institut de science financiere et d’assurances laboratoire saf UniversitéClaudeBernardLyon1 InstitutdeScienceFinancièreetd’Assurances A New Non-parametric approach to Smoothing and Forescating of Mortality Julien Tomas - Frédéric Planchet InstitutdeScienceFinancièreetd’Assurances LaboratoirederecherchedeSciencesActuarielleetFinancière 26/06/2013-IAALIFEColloquium-Lyon Slide1/30 institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon institut de science financiere et d’assurances laboratoire saf Contents 1 Introduction 4 Numerical application A a new robust and non-parametric The data framework Comparison of the fits (step i.) Two famillies of approaches Comparisons of basis functions and 2 Notation, assumption and approach corresponding coefficients (step ii.) Notation & assumption Description of the ARIMA models Summary of our methodology for the time-varying coefficients The proposed models (step iii.) 3 Identifying the mortality components Projections of the time-varying and their importance over time coefficients (step iv.) Lee and Carter (1992) and its Graphical comparisons of the fits variants and forecasts (step v.) Functional principal components analysis 5 Conclusion Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon