Isnb 978-9984-888-20-0 Ginters Bušs Forecasting and Signal Extraction with Regularised Multivariate Direct Filter Approach

2 Introduction 3 1. Regularised Multivariate Direct Filter Approach 4 1.1 Univariate direct filter approach 5 1.2 Multivariate direct filter approach 6 1.3 Rewriting filtration problem in a least squares form 7 1.4 Regularisation 8 1.5 Level and time shift constraints 10 1.6 Effective degrees of freedom 11 2. Tracking Economic Activity in the Euro Area 11 2.1 Tracking trendcycle in yearly growth of GDP 11 2.1.1 Target 12 2.1.2 Explanatory variables 12 2.1.3 Regularisation features 12 2.1.4 Indicator design 22 2.2 Tracking trendcycle in quarterly growth of GDP 26 2.2.1 Target and data 26 2.2.2 Indicator design 26 3. Robustness Check on Less Homogeneous Dataset for Latvia 30 Conclusions 34 Appendix 34 Bibliography 38 ABBREVIATIONS CSB – Central Statistical Bureau DE – Germany d.f. – degrees of freedom DFT – discrete Fourier transform DG Ecfin – Directorate General for Economic and Financial Affairs (e.)d.f. – (effective) degrees of freedom EA – euro area EE – Estonia ES – Spain EU – European Union Eurocoin – Euro Area Business Cycle Coincidence Indicator FR – France GDP – gross domestic product IT – Italy Latcoin – Latvian Business Cycle Coincidence Indicator LT – Lithuania LV – Latvia MSFE – mean squared filter error NSA – seasonally unadjusted q-o-q – quarter-on-quarter RMDFA – regularised multivariate direct filter approach SA – seasonally adjusted US – United States w.r.t. – with respect to y-o-y – year-on-year