Motivated by Lee and Ko (Appl. Stochastic Models. Bus. Ind. 2007; 23:493–502) but not limited to the study, this paper proposes a wavelet-based Bayesian power transformation procedure through the well-known Box–Cox transformation to induce normality from non-Gaussian long memory processes. We consider power transformations of non-Gaussian long memory time series under the assumption of an unknown transformation parameter, a situation that arises commonly in practice, while most research has been devoted to non-linear transformations of Gaussian long memory time series with known transformation parameter. Specially, this study is mainly focused on the simultaneous estimation of the transformation parameter and long memory parameter. To this end, posterior estimations via Markov chain Monte Carlo methods are performed in the wavelet domain. Performances are assessed on a simulation study and a German stock return data set.

In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.

This paper proposes an accurate condence interval for the trend parameter in a linear regression model with long memory errors. The interval is based upon an equivalent sum of squares method and is shown to perform comparably to a weighted least squares interval. The advantages of the proposed interval lies in its relative ease of computation and should be attractive to practitioners.

Long memory processes are widely used in many scientific fields, such as economics, physics, and engineering. Change point detection problems have received considerable attention in the literature because of their wide range of possible applications. Here we describe a wavelet-based Bayesian procedure for the estimation and location of multiple change points in the long memory parameter of Gaussian autoregressive fractionally integrated moving average models (ARFIMA(p, d, q)), with unknown autoregressive and moving average parameters. Our methodology allows the number of change points to be unknown. The reversible jump Markov chain Monte Carlo algorithm is used for posterior inference. The method also produces estimates of all model parameters. Performances are evaluated on simulated data and on the benchmark Nile river dataset

The wavelet deconvolution method WaveD using band-limited wavelets offers both theoretical and computational advantages over traditional compactly supported wavelets. The translation-invariant WaveD with a fast algorithm improves further. The twofold cross-validation method for choosing the threshold parameter and the finest resolution level in WaveD is introduced. The algorithm’s performance is compared with the fixed constant tuning and the default tuning in WaveD.