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Statistical Tests for Multiple Forecast Comparison
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
2012 (English)In: Journal of Econometrics, ISSN 0304-4076, E-ISSN 1872-6895, Vol. 169, no 1, 123-130 p.Article in journal (Refereed) Published
Abstract [en]

We consider a multivariate version of the Diebold-Mariano test for equal predictive ability of three or more forecasting models. The Wald-type test, S, which has a null distribution that is asymptotically chi-squared, is shown to be generally invariant with respect to the ordering of the models being compared. Finite-sample corrections for the test are also developed. Monte Carlo simulations indicate that S has reasonable size properties in large samples but tends to be oversized in moderate samples. The finite-sample correction succeeds in correcting for size, but only partially. For the size-adjusted tests, power increases with sample size, as expected. It is speculated that further finite-sample improvements can be achieved using Hotelling's T-2 or bootstrap critical values.

Place, publisher, year, edition, pages
2012. Vol. 169, no 1, 123-130 p.
Keyword [en]
forecast comparison, multivariate tests of equal predictive ability, diebold–Mariano test, finite-sample correction
National Category
Social Sciences
URN: urn:nbn:se:uu:diva-97032DOI: 10.1016/j.jeconom.2012.01.014ISI: 000306046900012OAI: oai:DiVA.org:uu-97032DiVA: diva2:171805
Available from: 2008-04-16 Created: 2008-04-16 Last updated: 2012-08-06Bibliographically approved
In thesis
1. Essays on Time Series Analysis: With Applications to Financial Econometrics
Open this publication in new window or tab >>Essays on Time Series Analysis: With Applications to Financial Econometrics
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This doctoral thesis is comprised of four papers that all relate to the subject of Time Series Analysis.

The first paper of the thesis considers point estimation in a nonnegative, hence non-Gaussian, AR(1) model. The parameter estimation is carried out using a type of extreme value estimators (EVEs). A novel estimation method based on the EVEs is presented. The theoretical analysis is complemented with Monte Carlo simulation results and the paper is concluded by an empirical example.

The second paper extends the model of the first paper of the thesis and considers semiparametric, robust point estimation in a nonlinear nonnegative autoregression. The nonnegative AR(1) model of the first paper is extended in three important ways: First, we allow the errors to be serially correlated. Second, we allow for heteroskedasticity of unknown form. Third, we allow for a multi-variable mapping of previous observations. Once more, the EVEs used for parameter estimation are shown to be strongly consistent under very general conditions. The theoretical analysis is complemented with extensive Monte Carlo simulation studies that illustrate the asymptotic theory and indicate reasonable small sample properties of the proposed estimators.

In the third paper we construct a simple nonnegative time series model for realized volatility, use the results of the second paper to estimate the proposed model on S&P 500 monthly realized volatilities, and then use the estimated model to make one-month-ahead forecasts. The out-of-sample performance of the proposed model is evaluated against a number of standard models. Various tests and accuracy measures are utilized to evaluate the forecast performances. It is found that forecasts from the nonnegative model perform exceptionally well under the mean absolute error and the mean absolute percentage error forecast accuracy measures.

In the fourth and last paper of the thesis we construct a multivariate extension of the popular Diebold-Mariano test. Under the null hypothesis of equal predictive accuracy of three or more forecasting models, the proposed test statistic has an asymptotic Chi-squared distribution. To explore whether the behavior of the test in moderate-sized samples can be improved, we also provide a finite-sample correction. A small-scale Monte Carlo study indicates that the proposed test has reasonable size properties in large samples and that it benefits noticeably from the finite-sample correction, even in quite large samples. The paper is concluded by an empirical example that illustrates the practical use of the two tests.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2008. 21 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 39
non-Gaussian time series, nonnegative autoregression, robust estimation, strong convergence, realized volatility, volatility forecast, forecast comparison, Diebold-Mariano test
National Category
Probability Theory and Statistics
urn:nbn:se:uu:diva-8638 (URN)978-91-554-7158-3 (ISBN)
Public defence
2008-05-09, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 10:15
Available from: 2008-04-16 Created: 2008-04-16Bibliographically approved

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