Worksheet – Case #9 – Using Correlation to determine the best lag

Finding Data

In this case, we will reuse the document from Case #3 which can be downloaded here. As such, all data needed for this exercise can be found in the document.

Document preparation

Reverting adjustments

As we are reusing a document, some adjustments need to be reverted from the earlier case.

  • Select “Time chart” in the tree
  • Open the chart layout and change Industrial production from “Area” to “Line”

Analysis

Correlation

You need to use the Correlation analysis to determine the best lag correlation between the two series.

  • Select the Rate of Change analysis
  • Add a Correlation analysis

In this case we are interested in the correlation between the two series from the year 2000.

  • Input 2000 as the start of the “Calculation range” and leave the end value blank
  • Change the "Lag Range" from -12 to 12.
  • For the ISM PMI, in the “Correlate to” drop-down menu, choose Industrial production
  • Leave the “Correlate to” setting to None for the Industrial production

Visualizing the result

  • Select “Correlation” in the tree
  • Click on “Add” and pick Category chart

By looking at the Category chart, you can see that the best correlation is reached when the value of the x-axis is 4. This means that lagging the ISM PMI by 4 observations (or months in our case) gives the best correlation between the series.

Lag

Having found the optimal lag, you can now come back to the Time chart and insert a Lag analysis.

  • Select “Time chart” in the tree
  • Click on “Insert” and choose Lag

For ISM PMI, choose Lag as the “Method” and 4 obs as the “Base”

Charting

Time axis adjustment

As we are interested in the correlation beyond the year 2000:

  • Select the x-axis
  • On the “Presentation properties” tab set the display range to start at 2000

Highlighting a range of values

You can use some chart annotations to circle these values.

  • Go to the “Chart annotations” tab and select Observation label
  • On the ISM PMI graph line, click on the last observation
  • Select the annotation by clicking on the textbox containing date and value
  • In the “Presentation properties” tab, change the start of the range to -3
    • This will include the lagged observations in the range, indexed by: 0,1,2,3
  • Tick the “Custom style” text-box and in “Anchor appearance” change the style to Ellipse
  • Finally, change the background color of the annotation
    • Set the opacity to 50% or lower so that the line remains visible.

Changing the observation label text

To change the text of the observation label, simply double-click on the textbox and a customization window will appear.