X-13ARIMA-SEATS Modeling - Regression

This tutorial outlines the steps to define a RegARIMA model (aka SARIMAX) in the X13AS framework and generate forecasting values and confidence intervals.

For our sample data, we will use the monthly flow of international airline passengers between January 1949 and December 1960. This dataset is a popular time series sample first covered by Box-Jenkins in their time-series reference manual back in 1970.

Step 1 – Data Preparation

We arranged the observations of the sample data in two adjacent columns: dates and values, in ascending chronological order, so that the first data point corresponds to the earliest date (i.e., Jan 1949), and the last data point corresponds to the latest (i.e., Dec 1960).

Although the X13ARIMA-SEATS model accepts datasets in reverse chronological order (i.e., descending), we chose the ascending order for our demonstration here.

Step 2 – Define an X13ARIMA-SEATS Model

1. Select an empty cell in your worksheet, preferably on that is close to the input data set and that has a free adjacent cell (to store the model specifications).
   
2. From the NumXL toolbar, locate the ARMA icon, click on it, and select the U.S. Census X13-ARIMA-SEATS from the drop-down menu.
   
3. The X13ARIMA-SEATS Model (aka X13AS) wizard or dialog box pops up on the screen.
   
4. In the X13AS window, the Input tab is active and displayed. We need to select and describe the input data set.
   1. In the Input Data field, select the cells range in the worksheet of your data. You may include additional empty rows for future data points.
   2. In the Date Start field, select the cell with the earliest date value.
   3. The data set is collected every month, so there is no need to change the Frequency field.
   4. Finally, select the empty cell above the currently selected cell to store the X13AS specification.
5. Now, select the Transform tab and click on the Auto option for the transform function. Leave everything else on this tab unchanged.
   
6. Switch now to the ARIMA tab. By default, the Auto (TRAMO) option is selected. Leave it there but change the forecast horizon to 3 years.
   
7. Switch to the Regression tab. By default, the regression is set to none (i.e., disabled). Click on the Add Regression component option to enable it.
   
   

   Note:

   Once you enable the regression, the inner tabs (e.g., Built-in, Holidays) become available to you.

8. In the inner tab Built-in, select the Constant Trend and trading-day flow effect (td) options. Press the Validate command button to check our model’s settings consistency.
   
9. Let’s switch to the Holidays inner tab. In this tab, select the holidays that are relevant to your data sets.
   1. For our dataset – international airline passengers – we expect the holidays to have an impact on international travel activities.
   2. Select Easter Holiday (easter[w]), Labor Day (labor[w]) and Thanksgiving holiday (thanks[w]). Leave the Leading Effect (Days) as default, except for Thanksgiving, which you should set to one (1).
   3. Press the Validate command button.
   
10. Press the Apply button.
11. Similar to what we did in “X13AS Tutorial II – Forecasting,” construct a forecasting table and plot the forecast along with the confidence intervals on the same chart.
    
12. Comparing the forecast table (and plot) with the ones in “X13AS Tutorial II – Forecasting,” we notice that this chart has tighter confidence intervals. In other words, the ARIMA model with regression variables captures/explains more variance in the input dataset than it did before.
13. Before we wrap this tutorial, let us take a quick look at the Output File, generated by the U.S. Census X13AS program.
    1. Launch the X13AS wizard for your model.
    2. Click the Validate button, followed by the Run X13AS control.
       
    3. Click the Output File command button. NumXL will launch the Notepad application and open the output file generated by the underlying X13AS program.
       
    4. Scroll down in the Notepad window until you see the Regression Model section.
       
    5. Examine the t-value for regressor. The trading day effect for Thanksgiving [1] has a low value, making it a candidate for elimination.

Finding an optimal set of regressors in RegARIMA deserves more time than we have devoted here, but we hope this tutorial provides you with a good start.