Well known CPI of urban consumers is never revised. Recently initiated chained CPI is initially released every month (ICPI), for that month without delay within BLS and for the previous month with one month delay to the public. Final estimates of chained CPI (FCPI) are released every February for January to December of the calendar year two years before. Every month, simultaneously with the release of ICPI, we would like to have a best estimate, given current information, of FCPI for that month, which will not be released until two calendar years later. ICPI and FCPI data may be indexed in historical time by months of occurrence or in current or real time by months of observation or release. The essence of the solution method is to use data indexed in historical time to estimate models and, then, for an estimated model, to use data indexed in real time to estimate FCPI. We illustrate the method with regression and VARMA models. Using a regression model, estimated FCPI is given directly by an estimated regression line; and, using a VARMA model, estimated FCPI is computed using a Kalman filter.