There are a few reasons why we might want to calculate a centered moving average:
1. To smooth out data that contains a lot of short-term noise
2. To better visualize trends in the data
3. To make it easier to perform further analysis, such as constructing forecasting models
The steps for calculating a centered moving average are as follows:
1. Determine the length of the window you want to use (i.e., the number of periods over which you will average the data)
2. Calculate the simple moving averages for each period in your dataset using this window length
3. For each period, subtract the current period's SMA from the next period's SMA (i.e., compute the difference between successive SMAs)
4. Divide this difference by 2 to get the centered moving average for that period