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_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

• 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

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

• 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

• 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

• 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

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