timsac (version 1.3.8-4)

markov: Maximum Likelihood Computation of Markovian Model

Description

Compute maximum likelihood estimates of Markovian model.

Usage

markov(y)

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.

Arguments

y

a multivariate time series.

Details

This function is usually used with simcon.

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)