Various macros, including arima(), hannriss(), innovest(), neg2logLarma(), acfarma() and specarma(), allow for different sign conventions in the definition of autoregression and moving average coefficients. The convention to be used may be determined by keyword phrases 'arsign:Arsign' and 'masign:Masign' or the values of variables ARSIGN or MASIGN, when they exist. Some functions and macros, including movavg(), autoreg(), polyroot(), and moveoutroots() *always* use a sign convention equivalent to Arsign = Masign = -1 and are *not* affected by keywords 'arsign' and 'masign' or the values of ARSIGN and MASIGN. For the the affected macros, an ARMA model is assumed to have the form X[t] + Arsign*(phi[1]*X[t-1]+phi[2]*X[t-2]+...+phi[p]*X[t]) = Z[t] + Masign*(theta[1]*Z[t-1]+theta[2]*Z[t-2]+...+theta[q]*Z[t-q]) where {Z[t]} is white noise. Arsign is -1 or +1. Without 'arsign:Arsign', the default value of Arsign is the value of variable ARSIGN when it exists or -1 when it does not. Masign is -1 or +1. Without 'masign:Masign', the default value of Masign is the value of variable MASIGN when it exists or -1 when it does not. Examples for an ARMA(2,2) model with zero mean and AR coefficients phi and MA coefficients theta. For the defaults arsign:-1 and masign:-1, the model is Y[t] = phi[1]*Y[t-1] + phi[2]*Y[t-1] + Z[t] - theta[1]*Z[t-1] - theta[2]*Z[t-2] With arsign:-1 and masign:1, the model is Y[t] = phi[1]*Y[t-1] + phi[2]*Y[t-1] + Z[t] + theta[1]*Z[t-1] + theta[2]*Z[t-2] With arsign:1 and masign:-1, the model is Y[t] = -phi[1]*Y[t-1] - phi[2]*Y[t-1] + Z[t] - theta[1]*Z[t-1] - theta[2]*Z[t-2] With arsign:1 and masign:1, the model is Y[t] = -phi[1]*Y[t-1] - phi[2]*Y[t-1] + Z[t] + theta[1]*Z[t-1] + theta[2]*Z[t-2] The convention used by Box and Jenkins and many others corresponds to Arsign = -1 and Masign = -1. This is the convention that is implicit in the definition of MacAnova functions autoreg(), movavg() and polyroot(). These functions do not recognize 'arsign' and 'masign' and are not affected by the values of ARSIGN and MASIGN. The convention used by Brockwell and Davis corresponds to Arsign = -1 and Masign = +1. If you want results consistent with this convention you should do the following before you start your work: Cmd> MASIGN <- 1; ARSIGN <- -1 This is easier than using 'masign:1' whenever you are using one of the affected macros. Note that macros innovations() and arimares() are not affected by this notation, but macros that use these compensate. See also autoreg(), movavg(), polyroot(), acfarma(), arima(), arimares(), hannriss(), innovest(), neg2logLarma(), specarma().

Gary Oehlert 2003-01-15