garma_fit: Fit generalized ARMA
In JieGroup/tsms: Modeling Univariate Time Series with Multiple Seasonality

Description Usage Arguments Details Value Author(s)

Fit a generalized ARMA model for univariate time series. The ARMA is generalized in a way that AR and MA components can be specified in any lag orders.

1	garma.fit(X,U,p,q,S1,S2,W=NULL,crit='AIC')

`X`	a data vector or a n by 1 matrix
`U`	number of data points burned-in. Upper bound for seasonality, i.e. U > max(S1,S2)
`p`	number of regular AR components
`q`	number of regular MA components
`S1`	a set of lag orders of additional AR components
`S2`	a set of lag orders of additional MA components
`W`	exogenous variable matrix p by n
`crit`	selection criterion. crit = c('BC','AIC','BIC')

The model is estimated by BFGS algorithm in optim(). Note that in univariate ARMA estimation, quasi-Newton method usually provide a robust result rather than aggressive ML with second order algorithms.

The algorithm optimize conditional likelihood based on burned in samples. This is specified by argument U. U has to be greater than p,q or any element in seasonality terms.

For models that have diverging estimation, the aic value will be recorded as Inf.

`U`	n-burnin
`p`	number of regular AR components
`phi`	estimated coefficients of regular AR components
`q`	number of regular MA components
`psi`	estimated coefficients of regular MA components
`r1`	length of S1
`S1`	a set of lag orders of additional AR components
`tau1`	estimated coefficients of additional AR components
`r2`	length of S2
`S2`	a set of lag orders of additional MA components
`tau2`	estimated coefficients of additional MA components
`gamma`	estimated coefficients of exogenous variables
`sigma`	estimated sigma of white noise
`ic`	information criterion