markov: Maximum Likelihood Computation of Markovian Model

In timsac: Time Series Analysis and Control Package

Maximum Likelihood Computation of Markovian Model

Description

Compute maximum likelihood estimates of Markovian model.

Usage

markov(y)

Arguments

y	a multivariate time series.

Details

This function is usually used with simcon.

Value

id	id[i]=1 means that the i-th row of F contains free parameters.
ir	ir[i] denotes the position of the last non-zero element within the i-th row of F.
ij	ij[i] denotes the position of the i-th non-trivial row within F.
ik	ik[i] denotes the number of free parameters within the i-th non-trivial row of F.
grad	gradient vector.
matFi	initial estimate of the transition matrix F.
matF	transition matrix F.
matG	input matrix G.
davvar	DAVIDON variance.
arcoef	AR coefficient matrices. arcoef[i,j,k] shows the value of i-th row, j-th column, k-th order.
impulse	impulse response matrices.
macoef	MA coefficient matrices. macoef[i,j,k] shows the value of i-th row, j-th column, k-th order.
v	innovation variance.
aic	AIC.

References

H.Akaike, E.Arahata and T.Ozaki (1975) Computer Science Monograph, No.5, Timsac74, A Time Series Analysis and Control Program Package (1). The Institute of Statistical Mathematics.

Examples

x <- matrix(rnorm(1000*2), nrow = 1000, ncol = 2)
ma <- array(0, dim = c(2,2,2))
ma[, , 1] <- matrix(c( -1.0,  0.0,
                        0.0, -1.0), nrow = 2, ncol = 2, byrow = TRUE)
ma[, , 2] <- matrix(c( -0.2,  0.0,
                       -0.1, -0.3), nrow = 2, ncol = 2, byrow = TRUE)
y <- mfilter(x, ma, "convolution")
ar <- array(0, dim = c(2,2,3))
ar[, , 1] <- matrix(c( -1.0,  0.0,
                        0.0, -1.0), nrow = 2, ncol = 2, byrow = TRUE)
ar[, , 2] <- matrix(c( -0.5, -0.2,
                       -0.2, -0.5), nrow = 2, ncol = 2, byrow = TRUE)
ar[, , 3] <- matrix(c( -0.3, -0.05,
                       -0.1, -0.30), nrow = 2, ncol = 2, byrow = TRUE)
z <- mfilter(y, ar, "recursive")
markov(z)

timsac documentation built on Sept. 30, 2023, 5:06 p.m.