Non‐parametric smoothing and prediction for nonlinear circular time series

Marzio, Macro Di; Panzera, Agnese; Taylor, Charles

doi:10.1111/j.1467-9892.2012.00794.x

Cited by 18 publications

(15 citation statements)

References 15 publications

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“…Now, with b =1 we have the estimation of autoregressive functions, whilst the conditional variance can be estimated by taking b =2 and a =1. Interestingly, many circular datasets are time series (wind and ocean current directions are obvious examples), and few researchers appear to have addressed this topic; see Breckling (1989) and Fisher & Lee (1994), both aimed to wrapping parametric autoregressive processes and Di Marzio et al. (2012) who estimate trend.…”

Section: Data From Mixing Processesmentioning

confidence: 99%

“…Nor we should use undersmoothing, as instead the author suggests, to highlight small‐scale trend. These approaches would not allow to separate signal from noise for several serious reasons, see the detailed discussion provided by Di Marzio et al (2012). Thus, we think that trend estimation in circular time series constitutes a promising topic for future research.…”

Section: Interpretation and Links To Previous Workmentioning

confidence: 99%

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Non‐parametric Regression for Circular Responses

Marzio

Panzera

Taylor

2012

Scandinavian J Statistics

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Abstract. Regression with a circular response is a topic of current interest. We introduce non‐parametric smoothing for this problem. Simple adaptations of a weight function enable a unified formulation for both real‐line and circular predictors, whereas these cases have been tackled by quite distinct parametric methods. Additionally, we discuss various methodological extensions, obtaining a number of promising techniques – totally new in circular statistics – such as confidence intervals for the value of a circular regression and non‐parametric autoregression in circular time series. The findings are also illustrated through real data examples.

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Section: Data From Mixing Processesmentioning

confidence: 99%

Section: Interpretation and Links To Previous Workmentioning

confidence: 99%

Non‐parametric Regression for Circular Responses

Marzio

Panzera

Taylor

2012

Scandinavian J Statistics

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“…(2) (Jammalamadaka and Sarma, 1988). With the exception of Di Marzio et al (2012), circular time series models discussed in the literature are weakly dependent. In contrast, here we will define circular time series with long-range dependence (or strong dependence).…”

Section: Strongly Dependent Circular Time Seriesmentioning

confidence: 99%

Estimating the Mean Direction of Strongly Dependent Circular Time Series

Beran

Ghosh

2019

Journal Time Series Analysis

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A class of circular processes based on Gaussian subordination is introduced. This allows for flexible modelling of directional time series with long‐range dependence. Based on limit theorems for subordinated processes and consistent estimation of nuisance parameters, asymptotic confidence intervals for the mean direction are derived. Extensions to cases where the direction depends on explanatory variables are also considered. Simulations and a data example illustrate the proposed method.

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“…where σ 2 = ψ −1 2 . Here it is important to remind the reader that in this paper our motive of introducing the kernels k 1 and k 2 is entirely different from the other existing works involving circular and spherical data, where the goals are density estimation, nonparametric regression and smoothing (see, for example, Hall et al (1987), , ), Marzio et al (2011), Marzio et al (2012b, Marzio et al (2012a), Marzio et al (2014)). Hence, our kernels need not satisfy the optimality properties required for the aforementioned works.…”

Section: A2 Covariance Structure Of Our Gaussian Processmentioning

confidence: 99%

Bayesian nonparametric dynamic state space modeling with circular latent states

Mazumder

Bhattacharya

2015

Journal of Statistical Theory and Practice

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State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are wellstudied, nonparametric approaches are much less explored in comparison. In this article we propose a novel Bayesian nonparametric approach to state space modeling assuming that both the observational and evolutionary functions are unknown and are varying with time;crucially, we assume that the unknown evolutionary equation describes dynamic evolution of some latent circular random variable.Based on appropriate kernel convolution of the standard Weiner process we model the time-varying observational and evolutionary functions as suitable Gaussian processes that take both linear and circular variables as arguments. Additionally, for the time-varying evolutionary function, we wrap the Gaussian process thus constructed around the unit circle to form an appropriate circular Gaussian process. We show that our process thus created satisfies desirable properties.For the purpose of inference we develop an MCMC based methodology combining Gibbs sampling and Metropolis-Hastings algorithms. Applications to a simulated dataset, a real wind speed dataset and a real ozone dataset demonstrated quite encouraging performances of our model and methodologies.

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Non‐parametric smoothing and prediction for nonlinear circular time series

Cited by 18 publications

References 15 publications

Non‐parametric Regression for Circular Responses

Non‐parametric Regression for Circular Responses

Estimating the Mean Direction of Strongly Dependent Circular Time Series

Bayesian nonparametric dynamic state space modeling with circular latent states

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