The Trilemma Between Accuracy, Timeliness, and Smoothness in Real-Time Forecasting and Signal Extraction

• Activity Number: 119
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Marc Wildi*+ and tucker mcelroy
• Companies: and census bureau
• Keywords: Direct Filter Approach ; trilemma ; customization ; accuracy ; timeliness ; snoothness

Abstract

The classic model-based paradigm in time series analysis is rooted in the Wold decomposition of the data-generating process (DGP) into an uncorrelated ``white noise" process. By design, this universal decomposition is indifferent to particular features of a specific prediction problem (e.g., forecasting or signal extraction) -- features driven by the priorities of the data-users. A single optimization principle is proposed to address a plethora of prediction problems. In contrast, this paper proposes to reconcile problem structures, user priorities, and optimization principles into a general framework whose scope encompasses the classic approach. We introduce the generalized prediction problem (GPP), which serves to formalize optimization algorithms in either of two ways: by model fitting, via GPP mean-square minimization, or by the so-called direct filter approach (DFA). We provide theoretical results and practical algorithms for both approaches, and discuss the merits and limitations of each. Furthermore, we propose a novel decomposition of the mean square error (MSE) of each