Regularized Estimation in High-dimensional Time Series Models Sumanta Basu Cornell University IMA Workshop on Forecasting from Complexity April 27, 2018 Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 1 / 33
Outline Introduction 1 Sparse Vector Autoregression (VAR) 2 Motivation: Measuring Systemic Risk Network Granger Causality and VAR Modeling and Implementation Estimation in Sparse VAR Inference in Sparse VAR Back to Measuring Systemic Risk Incorporating Latent Structure in VAR 3 Extension to Other Time Series Models 4 Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 1 / 33
Why High-dimensional Time Series? Economics and Finance: Macroeconomic policy making (hundreds of macroeconomic series), risk management and monitoring (hundreds of firm health characteristics) Neuroimaging: Functional and effective connectivity analysis from EEG/MEG/fMRI data (hundreds to thousands of brain regions (ROI)) Genomics: Regulatory networks among thousands of genes from short time course (tens of samples) Central questions: structure learning and forecasting of a large, dynamical system Penalized/Regularized estimation/inference methods can be useful Formal theory (beyond i.i.d. data) can guide method development Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 1 / 33
Outline Introduction 1 Sparse Vector Autoregression (VAR) 2 Motivation: Measuring Systemic Risk Network Granger Causality and VAR Modeling and Implementation Estimation in Sparse VAR Inference in Sparse VAR Back to Measuring Systemic Risk Incorporating Latent Structure in VAR 3 Extension to Other Time Series Models 4 Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 1 / 33
Outline Introduction 1 Sparse Vector Autoregression (VAR) 2 Motivation: Measuring Systemic Risk Network Granger Causality and VAR Modeling and Implementation Estimation in Sparse VAR Inference in Sparse VAR Back to Measuring Systemic Risk Incorporating Latent Structure in VAR 3 Extension to Other Time Series Models 4 Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 1 / 33
Motivation Systemic risk: widespread failure of the entire financial system Requires understanding of connectivity among financial firms Develop macro-prudential policy: from “too-big-to-fail” to “too-connected-to-fail” Goals: Monitor system-wide risk of financial firms Identify systemically risky institutions How should we measure “systemic risk”? No well defined theoretical agreement so far Extant models lean heavily on “sensible measures” of systemic risk Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 2 / 33
“too-big-to-fail” or “too-central-to-fail”? Clinton: “ ... both the governor and the senator have focused only on the big banks. Lehman Brothers, AIG, the shadow banking sector were as big a problem in what caused the Great Recession, I go after them. And I can tell you that the hedge fund billionaires ... ” 1 1 https://www.washingtonpost.com/news/the-fix/wp/2016/01/17/the-4th-democratic-debate- transcript-annotated-who-said-what-and-what-it-meant/ Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 3 / 33
Econometric Measures of Systemic Risk Use publicly available data on firm health (e.g., return, volatility, leverage), study commonality, co-movement, lead-lag relationships: CoVar (Adrian and Brunnermeier, 2011) Marginal and Systemic Expected Shortfall (Acharya et al., 2012) Pairwise vector autoregression (VAR) or Granger causality Network (Billio et al., 2012) Our key point: Co-movements/associations measured in a firm-firm or firm-system basis ( pairwise ) may lead to incorrect capital requirement policy A system-wide, joint modeling strategy can be more useful Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 4 / 33
Learning Financial Networks: pairwise vs. system-wide Aug’06 - J ul’09 B ANK OF AME R ICA COR P B ANK OF AME R ICA COR P COVE NTR Y HE AL TH CAR E INC COVE NTR Y HE AL TH CAR E INC UNUM GR OUP CITIGR OUP INC UNUM GR OUP CITIGR OUP INC C N A FINANCIAL COR P JPMOR GAN CHAS E & CO C N A FINANCIAL COR P JPMOR GAN CHAS E & CO X L CAPIT AL L TD WE LLS F AR GO & CO NE W X L CAPIT AL L TD WE LLS F AR GO & CO NE W U B S AG U B S AG HUMANA INC HUMANA INC GE NWOR TH FINANCIAL INC R O Y AL BANK CANADA MONTR E AL QUE GE NWOR TH FINANCIAL INC R O Y AL BANK CANADA MONTR E AL QUE AME R ICAN E XPR E S CO S AME R ICAN E XPR E S S CO C I G N A COR P C I G N A COR P AON COR P U S BANCOR P DE L AON COR P U S BANCOR P DE L DE UTS CHE BANK A G DE UTS CHE BANK A G PR INCIP AL FINANCIAL GR OUP INC PR INCIP AL FINANCIAL GR OUP INC T OR ONT O DOMINION BANK ONT T OR ONT O DOMINION BANK ONT LINCOLN NA TIONAL COR P IN LINCOLN NA TIONAL COR P IN BANK OF NOV A S COTIA BANK OF NOV A S COTIA PR OGR E S S IVE COR P OH PR OGR E S S IVE COR P OH BANK OF NE W Y OR K ME LLON COR P BANK OF NE W Y OR K ME LLON COR P MAR S H & MCLE NNAN COS INC MAR S H & MCLE NNAN COS INC FE DE R AL NA TIONAL MOR TGAGE AS S N FE DE R AL NA TIONAL MOR TGAGE AS S N ACE L TD NE W ACE L TD NE W BANK MONTR E AL QUE BANK MONTR E AL QUE CHUBB COR P CHUBB COR P CANADIAN IMPE R IAL BANK COMME R CE CANADIAN IMPE R IAL BANK COMME R CE HARTFOR D FINANCIAL S VCS GR P INC HARTFOR D FINANCIAL S VCS GR P INC T S A TE S TR E E T COR P S T A TE S TR E E T COR P AE TNA INC NE W AE TNA INC NE W FE DE R AL HOME LOAN MOR TGA GE COR P FE DE R AL HOME LOAN MOR TGA GE COR P S UN LIFE FINANCIAL INC S UN LIFE FINANCIAL INC P N C FINANCIAL S E R VICE S GR P INC P N C FINANCIAL S E R VICE S GR P INC A F L A C INC A F L A C INC CAPIT AL ONE FINANCIAL COR P CAPIT AL ONE FINANCIAL COR P ALLS T A TE COR P ALLS T A TE COR P S UNTR US T BANKS INC UNTR S US T BANKS INC TR AVE LE R S COMP ANIE S INC TR AVE LE S R COMP ANIE INC S B B & T COR P B B & T COR P PR UDE NTIAL FINANCIAL INC PR UDE NTIAL FINANCIAL INC R E GIONS FINANCIAL COR P NE W R E GIONS FINANCIAL COR P NE W ME TLIFE INC ME TLIFE INC NOR THE N TR R US T COR P NOR THE R N TR US T COR P MANULIFE FINANCIAL COR P MANULIFE FINANCIAL COR P S L M COR P S L M COR P UNITE DHE AL TH GR OUP INC UNITE DHE AL TH GR OUP INC AME R IPR IS E FINANCIAL INC AIG AME R IPR IS E FINANCIAL INC AIG GOLDMAN S ACHS GOLDMAN S GOLDMAN S GOLDMAN S ACHS ACHS ACHS WADDE LL & R E E D FINANCIAL INC WADDE LL & R E D FINANCIAL INC E MOR GAN S T ANLE Y DE AN WITTE R & CO MOR GAN S T ANLE Y DE AN WITTE R & CO LAZAR D L TD LAZAR D L TD FR ANKLIN R E S OUR CE S INC FR ANKLIN R S E OUR CE S INC MOR NINGS T AR INC MOR NINGS T AR INC S CHWAB CHAR LE S COR P NE W S CHWAB CHAR LE S COR P NE W INTE R ACTIVE DA A COR T P INTE R ACTIVE DA T A COR P C M E GR OUP INC C M E GR OUP INC AFFILIA TE D MANAGE R S GR OUP INC AFFILIA TE D MANAGE R S GR OUP INC BLACKR OCK INC BLACKR OCK INC JE FFE R IE S GR OUP INC NE W N Y S E E UR ONE XT JE FFE R IE GR S OUP INC NE W N Y S E E UR ONE XT R A YMOND JAME S FINANCIAL INC T R OWE PR ICE GR OUP INC R A YMOND J AME FINANCIAL INC S T R OWE PR ICE GR OUP INC FE DE R A TE D INVE S T OR S INC P A T D AME R ITR ADE HOLDING COR P FE DE R A TE D INVE S T OR S INC P A T D AME R ITR ADE HOLDING COR P JANUS CAP GR OUP INC LE GG MAS ON INC J ANUS CAP GR OUP INC LE GG MAS ON INC A E T ON V ANCE COR P ALLIANCE BE R NS TE IN HOLDING L P E T A ON V ANCE COR P ALLIANCE BE NS R TE IN HOLDING L P E TR ADE FINANCIAL COR P NAS DAQ O M X GR OUP INC E TR ADE FINANCIAL COR P NAS DAQ O M X GR OUP INC S E I INVE TME S NTS COMP ANY INVE S CO L TD S E I INVE S TME NTS COMP ANY INVE S CO L TD P airwis e G ranger C aus ality Network G ranger C aus ality Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 5 / 33
Outline Introduction 1 Sparse Vector Autoregression (VAR) 2 Motivation: Measuring Systemic Risk Network Granger Causality and VAR Modeling and Implementation Estimation in Sparse VAR Inference in Sparse VAR Back to Measuring Systemic Risk Incorporating Latent Structure in VAR 3 Extension to Other Time Series Models 4 Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 5 / 33
Granger Causality Time series X Granger causal for time series Y 2 3 2 1 X 0 -1 -2 -3 0 10 20 30 40 50 60 70 80 90 100 4 2 Y 0 -2 0 10 20 30 40 50 60 70 80 90 100 Time Network modeling from multivariate systems ◮ independent samples: Correlation, Partial Correlation ◮ time series data: Granger causality, Network Granger causality (NGC) Vector Autoregression (VAR): flexible modeling framework to capture lead-lag patterns in multivariate systems 2 https://en.wikipedia.org/wiki/Granger_causality Sumanta Basu (Cornell) High-dimensional Time Series April 27, 2018 6 / 33
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