Control Chart with Predictors.

Note that a Moving Range Chart and Tests for Special Causes are not available here, but the user can store and select Residuals, then create with SigmaXL > Control Charts > Individuals & Moving Range.

Open Daily Electricity Demand with Predictors – ElecDaily.xlsx (Sheet 1 tab). This is daily electricity demand (GW) for the state of Victoria, Australia, every day during 2014. Temp (C) is the maximum daily temperature in degrees Celsius for the city of Melbourne. TempSq is Temperature squared. WorkDay takes on the value 1 on work days and 0 otherwise. This data has a seasonal frequency = 7 (observations per week). See the Run Chart, ACF/PACF Plots, Spectral Density Plot and Seasonal Trend Decomposition Plots for this data.
Click SigmaXL > Time Series Forecasting > ARIMA Control Chart > Control Chart with Predictors. Ensure that the entire data table is selected. If not, Use Entire Data Table. Click Next.
Select Demand, click Numeric Time Series Data (Y) >>; select Date, click Optional X-Axis Labels >>; select Temp (C) and TempSq, click Optional Continuous Pred. >>; select WorkDay, click Optional Categorical Pred. >>. Uncheck Display ACF/PACF/LB Plots and Display Residual Plots. Check Seasonal Frequency with Select = 7 - Daily (or Specify = 7). Leave Specify Model Periods and Box-Cox Transformation unchecked.
Click Model Options. Select Automatic Model Selection. We will use the defaults: Stepwise Procedure and Model Selection Criterion: AICc – Akaike information criterion with small sample size correction, leave Specify Nonseasonal Differencing (d) and Specify Seasonal Differencing (D) unchecked.
Click OK to return to the ARIMA with Predictors Control Chart dialog. Click OK. This is a complex model, so computation time will be approximately one to two minutes. The ARIMA with Predictors control charts are produced:
Scroll down to view the ARIMA Model header:
The ARIMA Model Summary is given as:

This is a summary of the model information: ARIMA (2,1,2) (2,0,0) with no constant and 3 predictors. Seasonal Frequency = 7; Model Selection Criterion = “AICc” and Box-Cox Transformation = “N/A” because Box-Cox Transformation was unchecked.