mixest1 {dynmix}

Computes Mixture Estimation with State-Space Components.

Description

This function estimates recursively mixtures with state-space components with a dynamic model of switching. The components are normal linear models. Suppose there are available k potentially important predictors of y, i.e., x_1, \dots, x_k. Then up to 2^{k} linear models including constant term can be created by inclding or not including each of these predictors in the individual model, i.e., component of the mixture.

Usage

mixest1(y,x,mods=NULL,ftype=NULL,lambda=NULL,kappa=NULL,V=NULL,W=NULL,atype=NULL)

Arguments

y

one column matrix of forecasted time-series, observations inserted rowwise

x

matrix of independent time-series (predictors), observations inserted rowwise

mods

optional, matrix indicating which models should be used as components, the first column indicates inclusion of a constant in a component model, by default all possible models with a constant are used, inclusion of a variable is indicated by 1, omitting by 0, component models are indexed by rows, variables (time-series) are indexed by columns

ftype

optional, numeric indicating type of forecasting, 0 represents forecasting based on coefficients derived from the estimated mixture, 1 represents averaging forecasts from all components by the estimated weights, 2 represents selecting the forecast given by the model with the highest weight, 3 represents selecting the forecast from the so-called median probability model (Barbieri and Berger, 2004), by default ftype=0 is taken

lambda

optional, numeric between 0 and 1, a forgetting factor in covariance estimation method described by Raftery et al. (2010), by default the method of Nagy and Suzdaleva (2013) is used

kappa

optional, numeric between 0 and 1, a parameter for the exponentially weighted moving average estimation of components variances, described for example by Koop and Korobilis (2012), if lambda is specified but kappa is not, then the method of recursive moments described by Raftery et al. (2010) is used, by default the method of Nagy and Suzdaleva (2013) is used

V

optional, numeric initial variance for all components (output equation), by default V=1 is taken

W

optional, numeric initial value to be put in the diagonal matrix representing the covariance matrices (state equation), by default W=1 is taken

atype

optional, numeric indicating approximation of pdf, 0 represents quasi-Bayesian approach, 1 represents minimization of the Kerridge inaccuracy (where suitiable optimization is done with the Gauss-Newton method, still this increases the computation time greatly), by default atype=0 is taken

Value

object of class mixest, i.e., list of

$y.hat

vector of predictions

$rvi

matrix of relative variable importances

$coef

matrix of regression coefficients corresponding to ftype method chosen

$weights

matrix of estimated weights of component models

$V

vector of updated variances from the selected models, consistent with ftype chosen

$R

matrix of updated diagonal of covariances corresponding to independent variables in regressions, consistent with ftype chosen

$components

matrix of mods

$parameters

character of parameters used in the model

$data.last

list of selected parameters obtained in the last iteration, necessary for the internal use by cauimp

Source

Nagy, I., Suzdaleva, E., 2013, Mixture estimation with state-space components and Markov model of switching. Applied Mathematical Modelling 37, 9970–9984.

References

Barbieri, M. M., Berger, J. O., 2004, Optimal predictive model selection. The Annals of Statistics 32, 870–897.

Burnham, K. P., Anderson, D. R., 2002, Model Selection and Multimodel Inference, Springer.

Karny, M. (ed.), 2006, Optimized Bayesian Dynamic Advising, Springer.

Koop, G., Korobilis, D., 2012, Forecasting inflation using Dynamic Model Averaging. International Economic Review 53, 867–886.

Nagy, I., Suzdaleva, E., 2017, Algorithms and Programs of Dynamic Mixture Estimation, Springer.

Quarteroni, A., Sacco, R., Saleri, F., 2007, Numerical Mathematics, Springer.

Raftery, A. E., Karny, M., Ettler, P., 2010, Online prediction under model uncertainty via Dynamic Model Averaging: Application to a cold rolling mill. Technometrics 52, 52–66.

See Also

mixest2

Examples

data(oil)
m1 <- mixest1(y=oil[,1,drop=FALSE],x=oil[,-1,drop=FALSE],ftype=1,V=100,W=100)

# Models with only one variable
mods <- diag(1,nrow=ncol(oil[,-1,drop=FALSE]),ncol=ncol(oil[,-1,drop=FALSE]))
mods <- cbind(1,mods)
m2 <- mixest1(y=oil[,1,drop=FALSE],x=oil[,-1,drop=FALSE],mods=mods,ftype=1,V=100,W=100)