Special Issue "Non-Linear Regression Modeling"

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A special issue of Econometrics (ISSN 2225-1146).

Deadline for manuscript submissions: closed (28 November 2014)

Special Issue Editor

Guest Editor
Prof. Dr. Timo Teräsvirta

Department of Economics and Business, Aarhus University, Fuglesangs Allé 4, Building 2628, 8210 Aarhus, Denmark

Special Issue Information

Dear Colleagues,

Regression models that are nonlinear in parameters are widely used in the natural sciences, engineering and economics, among other fields, for phenomena where linear regression does not provide an accurate fit of observational data. The purpose of this special issue is to study methods for building such nonlinear models and to tackle the challenges that arise from characterizing their statistical properties. We welcome papers that deal with the techniques of nonlinear modeling, as well as papers that apply nonlinear regression to topics in economics and related subject areas in the social sciences.

Professor Timo Teräsvirta
Guest Editor

 

Keywords

  • Non-linear least squares
  • Testing linearity
  • Nonlinear modeling and nonlinear model specification
  • Iterative numeric techniques
  • Gauss-Newton method
  • Maximum likelihood estimation
  • Generalized method of moments
  • Semi- and nonparametric estimation

Published Papers (3 papers)

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Research

Open AccessArticle Nonparametric Regression Estimation for Multivariate Null Recurrent Processes
Econometrics 2015, 3(2), 265-288; doi:10.3390/econometrics3020265
Received: 26 November 2014 / Revised: 27 March 2015 / Accepted: 2 April 2015 / Published: 14 April 2015
Cited by 1 | PDF Full-text (532 KB) | HTML Full-text | XML Full-text
Abstract
This paper discusses nonparametric kernel regression with the regressor being a \(d\)-dimensional \(\beta\)-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate \(\sqrt{n(T)h^{d}}\), where \(n(T)\) is the number of regenerations for a [...] Read more.
This paper discusses nonparametric kernel regression with the regressor being a \(d\)-dimensional \(\beta\)-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate \(\sqrt{n(T)h^{d}}\), where \(n(T)\) is the number of regenerations for a \(\beta\)-null recurrent process and the limiting distribution (with proper normalization) is normal. Furthermore, we show that the two-step estimator for the volatility function is consistent. The finite sample performance of the estimate is quite reasonable when the leave-one-out cross validation method is used for bandwidth selection. We apply the proposed method to study the relationship of Federal funds rate with 3-month and 5-year T-bill rates and discover the existence of nonlinearity of the relationship. Furthermore, the in-sample and out-of-sample performance of the nonparametric model is far better than the linear model. Full article
(This article belongs to the Special Issue Non-Linear Regression Modeling)
Open AccessArticle Finding Starting-Values for the Estimation of Vector STAR Models
Econometrics 2015, 3(1), 65-90; doi:10.3390/econometrics3010065
Received: 26 October 2014 / Revised: 26 November 2014 / Accepted: 4 January 2015 / Published: 29 January 2015
Cited by 2 | PDF Full-text (460 KB) | HTML Full-text | XML Full-text
Abstract
This paper focuses on finding starting-values for the estimation of Vector STAR models. Based on a Monte Carlo study, different procedures are evaluated. Their performance is assessed with respect to model fit and computational effort. I employ (i) grid search algorithms and [...] Read more.
This paper focuses on finding starting-values for the estimation of Vector STAR models. Based on a Monte Carlo study, different procedures are evaluated. Their performance is assessed with respect to model fit and computational effort. I employ (i) grid search algorithms and (ii) heuristic optimization procedures, namely differential evolution, threshold accepting, and simulated annealing. In the equation-by-equation starting-value search approach the procedures achieve equally good results. Unless the errors are cross-correlated, equation-by-equation search followed by a derivative-based algorithm can handle such an optimization problem sufficiently well. This result holds also for higher-dimensional Vector STAR models with a slight edge for heuristic methods. For more complex Vector STAR models which require a multivariate search approach, simulated annealing and differential evolution outperform threshold accepting and the grid search. Full article
(This article belongs to the Special Issue Non-Linear Regression Modeling)
Open AccessArticle Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity
Econometrics 2015, 3(1), 2-54; doi:10.3390/econometrics3010002
Received: 31 July 2014 / Accepted: 19 December 2014 / Published: 16 January 2015
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Abstract
We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility [...] Read more.
We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500) and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility. Full article
(This article belongs to the Special Issue Non-Linear Regression Modeling)

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