Ritme Informatique

The following product is developed by Ritme Informatique, a third party company for use with GAUSS. Technical support is provided directly through the developer.

TSM v1.2 Procedure Listing

The following is a list of the procedures in TSM version 1.2. Click here for a description of TSM.

ARMA processes

arma_ML: Conditional maximum likelihood for Vector ARMA models
arma_CML: Conditional maximum likelihood for Vector ARMA models under linear restrictions
arma_to_VAR1: VAR(1) representation of a Vector ARMA process
arma_roots: roots of the VAR(1) representation of a Vector ARMA process
canonical_arma: Canonical representation of a Vector ARMA process (infinite AR and MA orders)
arma_autocov: Autocovariances and autocorrelations of a Vector ARMA process
arma_impulse: Responses to Forecast Errors of a Vector ARMA process
arma_orthogonal: Responses to Orthogonal Impulses of a Vector ARMA process
arma_fevd: Forecast Error Variance Decomposition of a Vector ARMA process
arma_to_SSM: State space form of a Vector ARMA model
Hankel: Hankel matrix for multivariate time series

VARX processes

varx_LS: Multivariate Least Squares Estimation of VARX processes
varx_CLS: Multivariate Least Squares Estimation of VARX processes under linear restrictions
varx_ML: Maximum Likelihood of VARX processes
varx_CML: Maximum Likelihood of VARX processes under linear restrictions

Spectral analysis

fourier: Fourier transform
inverse_fourier: Inverse Fourier transform
fourier2: Fourier transform of two real time series
PDGM: Periodogram of a univariate time series
PDGM2: Periodogram of a multivariate time series
CPDGM: Cross-periodogram
CSpectrum: Coherency, cross-amplitude spectra and phase spectra
Smoothing: Data windowing in the frequency domain

Maximum Likelihood Estimation

A. Time domain estimation.

TD_ml: Estimation in the time domain
TD_cml: Estimation in the time domain under linear restrictions
TDml_derivatives: Computes the Jacobian, the gradient, the Hessian and the Information matrices in the time domain

B. Frequency domain estimation for univariate processes.

FD_ml: Estimation in the frequency domain
FD_cml: Estimation in the frequency domain under linear restrictions
FDml_derivatives: Computes the Jacobian, the gradient, the Hessian and the Information matrices in the frequency domain

Univariate models

sm_LL: Local level/random walk plus noise model
sm_LLT: Local linear trend model
BSM: Basic structural model
sm_cycle: Cycle model
arfima: Fractional ARMA model with constraints
canonical_arfima: Canonical representation of a fractional ARMA process
sgf_arfima: Spectral generating function of a fractional ARMA process

State space models and the Kalman filter

SSM: Print the state space model
SSM_build: Build the state space model
SSM_ic: Initial conditions for the state space model
KFiltering: Kalman filtering
KF_matrix: Matrices defined by the Kalman Filter
KF_gain: Compute the gain matrices $K_t$
KF_ml: Maximum likelihood of the innovations process
KSmoothing: Smoothing
KForecasting: Forecasting
ARE: Algebraic Riccati equation
sgf_SSM: Spectral generating function of a time-invariant state space model
SSM_autocov: Autocovariances and autocorrelations of a time-invariant state space model
SSM_impulse: Responses to Forecast Errors of a time-invariant state space model
SSM_orthogonal: Responses to Orthogonal Impulses of a time-invariant state space model
SSM_fevd: Forecast Error Variance Decomposition of a time-invariant state space model
SSM_Hankel: Hankel matrix of a time-invariant state space model

Resampling and simulation

Bootstrap: Boot-strapping a matrix
bootstrap_SSM: Bootstrapping state space models
surrogate: FT Surrogate data technique
Kernel: Density estimation with the Kernel method
RND_arma: Simulation of Vector ARMA processes
RND_arfima: Simulation of fractional ARMA processes
RND_SSM: Simulation of state space models

Estimation tools for time series analysis

FLS: Flexible least squares
GFLS: Generalized flexible least squares of Kalaba and Tesfatsion [1990]
GFLS2: Generalized flexible least squares of Lüktepohl and Herwartz [1996]
GMM: Generalized method of moments
RLS: Recursive least squares

Time-frequency analysis

A. Quadrature mirror filters

Coiflet: Coiflet filters
Daubechies: Daubechies filters
Haar: Haar filters
Pollen: Pollen filters

B. Wavelet analysis

1. Periodic discrete wavelet transform.

iwt: Inverse wavelet transform of a vector
iwt_matrix: matrix associated with the inverse wavelet transform
wt: Wavelet transform of a vector
wt_matrix: matrix associated with the wavelet transform

2. Wavelet Tools

extract: Wavelet decomposition coefficients subband extraction
insert: Wavelet decomposition coefficients subband insertion
Scalogram: Scalogram of the wavelet decomposition coefficients
select: Wavelet decomposition coefficients subband selection
split: Wavelet decomposition coefficients subband split
wPlot: Wavelet decomposition coefficients plot

C. Wavelet packet analysis

1. Wavelet packet transform

iwpkt: Inverse wavelet packet transform
wpkPlot: Wavelet packet table plot
wpkt: Wavelet packet transform

2. Wavelet packet basis

Basis: Wavelet packet basis selection
BasisPlot: Time-frequency plane tilings plot
BestBasis: Best basis selection (pruning algorithm)
BestLevel: Best level selection
Entropy: Shannon entropy cost function
isBasis: check whether ß is a basis
LogEnergy: Log-energy cost function
LpNorm: lp norm cost function

D. Thresholding methods

SemiSoft: Semi-soft shrinkage
Thresholding: Quantile thresholding
VisuShrink: Visu shrinkage (or universal thresholding)
WaveShrink: Wavelet shrinkage (hard and soft shrinkages)

Matrix operators

vech_: operator
xpnd_: operator
Elimination_: Elimination matrix
Duplication_: Duplication matrix
Commutation_: Commutation matrix
xpnd2: Procedure for coding square matrices
Explicit_to_Implicit: Convert explicit linear restrictions C(theta) = c to implicit linear restrictions (theta) = R(gamma) + r
Implicit_to_Explicit: Convert implicit linear restrictions (theta) = R(gamma) + r to explicit linear restrictions C(theta) = c