## May 11, 2021

### Calculating The Metrics in a Time Lapse Analysis

There are several key components of a Time Lapse Analysis.

First, I tackle the concept of "weighting". I create a regression model that weights historical dollars in terms of how much historical dollars contribute to future spend. For instance, a purchase in the past month might count for a weight of 1.000 ... a purchase twelve months ago might count toward a weight of 0.50. The purchase 12 months ago is half as important as a purchase yesterday.

Here's an example. Say we have a customer who spent \$100 one month ago, \$100 six months ago, and \$100 twenty-four months ago. Say that the weights are 1.00 for one month ago, 0.65 for six months ago, and 0.30 for twenty-four months ago. Weighted spend is 100*1.00 + 100*0.65 + 100*0.30 = \$195.

I sum weighted spend for every twelve-month customer.

Then I create twenty-five "tiles" ... four percentile groups of customers, based on weighted historical spend.

I count how many twelve-month buyers reside in each of the twenty-five "tiles".

I then replicate this analysis twenty-four more times, going back in time on a monthly basis.

Say I have 10,000 customers in the top 4%-tile as of today. Say I had 9,800 customers in that tile a month ago. My index becomes 10,000 / 9,800 = 1.02.

Any index > 1.00 is progressively greener in the image above.

Any index < 1.00 is progressively more red in the image above.

More on the Time Lapse Analysis tomorrow.