Simultaneous inference and trend specification testing in ARMA model with trend via innovation distribution function

The innovation distribution function in the ARMA model with trend is estimated by the kernel distribution estimator (KDE). The KDE is shown to converge weakly to a Gaussian process with certain covariance structure, yielding a simultaneous confidence band (SCB) for the innovation distribution functi...

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Vydáno v:Statistical papers (Berlin, Germany) Ročník 66; číslo 5; s. 120
Hlavní autor: Zhong, Chen
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2025
Springer Nature B.V
Témata:
Air temperature
Asymptotic methods
Asymptotic properties
Distribution functions
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Efficiency
Finance
Gaussian process
Goodness of fit
Innovations
Insurance
Management
Mathematics and Statistics
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Regular Article
Specifications
Statistical inference
Statistical methods
Statistical tests
Statistics
Statistics for Business
Time series
62G05
62M10
Gaussian process
Goodness-of-fit test
Kernel distribution estimator
Simultaneous confidence band
B-spline
62F03
ISSN:0932-5026, 1613-9798
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Shrnutí:The innovation distribution function in the ARMA model with trend is estimated by the kernel distribution estimator (KDE). The KDE is shown to converge weakly to a Gaussian process with certain covariance structure, yielding a simultaneous confidence band (SCB) for the innovation distribution function. Additionally, a goodness-of-fit test statistics for testing whether the trend function belongs to some parametric form is proposed through measuring the difference between the nonparametric and parametric residuals via the KDE of innovation distribution function. The asymptotic distribution of the test statistics under the null is developed and the asymptotic power against local alternatives is examined as well. Bootstrap methods are employed to implement the trend specification test and work well in the numerical studies. The proposed theory is illustrated by two data sets including spot price returns and global air temperature data.
Bibliografie:ObjectType-Article-1
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ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-025-01743-5