State Space Models for Temporal Distribution and Benchmarking

• Activity Number: 675
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Benoit Quenneville*+ and Susie Fortier and Frederic Picard
• Companies: Statistics Canada and Statistics Canada and Statistics Canada
• Keywords: Cubic Splines ; Interpolation ; Local Linear Trend Model

Abstract

We provide discrete state space models for temporal distribution and benchmarking that generalize the benchmarking methods of Denton (JASA, 1971) modified by Cholette (Survey Methodology Journal, 1984); those based on the regression method of Cholette and Dagum (ISR, 1994); and, those using interpolating splines by Quenneville, Picard and Fortier (Joint Statistical Meetings, 2010). For the simplest case, the method consists in interpolating a series of values observed at variable time points using the local linear trend model with the variances for the error terms in the observation equation and in the level equation set to zero. The state space formulation enables the computation of standard errors. We apply the method to the calandarization of an artificial series of benchmarks covering 28 days that need to be converted into daily values, and to the interpolation of the Annual US Gross Domestic Product into quarterly values with and without using the Quarterly Index of Industrial Production as an indicator series for the quarterly movement.