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A Consistent Test for Nonlinear Out of Sample Predictive Accuracy

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Author Info
Corradi, V.
Swanson, N.R.

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Abstract

In this paper, we draw on both the consistent specification testing and the predictive ability testing literatures and propose a test for predictive accuracy which is consistent against generic nonlinear alternatives. Broadly speaking, given a particular reference model, assume that the objective is to test whether there exists any alternative model, among an infinite number of alternatives, that has better predictive accuracy than the reference model, for a given loss function. A typical example is the case in which the reference model is a simple autoregressive model and the objective is to check whether a more accurate forecasting model can be constructed by including possibly unknown (non)linear functions of the past of the process or of the past of some other process(es). We propose a statistic which is similar in spirit to that of White (2000), although our approach differs from his as we allow for an infinite number of competing models that may be nested. In addition, we allow for non vanishing parameter estimation error. In order to construct valid asymptotic critical values, we implement a conditional p-value procedure which extends the work of Inoue (1999) by allowing for non vanishing parameter estimation error.

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Publisher Info
Paper provided by University of Exeter, School of Business and Economics in its series Discussion Papers with number 00/12.

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Length: 27 pages
Date of creation: 2000
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Handle: RePEc:fth:exetec:00/12

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Related research
Keywords: TESTS ; MODELS ; MATHEMATICS;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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  1. Jonathan B. Hill, 2004. "Consistent Model Specification Tests Against Smooth Transition Alternatives," Econometrics 0402004, EconWPA, revised 01 Mar 2004. [Downloadable!]
  2. Jonathan B. Hill, 2004. "Consistent LM-Tests for Linearity Against Compound Smooth Transition Alternatives," Econometric Society 2004 North American Summer Meetings 42, Econometric Society. [Downloadable!]
  3. Lutz Kilian & Atsushi Inoue, 2002. "In-Sample or out-of-sample tests of predictability: which one should we use?," Working Paper Series 195, European Central Bank. [Downloadable!]
    Other versions:
  4. Valentina Corradi & Norman Swanson, 2003. "Some Recent Developments in Predictive Accuracy Testing With Nested Models and (Generic) Nonlinear Alternatives," Departmental Working Papers 200316, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  5. Jonathan Hill, 2006. "Asymptotically Nuisance-Parameter-Free Consistent Tests of Lp-Functional Form," Working Papers 0608, Florida International University, Department of Economics. [Downloadable!]
  6. Elliott, Graham & Komunjer, Ivana & Timmermann, Allan G, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  7. Todd E. Clark & Michael W. McCracken, 2007. "Tests of equal predictive ability with real-time data," Research Working Paper RWP 07-06, Federal Reserve Bank of Kansas City. [Downloadable!]
    Other versions:
  8. Jonathan B. Hill, 2004. "Efficient Tests of Long-Run Causation in Trivariate VAR Processes with a Rolling Window Study of the Money-Income Relationship," Working Papers 0413, Florida International University, Department of Economics. [Downloadable!]
    Other versions:
  9. Rosario Dell'Aquila & Elvezio Ronchetti, 2004. "Robust tests of predictive accuracy," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 161-184. [Downloadable!]
  10. Valentina Corradi & Norman R. Swanson, 2003. "The Effect of Data Transformation on Common Cycle, Cointegration and Unit Root Tests: Monte Carlo Results and a Simple Test," Departmental Working Papers 200322, Rutgers University, Department of Economics. [Downloadable!]
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  11. Allan Timmermann & Andrew J. Patton, 2004. "Properties of Optimal Forecasts," Econometric Society 2004 North American Winter Meetings 234, Econometric Society. [Downloadable!]
    Other versions:
  12. Teräsvirta, Timo, 2005. "Forecasting economic variables with nonlinear models," Working Paper Series in Economics and Finance 598, Stockholm School of Economics, revised 29 Dec 2005. [Downloadable!]
    Other versions:
  13. Andrew J. Patton & Allan Timmermann, 2005. "Testable Implications of Forecast Optimality," STICERD - Econometrics Paper Series /2005/485, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  14. Valentina Corradi & Andres Fernandez & Norman Swanson, 2008. "Information in the revision process of real-time datasets," Working Papers 08-27, Federal Reserve Bank of Philadelphia. [Downloadable!]
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