Multivariate singular spectrum analysis for forecasting revisions to real-time data

Real-time data on national accounts statistics typically undergo an extensive revision process, leading to multiple vintages on the same generic variable. The time between the publication of the initial and final data is a lengthy one and raises the question of how to model and forecast the final vintage of data – an issue that dates from seminal articles by Mankiw et al. [51], Mankiw and Shapiro [52] and Nordhaus [57]. To solve this problem, we develop the non-parametric method of multivariate singular spectrum analysis (MSSA) for multi-vintage data. MSSA is much more flexible than the standard methods of modelling that involve at least one of the restrictive assumptions of linearity, normality and stationarity. The benefits are illustrated with data on the UK index of industrial production: neither the preliminary vintages nor the competing models are as accurate as the forecasts using MSSA.

[1]  Andrew L. Rukhin,et al.  Analysis of Time Series Structure SSA and Related Techniques , 2002, Technometrics.

[2]  Tom Stark and Dean Croushore.  Forecasting with a Real-Time Data Set for Macroeconomists , 2001 .

[3]  R. D'Agostino.  Transformation to normality of the null distribution of g1 , 1970 .

[4]  Dimitrios D. Thomakos,et al.  A review on singular spectrum analysis for economic and financial time series , 2010 .

[5]  Anthony Garratt,et al.  UK Real-Time Macro Data Characteristics , 2006 .

[6]  Anatoly A. Zhigljavsky,et al.  Singular spectrum analysis: methodology and application to economics data , 2009, J. Syst. Sci. Complex..

[7]  Ramazan Gençay,et al.  Testing chaotic dynamics via Lyapunov exponents , 1998 .

[8]  Kerry Patterson.  Rebasing, Common Cycles, and Some Practical Implications of Modelling Data Revisions , 2004 .

[9]  G. P. King,et al.  Extracting qualitative dynamics from experimental data , 1986 .

[10]  Hossein Hassani,et al.  Singular Spectrum Analysis: Methodology and Comparison , 2021, Journal of Data Science.

[11]  D. R. Salgado,et al.  Tool wear detection in turning operations using singular spectrum analysis , 2006 .

[12]  David E. Runkle,et al.  Are preliminary announcements of the money stock rational forecasts , 1984 .

[13]  Alain Hecq,et al.  Advanced Revision Analysis for Economic Time Series and Their Role for Improving Forecast accuracy , 2008 .

[14]  Sucharita Ghosh,et al.  Forecasting with preliminary data , 1997 .

[15]  Michael P. Clements,et al.  Real-time forecasting of inflation and output growth with autoregressive models in the presence of data revisions , 2013 .

[16]  V. Moskvina,et al.  An Algorithm Based on Singular Spectrum Analysis for Change-Point Detection , 2003 .

[17]  K. D. Patterson.  Modelling the data measurement process for the index of production , 2002 .

[18]  Hans-Eggert Reimers,et al.  Dealing with Benchmark Revisions in Real-Time Data: The Case of German Production and Orders Statistics , 2009 .

[19]  Shlomo Maital,et al.  What Do Economists Know? An Empirical Study of Experts' Expectations , 1981 .

[20]  K. Daoudi.  News , 1988, Schizophrenia Research.

[21]  S. B. Aruoba,et al.  Data Revisions are Not Well-Behaved , 2004 .

[22]  A. Zhigljavsky,et al.  Forecasting European industrial production with singular spectrum analysis , 2009 .

[23]  Ronnie Driver,et al.  Dealing with Data Uncertainty , 2005 .

[24]  Dean Croushore,et al.  Forecasting with Real-Time Macroeconomic Data , 2006 .

[25]  Michael P. Clements,et al.  A Monte Carlo Study of the Forecasting Performance of Empirical Setar Models , 1999 .

[26]  Carol Corrado,et al.  Application of the Kalman filter to revisions in monthly retail sales estimates , 1979 .

[27]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

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

[29]  J. Doornik,et al.  An Omnibus Test for Univariate and Multivariate Normality , 2008 .

[30]  Kerry Patterson,et al.  Revisions to Official Data on U.S. GNP: A Multivariate Assessment of Different Vintages , 2004 .

[31]  Paul Newbold,et al.  Testing the equality of prediction mean squared errors , 1997 .

[32]  Jan P. A. M. Jacobs,et al.  Modeling data revisions: Measurement error and dynamics of 'true' values , 2011 .

[33]  L. Shenton,et al.  A Bivariate Model for the Distribution of √b1 and b2 , 1977 .

[34]  Fabio Busetti,et al.  Preliminary Data and Econometric Forecasting: An Application with the Bank of Italy Quarterly Model , 2004 .

[35]  Chris Aldrich,et al.  Process system identification strategies based on the use of singular spectrum analysis , 2003 .

[36]  Dennis J. Fixler,et al.  News, Noise, and Estimates of the "True" Unobserved State of the Economy , 2013 .

[37]  E. Philip Howrey,et al.  Data Revision, Reconstruction, and Prediction: An Application to Inventory Investment , 1984 .

[38]  Wayne A. Fuller,et al.  Unit Root Tests Based on Unconditional Maximum Likelihood Estimation for the Autoregressive Moving Average , 1998 .

[39]  Lutz Kilian,et al.  NEW INTRODUCTION TO MULTIPLE TIME SERIES ANALYSIS, by Helmut Lütkepohl, Springer, 2005 , 2006, Econometric Theory.

[40]  George Kapetanios,et al.  A State Space Approach to Extracting the Signal From Uncertain Data , 2007 .

[41]  C. Granger,et al.  USING THE MUTUAL INFORMATION COEFFICIENT TO IDENTIFY LAGS IN NONLINEAR MODELS , 1994 .

[42]  Craig Richardson.  Revisions analysis: a time series approach , 2003 .

[43]  Terence C. Mills,et al.  Trends and Cycles in British Industrial Production, 1700–1913 , 1989 .

[44]  Dean Croushore,et al.  A real-time data set for macroeconomists , 2001 .

[45]  William D. Nordhaus,et al.  Forecasting Efficiency: Concepts and Applications , 1987 .

[46]  J. Stock,et al.  Efficient Tests for an Autoregressive Unit Root , 1992 .

[47]  Hisashi Tanizaki,et al.  Prediction of Final Data with Use of Preliminary and/or Revised Data , 1995 .

[48]  Kerry Patterson.  A state space approach to forecasting the final vintage of revised data with an application to the index of industrial production , 1995 .

[49]  L. Shenton,et al.  Bivariate model for the distribution of. sqrt. b/sub 1/ and b/sub 2/ , 1977 .

[50]  S. Pantula,et al.  Determining the Order of Differencing in Autoregressive Processes , 1987 .

[51]  Jennifer L. Castle,et al.  Building a Real-Time Database for Gdp(E) , 2005 .

[52]  K. A. Mork.  Ain't Behavin': Forecast Errors and Measurement Errors in Early GNP Estimates , 1987 .

[53]  Hossein Hassani,et al.  The effect of noise reduction in measuring the linear and nonlinear dependency of financial markets , 2010 .

[54]  E. P. Howrey,et al.  The Use of Preliminary Data in Econometric Forecasting , 1978 .

[55]  C. Granger,et al.  Handbook of Economic Forecasting , 2006 .

[56]  E. Maasoumi,et al.  A Dependence Metric for Possibly Nonlinear Processes , 2004 .

[57]  P. Newbold,et al.  Looking for Evolving Growth Rates and Cycles in British Industrial Production, 1700-1913 , 1991 .

[58]  Saeed Heravi,et al.  Linear versus neural network forecasts for European industrial production series , 2004 .

[59]  S. Sosvilla‐Rivero,et al.  Testing Chaotic Dynamics Via Lyapunov Exponents , 2000 .

[60]  Ahmed BenSaïda,et al.  Using the Lyapunov Exponent as a Practical Test for Noisy Chaos , 2007 .

[61]  The Accuracy of OECD Forecasts for Japan , 1997 .

[62]  N. Golyandina,et al.  SSA-based approaches to analysis and forecast of multidimensional time series , 2012 .

[63]  K D Patterson,et al.  An Integrated Model of the Data Measurement and Data Generation Processes with an Application to Consumers' Expenditure , 1995 .

[64]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[65]  Dean D. Croushore,et al.  Frontiers of Real-Time Data Analysis , 2008 .

[66]  Kerry Patterson,et al.  EFFICIENT FORECASTS OR MEASUREMENT ERRORS? SOME EVIDENCE FOR REVISIONS TO UNITED KINGDOM GDP GROWTH RATES* , 1992 .

[67]  Kerry Patterson,et al.  Forecasting the final vintage of real personal disposable income: A state space approach , 1995 .

[68]  Glenn Deane,et al.  Model selection procedures in social research: Monte-Carlo simulation results , 2008 .

[69]  N. Gregory Mankiw,et al.  News or Noise : An Analysis of GNP Revisions , 2007 .