R: Maximum Likelihood Computation of Markovian Model

markov {timsac} | R Documentation

## 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)

[Package timsac version 1.3.6 Index]