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SERIES C  
Applied Statistics

F. Battaglia and L. Fenga: Forecasting composite indicators with anticipated information: an application to the industrial production index, Journal of the Royal Statistical Society, Applied Statistics, volume 52 (2003), part 3, pages 279 - 290

The two FORTRAN programs contained in files PROG1.FOR and PROG2.FOR, provide code for selecting the best subset of k components out of m (where k=1,2,...,6) to be employed for forecasting with anticipated values.

We assume that m series of length n are given in the matrix x(i,j) (i=1,2,...,m; j=1,2,...,n) and the composite indicator is obtained as a static average Y(t)=b(1)x(1,t)+b(2)x(2,t)+....+b(m)x(m,t).

Also, we assume that a vector autoregressive model has been identified and fitted to the multivariate series x, or alternatively individual univariate autoregressive models have been fitted to each x(i,t) (i=1,...,m).

The two programs cover the two alternative frameworks.

Program VAREQM (contained in file PROGR1.FOR) computes the best mean square forecast error according to (6) in the paper,using k anticipated components for k from 0 (pure forecast) to 6, when a vector autoregressive model is fitted to the data. The number of series m is in PARAMETER, while the weights b(1),..,b(m) are in a DATA statement. The residual variance covariance matrix sigma is required, and it is read row-wise from a file named DATISIGMA according to the format 188. The output is written to the ascii file USCITA.TXT and provides, for any k=1,...,6, the best choice of the k components (labelled from 1 to m) and the resulting mean square forecast error computed according to(6).

Program UNIAREQM.FOR (contained in file PROG2.FOR) provides analogue results when only individual univariate autoregressive models of order two are fitted to each component. The parameters of such autoregressive models are put in DATA statements: the constant terms in DATA const, the first (lag one) parameters in DATA f1, and the second (lag two) parameters in DATA f2. The number of components m and the series length, ndati, are put in PARAMETER. Furthermore, the data themselves are read from file DATIVERI, each record relates to one time, and contains the m component series; the format has label 1000 and is found in subroutine faicova. The output is written to the ascii file USCITA.TXT and provides, for any k=1,2,..,6, the best choice of the k components (labelled from 1 to m) and the resulting mean square forecast error computed accordingly to theorem 2.

Francesco Battaglia Dipartimento di Statistica, Probabilità e Statistiche Applicate Università La Sapienza Piazzale Aldo Moro 5 00100 Roma Italy

E-mail: francesco.battaglia@uniroma1.it

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Applied Statistics

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