Based on your financial expertise, provide your response or viewpoint on the given financial question or topic. The response format is open.

Adjusting a value for inflation each month using rolling 12-monthly inflation figures
The actual increase in the cost of living for one month over the previous month cannot be calculated from the annualized increase in cost over the entire previous year. Consider the hypothetical case of a very stable economy, where prices stay constant for decades.  Nevertheless, the authorities issue monthly statements, reporting that the change in the cost of living, for the last month, year over year, is 0.00%.  Then they go back to sleep for another month. Then, something happens, say in August, 2001.  It causes a permanent large increase in the cost of many parts of the cost of living components. So, in September, the authorities announce that the cost of living for the end of August, 2001, compared to August a year ago, was up 10%. Great consternation results.  Politicians pontificate, unions agitate on behalf of their members, etc... The economy returns to its customary behavior, except for that one-time permanent increase from August, 2001.  So for the next eleven months, each month, the authorities compare the previous months prices to the prices from exactly a year ago, and announce that inflation, year over year, is still 10%.   Finally, we reach September, 2002.  The authorities look at prices for the end of August, 2002, and compare them to the prices from the end of August, 2001 (post "event").  Wonder of wonders, the inflation rate is back to 0.00%!!  Absolutely nothing happened in August 2002, yet the rate of inflation dropped from 10% to 0%.