MittnikReduction {dse1} | R Documentation

## Balance and Reduce a Model

### Description

Balance and reduce the state dimension of a state space model a la Mittnik.

### Usage

        MittnikReduction(model, data=NULL, criterion=NULL, verbose=TRUE,warn=TRUE)
        MittnikReduction.from.Hankel(M, data=NULL, nMax=NULL,
           criterion=NULL, verbose=TRUE, warn=TRUE,
           Spawn=if (exists(".SPAWN")) .SPAWN else FALSE)

### Arguments

`model` | An object of class TSmodel or TSestModel.
`data` | If the supplied model is of class TSestModel and data is not supplied then it is taken from the model. If the model is of class TSmodel then data must be supplied.
`criterion` | Criterion to be used for model selection. see `informationTestsCalculations`.
`verbose` | logical indicating if information should be printed during estimation.
`warn` | logical indicating if some warning messages should be suppressed.
`M` | a matrix. See details.
`nMax` | integer indicating the state dimension of the largest model considered.
`Spawn` | logical indicating if Splus For loops should be used.

### Details

`MittnikReduction` gives nested-balanced state space model using reduction by svd of the Hankel matrix generated from a model. If a state space model is supplied the max. state dimension for the result is taken from the model. If an ARMA model is supplied then singular values will be printed and the program prompts for the max. state dimension. criterion should be the name of one of the values returned by informationTests, that is, one of ("port","like","aic","bic","gvc","rice","fpe","taic", "tbic","tgvc","trice","tfpe"). If criteria is not specified then the program prompts for the state dimension (n) to use for the returned model. The program requires data to calculate selection criteria. (The program balanceMittnik calculates svd criteria only and can be used for reduction without data.)

The function `MittnikReduction.from.Hankel` is called by `MittnikReduction` and typically not by the user, but there are situations when the former might be called directly. It selects a reduced state space model by svd a la Mittnik. Models and several criteria for all state dimensions up to the max. state dim. specified are calculated. (If nMax is not supplied then svd criteria are printed and the program prompts for nMax). The output dimension p is taken from nrow(M). M is a matrix with p x (m+p) blocks giving the markov parameters, that is, the first row of the Hankel matrix. It can be generated from the model as in the function markovParms, or from the data, as in the function estSSMittnik.

`data` is necessary only if criteria (AIC,etc) are to be calculated.

### Value

A state space model balance a la Mittnik in an object of class TSestModel.

### References

Gilbert, P. D. (1993) State space and ARMA models: An overview of the equivalence. Working paper 93-4, Bank of Canada. Available at <www.bank-banque-canada.ca/pgilbert>

Gilbert, P. D. (1995) "Combining VAR Estimation and State Space Model Reduction for Simple Good Predictions" J. of Forecasting: Special Issue on VAR Modelling. 14:229-250.

Mittnik, S. (1989), Multivariate Time Series Analysis With State Space Models, Computers Math Appl. Vol 17, No 8/9, pp1189-1201.

Mittnik, S. (1990), Macroeconomic Forecasting Experience With Balance State Space Models, International Journal Of Forecasting, Vol 6, pp337-348.

Mittnik, S. (1990), Forecasting With Balanced State Space Representations of Multivariate Distributed Lag Models. J. of Forecasting, Vol.9, 207-218.

### See Also

`estVARXls` `bft` `balanceMittnik` `informationTests` `informationTestsCalculations`

### Examples

        if(is.R()) data("egJofF.1dec93.data", package="dse1")
        model <- toSS(estVARXls(egJofF.1dec93.data))
        newmodel <-MittnikReduction(model, criterion="taic")

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