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beyondWhittle (version 1.1.1)

Bayesian Spectral Inference for Stationary Time Series

Description

Implementations of Bayesian parametric, nonparametric and semiparametric procedures for univariate and multivariate time series. The package is based on the methods presented in C. Kirch et al (2018) and A. Meier (2018) . It was supported by DFG grant KI 1443/3-1.

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Install

install.packages('beyondWhittle')

Monthly Downloads

409

Version

1.1.1

License

GPL (>= 3)

Maintainer

Alexander Meier

Last Published

July 11th, 2019

Functions in beyondWhittle (1.1.1)

arma_conditional

Negative ARMA(p, q) log likelihood

beyondWhittle-package

Bayesian spectral inference for stationary time series

Construct Bernstein polynomial basis of degree k on omega

mean center a numerical vector

Fast Inverse Fourier Transform

This is a nearly exact copy of the MTS::VARMAcov function, where the output commands at the end are removed. This has to be done because the function is called repeatedly within the MCMC algorithm. For future versions of the package, a better solution is intended.

Fast Fourier Transform

adjoint of complex matrix

gibbs_VAR_nuisance_intern

Gibbs sampling algorithm for VAR model

Gibbs sampler for an autoregressive model with PACF parametrization.

cx_cube_from_ComplexVector

I/O: Only used within Rcpp

gibbs_multivariate_nuisance

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

gibbs_multivariate_nuisance_cpp

Gibbs sampler in Cpp

Construct Bernstein polynomial basises of degree up to kmax on omega

Gibbs sampler for multivaiate Bayesian nonparametric inference with Whittle likelihood

Log corrected parametric AR likelihood (Gaussian)

Build an nd times nd Block Toeplitz matrix from the (d times d) autocovariances gamma(0),...,gamma(n-1)

hasEigenValueSmallerZero

Does a matrix have an eigenvalue smaller than 0?

Build an n times n Toeplitz matrix from the autocovariance values gamma(0),...,gamma(n-1)

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

Check if a matrix is Hermitian positive definite

Is l quadratic?

complexValuedPsd

Inverse function to realValuedPsd

cube_from_NumericVector

I/O: Only used within Rcpp Note: Same workaround as cx_cube_from_ComplexVector

Get epsilon process (i.e. model residuals) for ARMA(p,q)

Range intervals I_l, see (63) in Mittelbach et al.

Plot method for gibbs_psd class

Compute Periodgram matrix from (complex-valued) Fourier coefficients

uniformmax_multi

Helping function for uci_matrix

Get mixture weights of Bernstein-Dirchlet-Mixtures

phiFromBeta_normalInverseWishart

Convert vector parametrization (beta) to matrix-parametrization (phi), the latter as e.g. used in MTS::VAR()$ar

coarsened_bernstein

Construct coarsened Bernstein polynomial basis of degree l on omega

unit_trace_log_f_l

Get log(f_l), see (66) in Mittelbach et al. Helping function for unit_trace_runif

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

Get U from phi, vectorized, cpp internal only

coarsened_bernstein_i

Helping function for coarsened_bernstein

Get mu vector, see (36) in Mittelbach et al. Helping function for unit_trace_runif

Help function to compute the mean.

Generate a random samples from a Dirichlet distribution

Fuller Logarithm

Gibbs sampler for vector autoregressive model.

Log posterior = log prior + log corrected parametric likelihood

Construct psd mixture

Construct a density mixture from mixture weights and density functions.

epsilon process (residuals) of VAR model

gibbs_AR_nuisance_intern

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

Log Posterior = Log Prior + (conditional) Log Likelihood

Multivariate discrete (fast) Fourier Transform

ARMA(p,q) spectral density function

Compute normalized PSD in the Bernstein-Dirichlet parametrization.

Log prior for PACF (~Beta) and sigma2 (~InverseGamma), unnormalized

Help function to print debugging messages

print.gibbs_psd

Print method for gibbs_psd class

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

Visualization of multivariate PSDs Used in plot.gibbs_psd

Store imaginary parts above and real parts below the diagonal

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

Check if a matrix is symmetric positive definite

llike_var_partial

VAR(p) partial likelihood (unnormalized) Note: Fine for fixed p, but not suited for model comparison

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

Multivariate inverse discrete (fast) Fourier Transform

print_mcmc_state

Help function to print MCMC state

Simulate from a VARMA model

missingValues_str_help

Get string representation for missing values position from vector index

print_summary_gibbs_psd_help

Helping function for print and summary (both are quite similar)

Fourier frequencies

logDet_stickBreaking

Log determinant of stick breaking transformation V -> p

Get log(nu) vector, see (38) in Mittelbach et al. Helping function for unit_trace_runif

Gibbs sampler for Bayesian semiparametric inference with the corrected AR likelihood

Gibbs sampler for Bayesian nonparametric inference with Whittle likelihood

Get p vector, see (67) in Mittelbach et al.

Get p from v in Stick Breaking DP representation

transfer_polynomial

VARMA transfer polynomials

psd_dummy_model

Time series model X_t=e_t, E[e_t]=0

Fourier frequencies rescaled on the unit interval

summary.gibbs_psd

Summary method for gibbs_psd class

Convert psd vector to array (compatibility: to use plotMPsd for univariate functions as well)

C++ function for computing AR coefficients from PACF. See Section III in Barndorff-Nielsen and Schou (1973)

VAR(p) likelihood

VAR(p) full likelihood

VARMA(p,q) spectral density function

sum of multivariate normal log densities with mean 0 and covariance Sigma, unnormalized

unit_trace_runif_single

Obtain one uniform draw from d times d Hpd matrices with unit trace See Algorithm 2 in Mittelbach et al. (adjusted to complex case)

uniformmax_help

Helping function for uci_matrix

Uniform maximum, as needed for uniform credible intervals

unit_trace_log_d

Get log(d) vector, see (39) in Mittelbach et al, adjusted to complex case Helping function for unit_trace_runif

unit_trace_log_c

Get log(c) vector, see (70) in Mittelbach et al. Helping function for unit_trace_runif

Negative log AR likelihood values for scree-type plots

Simulate from a Multivariate Normal Distribution

Convert partial autocorrelation coefficients to AR coefficients.

Helping function for uci_matrix

Uniform credible intervals in matrix-valued case

unit_trace_x_from_phi

Get x from phi, see (62) in Mittelbach et al.

Redundantly roll out a PSD from length N=floor(n/2) to length n

unit_trace_sigma2

Get sigma2 vector, see (70) in Mittelbach et al. Helping function for unit_trace_runif

Get v from p (DP inverse stick breaking) Note: p is assumed to have length L, i.e. it does NOT contain p_0

unit_trace_runif

Draw uniformly from Hpd matrices with unit trace

Get q vector, see (68) in Mittelbach et al.

unit_trace_L_from_x

Get L (lower triangular Cholesky) from x Called U^* in Mittelbach et al, see (60) there

unit_trace_U_from_phi

Get U (Hpd with unit trace) matrix from phi (hyperspherical coordinates) vector.

helping function for psd_varma

varma_transfer2psd

Get VARMA PSD from transfer polynomials Helping function for psd_varma

Computing acceptance rate based on trace Note: Only use for traces from continous distributions!

VAR_regressor_matrix

VAR regressor matrix, see Section 2.2.3 in Koop and Korobilis (2010)