DLMPlot

Indicator type for plotting recipe.

check_dimensions(F, G[; V, W, Y])

Utility function that checks for dimension mistmatches in the given arguments and returns the dimensions for the observations and for the state-space.

compute_prior(Y, F, m₀, C₀)

Utility function for computing a smart prior that's not informative and at the same does not lead to numerical or visualization issues. Only takes effect if one of m₀ is C₀ is nothing, otherwise it just returns m₀ and C₀.

estimate(Y, F, G, η, δ[, m₀, C₀; maxit, ϵ])

Obtains maximum a posteriori estimates for the states and observational covariance matrix for a Dynamic Linear Model (F, G), considering a discount factor δ for the evolutional covariance matrices, and weighted replicates. Prior parameters m₀ and C₀ may be omitted, in which case compute_prior kicks in to assign a prior. Parameters maxit and ϵ control the maximum number of iterations and the numerical precision for early convergence for the Coordinate Descent algorithm, respectively.

Returns point estimates for the states θ and point estimate for the covariance matrix V. Also returns the number of iterations until convergence. If negative, it means the algorithm stopped from reaching the maximum number of iterations.

estimate(Y, F, G, η, δ[, m₀, C₀; maxit, ϵ])

Obtains maximum a posteriori estimates for the states and observational covariance matrix for a Dynamic Linear Model (F, G), considering a discount factor δ for the evolutional covariance matrices, and dynamically weighted replicates. Prior parameters m₀ and C₀ may be omitted, in which case compute_prior kicks in to assign a prior. Parameters maxit and ϵ control the maximum number of iterations and the numerical precision for early convergence for the Coordinate Descent algorithm, respectively.

Returns point estimates for the states θ and point estimate for the covariance matrix V. Also returns the number of iterations until convergence. If negative, it means the algorithm stopped from reaching the maximum number of iterations.

estimate(Y, F, G, δ[, m₀, C₀; maxit, ϵ])

Obtains maximum a posteriori estimates for the states and observational covariance matrix for a Dynamic Linear Model (F, G), considering a discount factor δ for the evolutional covariance matrices. Prior parameters m₀ and C₀ may be omitted, in which case compute_prior kicks in to assign a prior. Parameters maxit and ϵ control the maximum number of iterations and the numerical precision for early convergence for the Coordinate Descent algorithm, respectively.

Returns point estimates for the states θ and point estimate for the covariance matrix V. Also returns the number of iterations until convergence. If negative, it means the algorithm stopped from reaching the maximum number of iterations.

evolutional_covariances(Y, F, G, V, η, δ[, m₀, C₀])

Compute the implied values of the evolutional covariances W[1], ..., W[T] when considering a discount factor approach, and weighted replicates.

evolutional_covariances(Y, F, G, V, δ[, m₀, C₀])

Compute the implied values of the evolutional covariances W[1], ..., W[T] when considering a discount factor approach, and dynamically weighted replicates.

evolutional_covariances(Y, F, G, V, δ[, m₀, C₀])

Compute the implied values of the evolutional covariances W[1], ..., W[T] when considering a discount factor approach.

extract(x, index)

Utility function that facilitates fetching the time series as a vector for one the objects used in the package.

If x is a Vector{Vector{RT}} it returns [x[t][index] for t = 1:T]; If x is a Vector{CovMat{RT}} it returns [x[t][index,index] for t = 1:T].

fitted(F, V, m, C)

Computes the fitted values for the data, for a model with observational matrix F, evolutional covariance matrix V, and state means m and C. Note that this can be done with the one-step ahead priors, online parameters or, more appropriately, smoother results.

Returns observational means and covariances f and Q.

forecast(F, G, V, W, μ, Σ, h)

Filtering routine for the Dynamic Linear Model (F, G) where the observational and evolutional covariance matrices V and W are known and constant. μ and Σ are the mean and covariance matrix for the last state given the most recent information, and h is the forecasting window.

Returns observational means and covariances f and Q.

forecast(F, G, V, δ, μ, Σ, h)

Filtering routine for the Dynamic Linear Model (F, G) where the observational covariance matrix V is known and constants, and evolutional covariance matrices W[1], ..., W[T] are indirectly modeled through a discount factor δ. μ and Σ are the mean and covariance matrix for the last state given the most recent information, and h is the forecasting window.

Returns observational means and covariances f and Q.

from_matrix(x)

Converts a matrix to a vector of vector.

kfilter(Y, F, G, V, δ[, m₀, C₀])

Filtering routine for a discount factor Dynamic Linear Model (F, G) where the observational covariance matrices V[1], …, V[T] are known and evolutional covariance matrices W[1], ..., W[T] are indirectly modelled through a discount factor δ. See West & Harrison (1996) for further information of the discount factor apporach. Y is the matrix of observations with T rows and n columns. Prior parameters m₀ and C₀ may be omitted, in which case compute_prior kicks in to assign a prior.

Returns one-step ahead prior means and covariances a and R, and online means and covariances m and C.

kfilter(Y, F, G, V, η, δ[, m₀, C₀])

Filtering routine for a discount factor Dynamic Linear Model (F, G) where the observational covariance matrix V is known and constants and evolutional covariance matrices W[1], ..., W[T] are indirectly modelled through a discount factor δ and observations have replications. Y is the matrix of observations with T rows and n * nreps columns, each replicate with a weightη[i]. Prior parameters m₀ and C₀ may be omitted, in which case compute_prior kicks in to assign a prior.

Returns one-step ahead prior means and covariances a and R, and online means and covariances m and C.

kfilter(Y, F, G, V, η, δ[, m₀, C₀])

Filtering routine for a discount factor Dynamic Linear Model (F, G) where the observational covariance matrix V is known and constants and evolutional covariance matrices W[1], ..., W[T] are indirectly modelled through a discount factor δ and observations have replications. Y is the matrix of observations with T rows and n * nreps columns, each replicate with dynamic weights η[t,i]. Prior parameters m₀ and C₀ may be omitted, in which case compute_prior kicks in to assign a prior.

Returns one-step ahead prior means and covariances a and R, and online means and covariances m and C.

kfilter(Y, F, G, V, W[, m₀, C₀])

Filtering routine for the Dynamic Linear Model (F, G) where the observational and evolutional covariance matrices V and W are known and constant. Y is the matrix of observations with T rows and n columns. Prior parameters m₀ and C₀ may be omitted, in which case compute_prior kicks in to assign a prior.

Returns one-step ahead prior means and covariances a and R, and online means and covariances m and C.

kfilter(Y, F, G, V, δ[, m₀, C₀])

Filtering routine for a discount factor Dynamic Linear Model (F, G) where the observational covariance matrix V is known and constant and evolutional covariance matrices W[1], ..., W[T] are indirectly modelled through a discount factor δ. See West & Harrison (1996) for further information of the discount factor apporach. Y is the matrix of observations with T rows and n columns. Prior parameters m₀ and C₀ may be omitted, in which case compute_prior kicks in to assign a prior.

Returns one-step ahead prior means and covariances a and R, and online means and covariances m and C.

ksmoother(G, a, R, m, C)

Filtering routine for a Dynamic Linear Model ( ⋅, G), where a and R are the filtered one-step ahead prior means and covariances, and m and C are the filtered online means and covariances.

Returns the posterior means and covariances s and S.

simulate(F, G, V, W, θ₀, T[, nreps])

Simulates a time-series Dynamic Linear Model specified by the quadruple (F, G, V, W) with a starting state of θ₁ <- Nₚ(G θ₀, W), with T observations. A parameter nreps may be passed indicating the number of replicates to be generated. Returns the generated θ and y.

Note that the parametrizations being considered in this package is such that y[t] = F * y[t-1] + ϵ and not the notation from West and Harrison (1996) where y[t] = F' * y[t-1] + ϵ.

to_matrix(x)

Converts a vector of vectors to a matrix.

CovMat

Alias for symmetric, real valued, dense matrices.

exclude_low_weights(Y, η, ϵ)

Internal function which returns a version of the original Y and η variables, containing only the observations with weights above ϵ.

kfilter_core(y, F, G, V, W, a, R)

Internal function which actually performs the computation step.

kfilter_core(y, F, G, V, W, a, R)

Internal function which actually performs the computation step.

plot(::DLMPlot, Y, f, Q[, fh, Qh; factor = 1.64, index = 1])

Recipe for easily plotting the results obtained by the package routines, where Y is the observations matrix, f and Q are results from fitted, and fh and Qh are the results from forecast. Factor implies the credibility or the credibility intervals interval, e.g. a factor of 1.64 implies a credibility of 90%. Index indicates which observational index is to be plotted.