The TSPRED subroutine provides predicted values of univariate and multivariate ARMA processes when the ARMA coefficients are input.

The input arguments to the TSPRED subroutine are as follows:

data

specifies a data matrix if the intercept is not included, where denotes the length of the time series and is the number of variables to be analyzed. If the univariate time series is analyzed, the input data should be a column vector.

coef

refers to the ARMA coefficient matrix, where is an AR order and is an MA order. If the intercept term is included (constant=1), the first row of the coefficient matrix is considered as the intercept term and the coefficient matrix is an matrix. If there are missing values in the coef matrix, these are converted to zero.

nar

specifies the order of the AR process. If the subset AR process is requested, nar should be a row or column vector. The default is nar=0.

nma

specifies the order of the MA process. If the subset MA process is requested, nma should be a vector. The default is nma=0.

ev

specifies the error variance matrix. If the ev matrix is not provided, the prediction error covariance will not be computed.

npred

specifies the maximum length of multistep forecasting. The default is npred=0.

start

specifies the position where the multistep forecast starts. The default is start=.

constant

specifies the intercept option. No intercept estimate is included if constant=0; otherwise, the intercept estimate is included in the first row of the coefficient matrix. If constant=, the coefficient matrix is estimated by using mean deleted series. By default, constant=0.

The TSPRED subroutine returns the following values:

forecast

refers to predicted values.

impulse

refers to the impulse response function.

mse

refers to the mean square error of -step-ahead forecast. A scalar missing value is returned if the error variance (ev) is not provided.