Package 'varmapack'

Sample autocovariances of an observed series

Description

Compute sample autocovariance matrices up to a specified lag for a numeric time-series matrix with variables in rows and observations in columns.

Usage

varmapack_autocov(X, maxlag, norm = "ML")

Arguments

X	Numeric r by n observed time-series matrix.
maxlag	Largest lag to compute, between zero and n - 1.
norm	Either "ML", which divides every lag by n, or "C", which divides the lag-k covariance by n - k.

Value

An r by r by maxlag + 1 array. Its k + 1 plane estimates ⁠Cov(x_t, x_{t-k})⁠.

Examples

X <- rbind(1:10, (1:10)^2)
varmapack_autocov(X, maxlag = 2)

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Convert covariances to correlations

Description

Convert a covariance matrix or sequence of autocovariance matrices to correlations using the marginal standard deviations at lag zero.

Usage

varmapack_cov2corr(cov)

Arguments

cov	A finite numeric r by r matrix or r by r by maxlag + 1 array. The diagonal entries of its lag-zero matrix must be positive.

Value

A numeric array with the same dimensions as cov. Lag-zero diagonal entries are exactly one. Other entries are not clipped to ⁠[-1,1]⁠.

Examples

cov <- array(c(4, 3, 3, 9, 2, 6, -3, 1.5), dim = c(2, 2, 2))
varmapack_cov2corr(cov)

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Create a VARMA or VARMAX model

Description

Create a model object for simulation of a Gaussian VAR, VMA, VARMA, or VARMAX time series. The object stores model parameters and provides a ⁠$sim()⁠ method for generating one or more independent series.

Usage

varmapack_model(A = NULL, B = NULL, C = NULL, Sig, mu = NULL)

Arguments

A	Autoregressive coefficient matrices as an r by r matrix or an r by r by p array. NULL gives no autoregressive terms.
B	Moving-average coefficient matrices as an r by r matrix or an r by r by q array. NULL gives no moving-average terms.
C	Exogenous coefficient matrices as an r by d matrix or an r by d by s array. NULL gives a VARMA model rather than VARMAX.
Sig	r by r innovation covariance matrix.
mu	Optional r vector or r by nmu matrix of time-series means. The last mean vector repeats for the rest of each series. Means are not supported for VARMAX models.

Value

A VarmapackModel object.

Simulation

model$sim(length, nrep = 1L, X0 = NULL, z = NULL, rng = NULL, return_shocks = FALSE) simulates nrep independent series of the supplied length.

For VARMA models, X0 is optional. If provided, it is an r by nX0 matrix or an r by nX0 by nrep array. Its second dimension must be at least max(p, q), and its third dimension, when present, must be 1 or nrep. Nonstationary VARMA models require X0; with MA terms, Sig must be positive definite and startup shocks are conditioned on the residual equations implied by the supplied history.

For VARMAX models, z is required. X0 has the same form and its second dimension must be at least max(p, q, s - 1). It may be omitted when this minimum is zero. The exogenous input z is a d by length matrix or a d by length by nrep array. Its third dimension, when present, must be 1 or nrep.

Pass a randompack::randompack_rng() object through rng to control the random stream. When it is omitted, Varmapack uses a temporary randomized default Randompack generator. With return_shocks = FALSE, the result is an r by length by nrep array. With return_shocks = TRUE, it is a list with components X and E, each with that shape.

Model analysis

model$acvf(maxlag) returns theoretical VARMA autocovariances, model$psi(maxlag) returns impulse-response matrices, and model$irf(maxlag) returns orthogonalized impulse-response matrices. model$specrad() and model$ma_specrad() return the AR and MA spectral radii, respectively. Theoretical autocovariances are not available for VARMAX models with exogenous terms.

Examples

A <- matrix(c(0.4, 0.1, -0.2, 0.3), 2, 2)
model <- varmapack_model(A = A, Sig = diag(2))
X <- model$sim(100)

rng <- randompack::randompack_rng()
rng$seed(123)
X <- model$sim(100, nrep = 3, rng = rng)

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Create a VARMA testcase model

Description

Create a built-in named testcase or an unnamed random, deterministic, or spectral-radius-controlled VARMA testcase.

Usage

varmapack_testcase(
  which = "random",
  p = NULL,
  q = NULL,
  r = NULL,
  rho = 0,
  rng = NULL
)

Arguments

which	A built-in testcase name, a one-based built-in testcase index, or one of "random", "deterministic", and "rho".
p, q, r	Required AR order, MA order, and series dimension for unnamed testcases.
rho	Target spectral radius when which = "rho".
rng	Optional randompack::randompack_rng() used for a random testcase.

Value

A VarmapackModel object.

Examples

model <- varmapack_testcase("smallARMA1")
model <- varmapack_testcase("rho", p = 3, q = 1, r = 2, rho = 0.8)

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List named VARMA testcases

Description

List named VARMA testcases

Usage

varmapack_testcases()

Value

A data frame with columns index, name, p, q, and r.

Examples

varmapack_testcases()

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