multicov {smooth}

Function returns the multiple steps ahead covariance matrix of forecast errors

Description

This function extracts covariance matrix of 1 to h steps ahead forecast errors for ssarima(), gum(), sma(), es() and ces() models.

Usage

multicov(object, type = c("analytical", "empirical", "simulated"), h = 10,
  nsim = 1000, ...)

## S3 method for class 'smooth'
multicov(object, type = c("analytical", "empirical",
  "simulated"), h = 10, nsim = 1000, ...)

Arguments

object

Model estimated using one of the functions of smooth package.

type

What method to use in order to produce covariance matrix:

1. analytical - based on the state space structure of the model and the one-step-ahead forecast error. This works for pure additive and pure multiplicative models. The values for the mixed models might be off.

2. empirical - based on the in-sample 1 to h steps ahead forecast errors (works fine on larger samples);

3. simulated - the data is simulated from the estimated model, then the same model is applied to it and then the empirical 1 to h steps ahead forecast errors are produced;

h

Forecast horizon to use in the calculations.

nsim

Number of iterations to produce in the simulation. Only needed if type="simulated"

...

Other parameters passed to simulate function (if type="simulated" is used). These are obs and seed. By default obs=1000. This approach increases the accuracy of covariance matrix on small samples and intermittent data;

Details

The function returns either scalar (if it is a non-smooth model) or the matrix of (h x h) size with variances and covariances of 1 to h steps ahead forecast errors. This is currently done based on empirical values. The analytical ones are more complicated.

Value

Scalar in cases of non-smooth functions. (h x h) matrix otherwise.

Author(s)

Ivan Svetunkov, [e-mail]

See Also

orders

Examples

x <- rnorm(100,0,1)

# A simple example with a 5x5 covariance matrix
ourModel <- ces(x, h=5)
multicov(ourModel)