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A likelihood ratio and Markov chain‐based method to evaluate density forecasting
Author(s) -
Li Yushu,
Andersson Jonas
Publication year - 2020
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.2604
Subject(s) - markov chain , parametric statistics , nonparametric statistics , computer science , likelihood ratio test , econometrics , distribution (mathematics) , mathematics , statistics , machine learning , mathematical analysis
In this paper, we propose a likelihood ratio‐based method to evaluate density forecasts, which can jointly evaluate the unconditional forecasted distribution and dependence of the outcomes. Unlike the well‐known Berkowitz test, the proposed method does not require a parametric specification of time dynamics. We compare our method with the method proposed by several other tests and show that our methodology has very high power against both dependence and incorrect forecasting distributions. Moreover, the loss of power, caused by the nonparametric nature of the specification of the dynamics, is shown to be small compared to the Berkowitz test, even when the parametric form of dynamics is correctly specified in the latter method.