dlmModARMA: Create a DLM representation of an ARMA process In dlm: Bayesian and Likelihood Analysis of Dynamic Linear Models

Description

The function creates an object of class dlm representing a specified univariate or multivariate ARMA process

Usage

 `1` ```dlmModARMA(ar = NULL, ma = NULL, sigma2 = 1, dV, m0, C0) ```

Arguments

 `ar` a vector or a list of matrices (in the multivariate case) containing the autoregressive coefficients. `ma` a vector or a list of matrices (in the multivariate case) containing the moving average coefficients. `sigma2` the variance (or variance matrix) of the innovations. `dV` the variance, or the diagonal elements of the variance matrix in the multivariate case, of the observation noise. `V` is assumed to be diagonal and it defaults to zero. `m0` m0, the expected value of the pre-sample state vector. `C0` C0, the variance matrix of the pre-sample state vector.

Details

The returned DLM only gives one of the many possible representations of an ARMA process.

Value

The function returns an object of class dlm representing the ARMA model specified by `ar`, `ma`, and `sigma2`.

Author(s)

Giovanni Petris [email protected]

References

Giovanni Petris (2010), An R Package for Dynamic Linear Models. Journal of Statistical Software, 36(12), 1-16. http://www.jstatsoft.org/v36/i12/.
Petris, Petrone, and Campagnoli, Dynamic Linear Models with R, Springer (2009).
Durbin and Koopman, Time series analysis by state space methods, Oxford University Press, 2001.

`dlmModPoly`, `dlmModSeas`, `dlmModReg`

Examples

 ```1 2 3 4 5``` ```## ARMA(2,3) dlmModARMA(ar = c(.5,.1), ma = c(.4,2,.3), sigma2=1) ## Bivariate ARMA(2,1) dlmModARMA(ar = list(matrix(1:4,2,2), matrix(101:104,2,2)), ma = list(matrix(-4:-1,2,2)), sigma2 = diag(2)) ```

Example output

```\$FF
[,1] [,2] [,3] [,4]
[1,]    1    0    0    0

\$V
[,1]
[1,]    0

\$GG
[,1] [,2] [,3] [,4]
[1,]  0.5    1    0    0
[2,]  0.1    0    1    0
[3,]  0.0    0    0    1
[4,]  0.0    0    0    0

\$W
[,1] [,2] [,3] [,4]
[1,]  1.0 0.40  2.0 0.30
[2,]  0.4 0.16  0.8 0.12
[3,]  2.0 0.80  4.0 0.60
[4,]  0.3 0.12  0.6 0.09

\$m0
[1] 0 0 0 0

\$C0
[,1]  [,2]  [,3]  [,4]
[1,] 1e+07 0e+00 0e+00 0e+00
[2,] 0e+00 1e+07 0e+00 0e+00
[3,] 0e+00 0e+00 1e+07 0e+00
[4,] 0e+00 0e+00 0e+00 1e+07

\$FF
[,1] [,2] [,3] [,4]
[1,]    1    0    0    0
[2,]    0    1    0    0

\$V
[,1] [,2]
[1,]    0    0
[2,]    0    0

\$GG
[,1] [,2] [,3] [,4]
[1,]    1    3    1    0
[2,]    2    4    0    1
[3,]  101  103    0    0
[4,]  102  104    0    0

\$W
[,1] [,2] [,3] [,4]
[1,]    1    0   -4   -3
[2,]    0    1   -2   -1
[3,]   -4   -2   20   14
[4,]   -3   -1   14   10

\$m0
[1] 0 0 0 0

\$C0
[,1]  [,2]  [,3]  [,4]
[1,] 1e+07 0e+00 0e+00 0e+00
[2,] 0e+00 1e+07 0e+00 0e+00
[3,] 0e+00 0e+00 1e+07 0e+00
[4,] 0e+00 0e+00 0e+00 1e+07
```

dlm documentation built on May 30, 2017, 3:37 a.m.