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The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison.

ABSTRACT: This paper evaluates the performance of eight tests with null hypothesis of cointegration on basis of probabilities of type I and II errors using Monte Carlo simulations. This study uses a variety of 132 different data generations covering three cases of deterministic part and four sample sizes. The three cases of deterministic part considered are: absence of both intercept and linear time trend, presence of only the intercept and presence of both the intercept and linear time trend. It is found that all of tests have either larger or smaller probabilities of type I error and concluded that tests face either problems of over rejection or under rejection, when asymptotic critical values are used. It is also concluded that use of simulated critical values leads to controlled probability of type I error. So, the use of asymptotic critical values may be avoided, and the use of simulated critical values is highly recommended. It is found and concluded that the simple LM test based on KPSS statistic performs better than rest for all specifications of deterministic part and sample sizes.

SUBMITTER: Aysan AF

PROVIDER: S-EPMC8726486 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature

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The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison.

Aysan Ahmet Faruk AF Guney Ibrahim I Isac Nicoleta N Khan Asad Ul Islam AUI

PloS one 20220104 1

This paper evaluates the performance of eight tests with null hypothesis of cointegration on basis of probabilities of type I and II errors using Monte Carlo simulations. This study uses a variety of 132 different data generations covering three cases of deterministic part and four sample sizes. The three cases of deterministic part considered are: absence of both intercept and linear time trend, presence of only the intercept and presence of both the intercept and linear time trend. It is found ...[more]

PMID: 34982763

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Project description:SignificancePerturbation and differential Monte Carlo (pMC/dMC) methods, used in conjunction with nonlinear optimization methods, have been successfully applied to solve inverse problems in diffuse optics. Application of pMC to systems over a large range of optical properties requires optimal "placement" of baseline conventional Monte Carlo (cMC) simulations to minimize the pMC variance. The inability to predict the growth in pMC solution uncertainty with perturbation size limits the application of pMC, especially for multispectral datasets where the variation of optical properties can be substantial.AimWe aim to predict the variation of pMC variance with perturbation size without explicit computation of perturbed photon weights. Our proposed method can be used to determine the range of optical properties over which pMC predictions provide sufficient accuracy. This method can be used to specify the optical properties for the reference cMC simulations that pMC utilizes to provide accurate predictions over a desired optical property range.ApproachWe utilize a conventional error propagation methodology to calculate changes in pMC relative error for Monte Carlo simulations. We demonstrate this methodology for spatially resolved diffuse reflectance measurements with ±20% scattering perturbations. We examine the performance of our method for reference simulations spanning a broad range of optical properties relevant for diffuse optical imaging of biological tissues. Our predictions are computed using the variance, covariance, and skewness of the photon weight, path length, and collision distributions generated by the reference simulation.ResultsWe find that our methodology performs best when used in conjunction with reference cMC simulations that utilize Russian Roulette (RR) method. Specifically, we demonstrate that for a proximal detector placed immediately adjacent to the source, we can estimate the pMC relative error within 5% of the true value for scattering perturbations in the range of [-15%,+20%]. For a distal detector placed at ∼3 transport mean free paths relative to the source, our method provides relative error estimates within 20% for scattering perturbations in the range of [-8%,+15%]. Moreover, reference simulations performed at lower (μs'/μa) values showed better performance for both proximal and distal detectors.ConclusionsThese findings indicate that reference simulations utilizing continuous absorption weighting (CAW) with the Russian Roulette method and executed using optical properties with a low (μs'/μa) ratio spanning the desired range of μs values, are highly advantageous for the deployment of pMC to obtain radiative transport estimates over a wide range of optical properties.

Dataset Information

The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison.

Publications

The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison.

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