timsac (version 1.3.0)

markov: Maximum Likelihood Computation of Markovian Model

Description

Compute maximum likelihood estimates of Markovian model.

Usage

markov(y)

Arguments

y

a multivariate time series.

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.
• impuls
  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.

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