R: Multivariate Case of Minimum AIC Method of AR Model Fitting

mulmar {timsac} | R Documentation

## Multivariate Case of Minimum AIC Method of AR Model Fitting

### Description

Fit a multivariate autoregressive model by the minimum AIC procedure. Only the possibilities of zero coefficients at the beginning and end of the model are considered. The least squares estimates of the parameters are obtained by the householder transformation.

### Usage

    mulmar(y, max.order = NULL, plot = FALSE)

### Arguments

`y` | a multivariate time series.
`max.order` | upper limit of the order of AR model, less than or equal to n/2d where n is the length and d is the dimension of the time series `y`. Default is min(2*sqrt(n), n/2d).
`plot` | logical. If `TRUE`, `daic[[1]]`, … , `daic[[d]]` are plotted.

### Details

Multivariate autoregressive model is defined by

y(t) = A(1)y(t-1) + A(2)y(t-2) +...+ A(p)y(t-p) + u(t),

where p is order of the model and u(t) is Gaussian white noise with mean 0 and variance matrix `matv`. AIC is defined by

AIC = n log(det(v)) + 2k,

where n is the number of data, v is the estimate of innovation variance matrix, det is the determinant and k is the number of free parameters.

### Value

`mean` | mean.
`var` | variance.
`v` | innovation variance.
`aic` | AIC.
`aicmin` | minimum AIC.
`daic` | AIC-aicmin.
`order.maice` | order of minimum AIC.
`v.maice` | MAICE innovation variance.
`np` | number of parameters.
`jnd` | specification of i-th regressor.
`subregcoef` | subset regression coefficients.
`rvar` | residual variance.
`aicf` | final estimate of AIC (=nlog(`rvar`)+2`np`).
`respns` | instantaneous response.
`matv` | innovation variance matrix.
`morder` | order of the MAICE model.
`arcoef` | AR coefficients. `arcoef[i,j,k]` shows the value of i-th row, j-th column, k-th order.
`aicsum` | the sum of aicf.

### References

G.Kitagawa and H.Akaike (1978) A Procedure for The Modeling of Non-stationary Time Series. Ann. Inst. Statist. Math., 30, B, 351–363.

H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

### Examples

    # Example 1
    data(Powerplant)
    z <- mulmar(Powerplant, max.order = 10)
    z$arcoef

    # Example 2
    ar <- array(0, dim = c(3,3,2))
    ar[, , 1] <- matrix(c(0.4,  0,   0.3,
                          0.2, -0.1, -0.5,
                          0.3,  0.1, 0), nrow = 3, ncol = 3, byrow = TRUE)
    ar[, , 2] <- matrix(c(0,  -0.3,  0.5,
                          0.7, -0.4,  1,
                          0,   -0.5,  0.3), nrow = 3, ncol = 3,byrow = TRUE)
    x <- matrix(rnorm(200*3), nrow = 200, ncol = 3)
    y <- mfilter(x, ar, "recursive")
    z <- mulmar(y, max.order = 10)
    z$arcoef

[Package timsac version 1.3.6 Index]