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beyondWhittle (version 1.0)

Bayesian Spectral Inference for Stationary Time Series

Description

Implementations of a Bayesian parametric (autoregressive), a Bayesian nonparametric (Whittle likelihood with Bernstein-Dirichlet prior) and a Bayesian semiparametric (autoregressive likelihood with Bernstein-Dirichlet correction) procedure are provided. The work is based on the corrected parametric likelihood by C. Kirch et al (2017) . It was supported by DFG grant KI 1443/3-1.

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Version

Install

install.packages('beyondWhittle')

Monthly Downloads

502

Version

1.0

License

GPL (>= 3)

Maintainer

Alexander Meier

Last Published

July 16th, 2018

Functions in beyondWhittle (1.0)

Help function to compute the mean.

generalizedGaussian.alpha

Help function for Generalized Gaussian

Help function: Fuller Logarithm

l_generalizedGaussian

Help function for Generalized Gaussian

beyondWhittle-package

Bayesian spectral inference for stationary time series

Log Posterior = Log Prior + (conditional) Log Likelihood

coarsened_bernstein

Help function for polynomial basis.

C++ function for generating epsilon process for AR(p)

Density of t-distribution in terms of excess kurtosis

C++ function to build a Toeplitz ACV matric, given an ACV vector.

my_ddirichlet_unnormalized

Help function for proposing new values of v's

C++ function for building a density mixture, given mixture weights and functions.

Help function for proposing new values of v's

Log prior of Bernstein-Dirichlet mixture and parametric working model -- all unnormalized

generalizedGaussian.kurtosis

Help function for Generalized Gaussian

Log prior for PACF (beta) and sigma2 (Inverse Gamma), unnormalized

Gibbs sampler for an autoregressive model with PACF parametrization.

reduceMemoryStorageMCMC

Help function for I/O

Compute a PSD in the Bernstein-Dirichlet parametrization.

Help function: Standard error for kurtosis

C++ function for generating epsilon process for ARMA(p,q)

nll_generalizedGaussian

Help function for Generalized Gaussian

Help function: Uniform maximu

nuisanceModel_linearTrend

Normal linear trend model, with nuisance time series

C++ function for computing mixture weights of Bernstein-Mixtures given the probabilities p, values w, and degree k.

Gibbs sampler for Bayesian nonparametric inference with Whittle likelihood

Log corrected parametric likelihood

Gibbs sampler for Bayesian semiparametric inference with the corrected AR likelihood

Negative log likelihood of iid standard normal observations [unit variance]

arma_conditional

Function for computing the ARMA(p, q) conditional likelihood Models with AR component: zt are from t = p + 1 to m Models with MA component: eps_0 = ... = eps_q+1 = 0 The input zt should be FCFZ, i.e., data corrected in freq. domain then IFTd FCFZ should be FCFZ[-c(1, n)]; i.e., have removed elements 1 and n beforehand No sigma2 in here anymore! ...: Further arguments to be passed to likelihood function

Time domain AR(p) likelihood for nuisance/noise time series

Help function for polynomial basis.

nll_norm_unnormalized

unnormalized negative log likelihood of iid standard normal observations [unit variance]

Fourier frequencies, rescaled on the unit interval

gibbs_NP_nuisance

Bayesian nonparametric inference in nuisance model with Whittle likelihood

nuisanceModel_mean

Normal mean model, with nuisance time series

gibbs_NPC_nuisance

Bayesian semiparametric inference in nuisance model

C++ function for generating p from v in Stick Breaking DP representation

Help function: Rosenthal Logarithm

plotPsdEstimate

Help function for visualizing

negative log likelihood of iid t observations with given excess kurtosis [unit variance]

Help function to print debugging messages

Convert partial autocorrelation coefficients to AR coefficients.

Log corrected posterior

C++ help function to redundantly roll out a PSD to length n

Help function for visualizing

Compute the ARMA(p,q) spectral density

C++ function for computing AR coefficients, given PACF.

psd_dummy_model

Time series model X_t=e_t, E[e_t]=0, without additional parameters Not public, since encapsulated in an extra function, for easier usage

C++ function for generating v from p (inverse stick breaking) NOTE: p is assumed to have length L, i.e. it does NOT contain p_0 !!

C++ function for computing ACV function, given PACF and variance.

C++ function for computing acceptance rate based on trace Note: Only use for traces from continous distributions!

Compute F_n X_n with the real-valued Fourier matrix F_n

Gibbs sampler for corrected parametric likelihood + Bernstein-Dirichlet mixture, including possibility of using time series as mere nuisance parameter

Compute F_n^t X_n with the real-valued Fourier matrix F_n

Likelihood of an autoregressive time series model with i.i.d. normal innovations

Negative log likelihood values for scree-type plots

Help function for I/O

C++ function for generating epsilon process for MA(q)

coarsened_bernstein_i

Help function for polynomial basis.

gibbs_AR_nuisance

Bayesian parametric (AR) inference in nuisance model, with PACF parametrization

logDet_stickBreaking

Help function for proposing new values of v's

Help function for polynomial basis.

gibbs_AR_nuisance_intern

Gibbs sampler for Bayesian AR model in PACF parametrization, including support for TS to be a nuisance parameter