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beyondWhittle (version 1.3.0)

Bayesian Spectral Inference for 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) , A. Meier (2018) and Y. Tang et al (2023) . It was supported by DFG grants KI 1443/3-1 and KI 1443/3-2.

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Install

install.packages('beyondWhittle')

Monthly Downloads

502

Version

1.3.0

License

GPL (>= 3)

Maintainer

Renate Meyer

Last Published

November 25th, 2024

Functions in beyondWhittle (1.3.0)

a generic method for bdp_dw_result class

MH sampler for BDP-DW method

bdp_dw_mcmc_params_gen

Generate a list of values for MCMC algorithm

bdp_dw_bayes_factor_k1

Estimating the Bayes factor of hypothesis "k1 = 1".

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

beyondWhittle-package

Bayesian spectral inference for time series

arma_conditional

Negative ARMA(p, q) log likelihood

Construct Bernstein polynomial basis of degree k on omega

Construct Bernstein polynomial basises of degree up to kmax on omega

mean center a numerical vector

Construct Bernstein polynomial bases of degree up to kmax on omega

coarsened_bernstein_i

Helping function for coarsened_bernstein

BDP-DW method: performing posterior sampling and calculating statistics based on the posterior samples

Gibbs sampler for an autoregressive model with PACF parametrization.

bdp_dw_est_post_stats

Calculating the estimated posterior mean, median and credible region (tv-PSD)

complexValuedPsd

Inverse function to realValuedPsd

dbList_dw_Bern_for_lambda

Construct Bernstein polynomial bases of degree up to kmax on omega for frequency parameter lambda

Fourier frequencies

epsilon process (residuals) of VAR model

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

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

VAR_regressor_matrix

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

bdp_dw_prior_params_gen

Generate a list of parameter values in prior elicitation

Gibbs sampler for Bayesian semiparametric inference with the corrected AR likelihood

cube_from_NumericVector

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

Construct psd mixture

Check if a matrix is Hermitian positive definite

cx_cube_from_ComplexVector

I/O: Only used within Rcpp

Construct Bernstein polynomial basis of degree k on omega

Get U from phi, vectorized, cpp internal only

Gibbs sampler for multivaiate Bayesian nonparametric inference with Whittle likelihood

Gibbs sampler for Bayesian nonparametric inference with Whittle likelihood

Construct a density mixture from mixture weights and density functions.

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

coarsened_bernstein

Construct coarsened Bernstein polynomial basis of degree l on omega

gibbs_VAR_nuisance_intern

Gibbs sampling algorithm for VAR model

gibbs_AR_nuisance_intern

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

gibbs_multivariate_nuisance

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

Is l quadratic?

Log corrected parametric AR likelihood (Gaussian)

gibbs_multivariate_nuisance_cpp

Gibbs sampler in Cpp

local_moving_FT_zigzag

Calculate the moving Fourier transform ordinates

Fast Inverse Fourier Transform

hasEigenValueSmallerZero

Does a matrix have an eigenvalue smaller than 0?

missingValues_str_help

Get string representation for missing values position from vector index

print.gibbs_psd

Print method for gibbs_psd class

print.bdp_dw_result

Print method for bdp_dw_result class

Get p from v in Stick Breaking DP representation

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

time-varying spectral density function of the tvARMA(1,2) processes for illustrations

plot.bdp_dw_result

Plot method for bdp_dw_result class

Convert partial autocorrelation coefficients to AR coefficients.

Get mixture weights of Bernstein-Dirchlet-Mixtures

summary.bdp_dw_result

Summary method for bdp_dw_result class

Help function to compute the mean.

Check if a matrix is symmetric positive definite

logDet_stickBreaking

Log determinant of stick breaking transformation V -> p

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

Fourier frequencies rescaled on the unit interval

Log posterior = log prior + log corrected parametric likelihood

print_summary_gibbs_psd_help

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

VAR(p) full likelihood

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

helping function for psd_varma

Calculation of log prior

print_mcmc_state

Help function to print MCMC state

Fuller Logarithm

plot.bdp_dw_tv_psd

Plot method for bdp_dw_tv_psd class

Gibbs sampler for vector autoregressive model.

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

Compute normalized PSD in the Bernstein-Dirichlet parametrization.

VARMA(p,q) spectral density function

llike_var_partial

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

transfer_polynomial

VARMA transfer polynomials

Helping function for uci_matrix

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

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

psd_dummy_model

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

Compute Periodgram matrix from (complex-valued) Fourier coefficients

Multivariate inverse discrete (fast) Fourier Transform

Multivariate discrete (fast) Fourier Transform

Uniform credible intervals in matrix-valued case

Uniform maximum, as needed for uniform credible intervals

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

unit_trace_x_from_phi

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

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

unit_trace_sigma2

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

Plot method for gibbs_psd class

ARMA(p,q) spectral density function

Generate a random samples from a Dirichlet distribution

phiFromBeta_normalInverseWishart

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

Help function to print debugging messages

Visualization of multivariate PSDs Used in plot.gibbs_psd

Store imaginary parts above and real parts below the diagonal

summary.gibbs_psd

Summary method for gibbs_psd class

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

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

Calculating log likelihood

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

Negative log AR likelihood values for scree-type plots

simulate from the tvARMA(1,2) process for illustration

Simulate from a Multivariate Normal Distribution

Simulate from a VARMA model

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

Log Posterior = Log Prior + (conditional) Log Likelihood

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

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

VAR(p) likelihood

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

unit_trace_L_from_x

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

unit_trace_log_d

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

varma_transfer2psd

Get VARMA PSD from transfer polynomials Helping function for psd_varma

unit_trace_log_f_l

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

qpsd_dw.tilde_zigzag_cpp_expedited

Evaluation of normalized time-varying spectral density function (for MCMC algorithm)

Evaluation of normalized time-varying spectral density function (based on posterior samples)

uniformmax_help

Helping function for uci_matrix

uniformmax_multi

Helping function for uci_matrix

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)

unit_trace_log_c

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

unit_trace_U_from_phi

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

unit_trace_runif

Draw uniformly from Hpd matrices with unit trace

adjoint of complex matrix

Psi-weight calculation for a VARMA model. NOTE: This is an exact copy of the MTS::PSIwgt function (only with the plot functionality removed, as not needed). This has to be done because the MTS package has been removed from CRAN in April 2022.

bayes_factor.bdp_dw_result

Extracting the Bayes factor of k1=1 from bdp_dw_result class

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

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