The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions

Numerous contexts in macroeconomics, finance, and quality control require real-time estimation of trends, turning points, and anomalies. The real-time signal extraction problem is formulated as a multivariate linear prediction problem, the optimal solution is presented in terms of a known model, and multivariate direct filter analysis is proposed to address the more typical situation where the process' model is unknown. It is shown how general constraints - such as level and time shift constraints - can be imposed on a concurrent filter in order to guarantee that real-time estimates have requisite properties. The methodology is applied to petroleum and construction data. Published by Elsevier B.V. on behalf of EcoSta Econometrics and Statistics.