# 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

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

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

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.