Smooth Dynamic Factor Analysis with Application to the U.S. Term Structure of Interest Rates

SUMMARY We consider the dynamic factor model and show how smoothness restrictions can be imposed on factor loadings by using cubic spline functions. We develop statistical procedures based on Wald, Lagrange multiplier and likelihood ratio tests for this purpose. The methodology is illustrated by analyzing a newly updated monthly time series panel of US term structure of interest rates. Dynamic factor models with and without smooth loadings are compared with dynamic models based on Nelson–Siegel and cubic spline yield curves. We conclude that smoothness restrictions on factor loadings are supported by the interest rate data and can lead to more accurate forecasts. Copyright © 2013 John Wiley & Sons, Ltd.

[1]  The Macroeconomy and the Yield Curve: A Nonstructural Analysis , 2003 .

[2]  Leo Krippner.  A Theoretical Foundation for the Nelson and Siegel Class of Yield Curve Models , 2010 .

[3]  Paul Dierckx,et al.  Curve and surface fitting with splines , 1994, Monographs on numerical analysis.

[4]  James T. Wassell,et al.  Numerical Methods of Statistics , 2002, Technometrics.

[5]  S. Koopman,et al.  Analyzing the Term Structure of Interest Rates Using the Dynamic Nelson–Siegel Model With Time-Varying Parameters , 2010 .

[6]  R. Engle,et al.  A One-Factor Multivariate Time Series Model of Metropolitan Wage Rates , 1981 .

[7]  Ricardo Reis,et al.  Relative Goods&Apos; Prices, Pure Inflation, and the Phillips Correlation , 2007 .

[8]  Clive G. Bowsher,et al.  The Dynamics of Economic Functions: Modeling and Forecasting the Yield Curve , 2008 .

[9]  Dale J. Poirier,et al.  The econometrics of structural change, with special emphasis on spline functions , 1976 .

[10]  Danny Quah,et al.  A Dynamic Index Model for Large Cross Sections , 1993 .

[11]  James D. Hamilton,et al.  Testable Implications of Affine Term Structure Models , 2011 .

[12]  Ralf Brüggemann,et al.  Model Reduction Methods for Vector Autoregressive Processes , 2004 .

[13]  R. Engle,et al.  Alternative Algorithms for the Estimation of Dynamic Factor , 1983 .

[14]  Glenn D. Rudebusch,et al.  The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models , 2007 .

[15]  S. Koopman,et al.  Likelihood-based Analysis for Dynamic Factor Models , 2008 .

[16]  N. Shephard,et al.  Exact score for time series models in state space form , 1992 .

[17]  A. Harvey,et al.  Forecasting Hourly Electricity Demand Using Time-Varying Splines , 1993 .

[18]  W. Newey,et al.  Automatic Lag Selection in Covariance Matrix Estimation , 1994 .

[19]  E. Fama,et al.  The Information in Long-Maturity Forward Rates , 1987 .

[20]  G. Duffee.  Forecasting with the term structure: The role of no-arbitrage restrictions , 2011 .

[21]  Matthias R. Fengler,et al.  The Analysis of Implied Volatilities , 2002 .

[22]  Robert R. Bliss,et al.  Movements in the term structure of interest rates , 1997 .

[23]  Ehud I. Ronn,et al.  Movements in the Term Structure of Interest Rates , 1997 .

[24]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[25]  Siem Jan Koopman,et al.  Fast Filtering and Smoothing for Multivariate State Space Models , 2000 .

[26]  J. Bai,et al.  Inferential Theory for Factor Models of Large Dimensions , 2003 .

[27]  Stephen Taylor,et al.  Forecasting Economic Time Series , 1979 .

[28]  Kenneth J. Singleton,et al.  A Latent Time Series Model of the Cyclical Behavior of Interest Rates , 1980 .

[29]  E. Mammen,et al.  Time Series Modelling With Semiparametric Factor Dynamics , 2007 .

[30]  J. Stock,et al.  Macroeconomic Forecasting Using Diffusion Indexes , 2002 .

[31]  Robert B. Litterman,et al.  Common Factors Affecting Bond Returns , 1991 .

[32]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[33]  Allan W. Gregory,et al.  Measuring World Business Cycles , 1997 .

[34]  D. Duffie,et al.  A Yield-factor Model of Interest Rates , 1996 .

[35]  Gregory Connor,et al.  A Test for the Number of Factors in an Approximate Factor Model , 1993 .

[36]  F. Diebold,et al.  Forecasting the Term Structure of Government Bond Yields , 2002 .

[37]  R. Engle.  Wald, likelihood ratio, and Lagrange multiplier tests in econometrics , 1984 .

[38]  M. Hallin,et al.  The Generalized Dynamic-Factor Model: Identification and Estimation , 2000, Review of Economics and Statistics.

[39]  Intelligible factors for the yield curve , 2010 .

[40]  Thomas J. Sargent,et al.  Business cycle modeling without pretending to have too much a priori economic theory , 1976 .

[41]  A Theoretical Foundation for the Nelson and Siegel Class of Yield Curve Models , 2011 .

[42]  J. McCulloch,et al.  Measuring the Term Structure of Interest Rates , 1971 .

[43]  John Geweke,et al.  Maximum Likelihood "Confirmatory" Factor Analysis of Economic Time Series , 1981 .

[44]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .