Time series reconciliation through flexible least squares estimation

Abstract

In the paper we optimize a procedure developed recently to reconcile time series by flexible least squares. In the previous version of the procedure the author assumed prior knowledge of the weighting parameter μ of Kalaba and Tesfatsion’s so-called “incompatibility cost function”. In the new version, this parameter is estimated from the sample using an iterative method based on the Newton-Raphson algorithm. We test the improved method by reconciling the monthly growth rates of the Monthly Economic Activity Estimator (EMAE) of Argentina with the quarterly growth rates of the Gross Domestic Product. The results suggest that optimal levels of μ would be close to 1 (the value suggested by Kalaba and Tesfatsion as prior value) but estimating μ from the sample instead of keeping it fixed at 1 hardly modifies the reconciled series.

Keywords

• time series reconciliation
• flexible least squares
• emae
• gross domestic product