Balancing SA Series as a Complement to the Direct and Indirect SA of Series

• Activity Number: 232
• Type: Topic Contributed
• Date/Time: Tuesday, August 8, 2006 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economics Statistics Section
• Author(s): Benoit Quenneville*+
• Companies: Statistics Canada
• Keywords: X-12-ARIMA ; seasonal adjustment ; benchmarking ; reconciliation ; raking

Abstract

It is possible with X-12-ARIMA to seasonally adjust (SA) an aggregate with either the direct or indirect approach. For example, a national total often is obtained indirectly from a first classification, such as an industry breakdown. However, when looking at a second classification, such as a regional breakdown, the indirectly obtained national total becomes fixed and the sum of the seasonally adjusted estimates from the second classification does not necessarily equal the national total. Unfortunately, nothing is available in X-12-ARIMA to impose a fixed aggregate on its components. We propose and illustrate simple methods based on constrained weighted least squares regression to restore the additivity. We also consider the case where the SA series must be benchmarked to annual control totals. The methods are designed to be easily programmable with the SAS statistical software.