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A flexible approach to parametric inference in nonlinear and time varying time series models

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  • Koop, Gary
  • Potter, Simon

Abstract

Many structural break and regime-switching models have been used with macroeconomic and financial data. In this paper, we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications. We build on earlier work showing the relationship between flexible functional forms and random variation in parameters. Our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring (reordered) observations. The range of priors produced in this way can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the amount of random variation in parameters to depend on the distance between (reordered) observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). Bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering. Conditional on a hypothetical reordering and distance function, a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation. We use artificial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth.

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  • Koop, Gary & Potter, Simon, 2010. "A flexible approach to parametric inference in nonlinear and time varying time series models," Journal of Econometrics, Elsevier, vol. 159(1), pages 134-150, November.
  • Handle: RePEc:eee:econom:v:159:y:2010:i:1:p:134-150
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    3. Claudio Morana, 2013. "The Oil Price-Macroeconomy Relationship Since the Mid-1980s: A Global Perspective," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    4. Chan, Joshua C.C. & Grant, Angelia L., 2015. "Pitfalls of estimating the marginal likelihood using the modified harmonic mean," Economics Letters, Elsevier, vol. 131(C), pages 29-33.
    5. Knotek, Edward S. & Zaman, Saeed, 2021. "Asymmetric responses of consumer spending to energy prices: A threshold VAR approach," Energy Economics, Elsevier, vol. 95(C).
    6. Philipp Piribauer, 2016. "Heterogeneity in spatial growth clusters," Empirical Economics, Springer, vol. 51(2), pages 659-680, September.
    7. Aue, Alexander & Horváth, Lajos & Hušková, Marie, 2012. "Segmenting mean-nonstationary time series via trending regressions," Journal of Econometrics, Elsevier, vol. 168(2), pages 367-381.
    8. Joshua C.C. Chan & Rodney W. Strachan, 2020. "Bayesian state space models in macroeconometrics," CAMA Working Papers 2020-90, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    9. Banu Kurtaran, 2015. "Re-examining the PPP Hypothesis via Nonlinearity and Smooth Breaks," Econometrics Letters, Bilimsel Mektuplar Organizasyonu (Scientific letters), vol. 2(1), pages 1-21.

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    More about this item

    Keywords

    Bayesian Structural break Threshold autoregressive Regime switching State space model;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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