Forecasting Treasury Yield Using Macroeconomic Diffusion Index: Big Data v.s. Small Data Weiqi (Vicky) Xiong Rutgers University wxiong@econ.rutgers.edu June 27, 2017 Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 1 / 29
Term structure of interest rates Issuer: U.S. Department of the Treasury. Maturity: 3-, 6-, 12-month, 2-, 5-, 10-year, etc. Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 2 / 29
Term structure of interest rates Issuer: U.S. Department of the Treasury. Maturity τ = 3, 6,..., 120 months. Bond price and yield: y t ( τ ) = − 1 τ ln ( P t ( τ )). Real-time data: 3-D yield curve (monthly). Buy or rent a house? Interest rate contingent asset pricing zero lower bound Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 3 / 29
Summary Goal: Improve real-time forecast of U.S. Treasury yields. Two general consensuses: (1) Look beyond yield cross-section: Macroeconomic variables. (2) Models with best track record: Latent factors with three (or less) parameters. Research Questions: (1) When incorporating macro-variables improves real-time forecast? (2) Possible causes of “forecast breakdowns”. Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 4 / 29
Summary Adding macro information improves bond yield forecasts? Yes. In subsamples 1 and 2 (1992-99, 2000-07), DNS+FB models win in 17/20 maturity/horizon permutations. Is predictive content in “big data” stable over time? It’s not stable over time. In subsample 3 (2008-16), data rich models win in only 2 of 20 cases. zero lower bound? Post Great Recession confusion? Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 5 / 29
Diffusion Index (DI) models: The h -step-ahead forecast of y t + h is formed as: y t + h = ˆ β 0 + ˆ β ′ F ˜ F t + ˆ ˆ β ′ y y t − 1 Unobserved latent factor: F t , Predictor variables: X t . X t = Λ F t + e t Data dimension reduction: X t (8 × 1) PCA → F t (3 × 1) − − − Baseline DI models with yield-information only. Use Treasury yield with maturity is τ = 3 , 6 , 12 , 24 , 36 , 60 , 84 , 120 (8 × 1). Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 6 / 29
Incorporating big data: Up to 3 macro factors extracted from a large panel of T × 103 macroeconomic variables. Data dimension reduction: X t (103 × 1) PCA → M t (3 × 1) − − − Percentage of total variance explained: Principle Component Raw Standardized 1st PC 71.32% 16.53% 2nd PC 16.51% 9.47% 3rd PC 7.85% 8.52% 4th PC 1.36% 5.48% 5th PC 0.96% 4.59% . . . . . . . . . 102nd PC ∼ 0% ∼ 0% 103rd PC ∼ 0% ∼ 0% Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 7 / 29
Macroeconomic data Source: Fred-MD https://research.stlouisfed.org/econ/mccracken/fred-databases/ 8 categories, 103 monthly time series. Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 8 / 29
Macroeconomic data (continue) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 9 / 29
Macroeconomic data (continue) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 10 / 29
Macroeconomic data (continue) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 11 / 29
Macroeconomic data (continue) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 12 / 29
Macroeconomic data (continue) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 13 / 29
Macroeconomic data (continue) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 14 / 29
Forecast Experiment The Models: Dynamic Nelson Siegel: a “small data” model β 2 t [1 − exp( − λ t τ ) β 3 t [1 − exp ( − λ t τ ) y t ( τ ) = ˆ β 1 t + ˆ ] + ˆ ˆ − exp ( − λ t τ )] + ǫ t λ t τ λ t τ curvature Loadings on slope level Big Data Models (Dimension Reduction with PCA) y t ( τ ) = ˆ 1 F b 2 F s ˆ β ′ W t + ˆ α ′ t + ˆ α ′ t + ǫ t Strawman Econometric Models y t ( τ ) = ˆ ˆ β ′ W t + ǫ t Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 15 / 29
Forecast Experiment Use zero coupon Treasury yield curve, monthly, 1982-2016. Gurkaynak, Sack and Wright (2006) Target variables are 1,2,3,5,10 year maturity yields Forecast horizons are h = 1, 3, 12 Prediction subsamples 1992-99, 2000-07, 2008-16, recession/expansion. Small data panel has N=10, T=415. Big data panel uses FRED-MD dataset with 103 macroeconomic variables. Predictions constructed in real-time, and estimations are based on rolling windows. Model Selection: MSFE and DM Tests. Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 16 / 29
Empirical Illustration Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 17 / 29
Empirical Illustration Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 18 / 29
Empirical Illustration Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 19 / 29
Empirical Illustration Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 20 / 29
Empirical Illustration +FB1, +FB2 == macro information (`big data' ) helped in 19 92-99 (subsample 1) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 21 / 29
Empirical Illustration +FB1, +FB2 == macro information (`big data' ) helped in 2000 - 07 (subsample 2 ) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 22 / 29
Empirical Illustration Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 23 / 29
Empirical Illustration +FB1, +FB2 == macro information (`big data' ) helped in recession subsamp le Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 24 / 29
Empirical Illustration Not so much in expansion subsamp le Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 25 / 29
Conclusion DNS+FB models usually win in first two samples for h = 1,3. Evidence for h = 12 much more mixed, AR, VAR and pure DNS often wins. AND the ‘best’ models are almost always significantly better that AR(1) straw-man model. Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 26 / 29
Conclusion DNS model ‘winners’ are used ‘vector’ variety. DNS factors do not evolve independently of one another, when predicting. Thus, DNS factors best predicted by other DNS factos AND bid data diffusion indexes. DNS+FB evidence even stronger for recession subsample: 13/15 horizon/maturity permutations. (7/15 for expansion subsample) Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 27 / 29
Future research Gaussian term structure model: Wu-Xia shadow rate (2016), Bauer and Rudebusch (2016), Christensen and Rudebusch (2015), Krippner (2015). Forecast breakdown test: Giacomini and Rossi (2009). Data shrinkage method (machine learning, variable selection): Kim and Swanson (2016). Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 28 / 29
The End Thank you. Weiqi (Vicky) Xiong (Rutgers University) Forecasting Interest Rates June 27, 2017 29 / 29
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