A Modified Box-Cox Transformation in the Multivariate ARMA Model

Terasaka, Takahiro; Hosoya, Yuzo

doi:10.14490/jjss.37.1

Cited by 4 publications

(3 citation statements)

References 38 publications

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“…The problem of establishing the asymptotic properties of the MLEs in our setting is a difficult one. It is similar to, but appears to be more technically challenging than, the problem of showing consistency and efficiency of MLEs for a Box-Cox-transformed Gaussian ARMA process, as discussed in Terasaka and Hosoya (2007). We are also working with a componentwise transformed ARMA process, although, in our case, the transformation (X t ) → (Z t ) is via the nonlinear, non-increasing volatility proxy transformation T (Z) (x) in ( 5), which is not differentiable at the change point µ T .…”

Section: Statistical Inferencementioning

confidence: 99%

Modelling Volatile Time Series with V-Transforms and Copulas

McNeil

2021

Risks

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An approach to the modelling of volatile time series using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the stationary distribution of the time series and quantiles of the distribution of a predictable volatility proxy variable. They can be represented as copulas and permit the formulation and estimation of models that combine arbitrary marginal distributions with copula processes for the dynamics of the volatility proxy. The idea is illustrated using a Gaussian ARMA copula process and the resulting model is shown to replicate many of the stylized facts of financial return series and to facilitate the calculation of marginal and conditional characteristics of the model including quantile measures of risk. Estimation is carried out by adapting the exact maximum likelihood approach to the estimation of ARMA processes, and the model is shown to be competitive with standard GARCH in an empirical application to Bitcoin return data.

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Section: Statistical Inferencementioning

confidence: 99%

Modelling Volatile Time Series with V-Transforms and Copulas

McNeil

2021

Risks

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“…The initial assumption of BCT restricted to positive data. Additionally, BCT restricts the sample space of the transformed variable by the two inequalities Z λ > −1\λ if λ > 0 and Z λ > −1\λ if λ < 0 so that it is not consistent with the normality assumption of the transformed variable [13]. Yeo and Johnson [14] generalized the BCT within the case of the negative random variable to achieve the advantage of working without having to fret about the domain of Z.…”

Section: Introductionmentioning

confidence: 99%

On the Use of the Power Transformation Models to Improve the Temperature Time Series

Othman

Ali

2023

Stat., optim. inf. comput.

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The aim of this paper is to select an appropriate ARIMA model for the time series after transforming the original responses. Box-Cox and Yeo-Johnson power transformation models were used on the response variables of two time series datasets of average temperatures and then diagnosed and built the appropriate ARIMA models for each time-series. The authors treat the results of the model fitting as a package in an attempt to decide and choose the best model by diagnosing the effect of the data transformation on the response normality, significant of estimated model parameters, forecastability and the behavior of the residuals. The authors conclude that the Yeo-Johnson model was more flexible in smoothing the data and contributedto accessing a simple model with good forecastability.

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“…In addition to the classic paper by Box and Cox , Gurka et al . examined Box–Cox transformations in linear mixed models, and Terasaka and Hosoya extended the Box–Cox transformation to the multivariate time series model. Bayesian papers include that of Pericchi and Sweeting who examined the choice of prior distribution for the Box–Cox transformed linear model.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference for multivariate meta‐analysis Box–Cox transformation models for individual patient data with applications to evaluation of cholesterol‐lowering drugs

Kim

Chen

Ibrahim

et al. 2013

Statistics in Medicine

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In this paper, we propose a class of Box-Cox transformation regression models with multidimensional random effects for analyzing multivariate responses for individual patient data (IPD) in meta-analysis. Our modeling formulation uses a multivariate normal response meta-analysis model with multivariate random effects, in which each response is allowed to have its own Box-Cox transformation. Prior distributions are specified for the Box-Cox transformation parameters as well as the regression coefficients in this complex model, and the Deviance Information Criterion (DIC) is used to select the best transformation model. Since the model is quite complex, a novel Monte Carlo Markov chain (MCMC) sampling scheme is developed to sample from the joint posterior of the parameters. This model is motivated by a very rich dataset comprising 26 clinical trials involving cholesterol lowering drugs where the goal is to jointly model the three dimensional response consisting of Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG) (LDL-C, HDL-C, TG). Since the joint distribution of (LDL-C, HDL-C, TG) is not multivariate normal and in fact quite skewed, a Box-Cox transformation is needed to achieve normality. In the clinical literature, these three variables are usually analyzed univariately: however, a multivariate approach would be more appropriate since these variables are correlated with each other. A detailed analysis of these data is carried out using the proposed methodology.

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A Modified Box-Cox Transformation in the Multivariate ARMA Model

Cited by 4 publications

References 38 publications

Modelling Volatile Time Series with V-Transforms and Copulas

Modelling Volatile Time Series with V-Transforms and Copulas

On the Use of the Power Transformation Models to Improve the Temperature Time Series

Bayesian inference for multivariate meta‐analysis Box–Cox transformation models for individual patient data with applications to evaluation of cholesterol‐lowering drugs

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