optOrd: Optimal Order Selection
In smoots: Nonparametric Estimation of the Trend and Its Derivatives in TS

Description Usage Arguments Details Value Author(s) Examples

From a matrix with values of an information criterion for different orders p and q of an autoregressive-moving-average (ARMA) model, the optimal orders are selected.

1	optOrd(mat, restr = NULL, sFUN = min)

`mat`	a numeric matrix, whose rows represent the AR orders p = 0, 1, ..., p_max and whose columns represent the MA orders q = 0, 1, q_max; the elements of the matrix are then the values of an information criterion calculated for ARMA models with the different order combinations; a matrix returned by the function `critMatrix` of the `smoots` package shares these characteristics.
`restr`	a single expression (not a character object) that defines further restrictions; the standard logical operators, e.g. `>=`, `&` or `==`, can be used; refer to the rows with `p` and to the columns with `q`; is set to `NULL` by default, i.e. no restrictions are imposed.
`sFUN`	the selection function; is set to `min`, i.e. the minimal value that meets the restrictions `restr` is selected and the corresponding orders p and q are returned.

Given a matrix mat filled with the values of an information criterion for different estimated ARMA(p,q) models, where the rows represent different orders p = 0, 1, ..., p_max and where the columns represent the orders q = 0, 1, ..., q_max, the function returns a vector with the optimal orders p and q. Further selection restrictions can be passed to the argument restr as an expression. To implement a restriction, the rows and columns are addressed via p and q, respectively. Moreover, standard boolean operators such as ==, >= or & can be used. See the Section Examples for examples of different restrictions. In many cases, the minimum value of a criterion is considered to indicate the best model. However, in some other cases a different selection approach might be appropriate. Therefore, a selection function can be considered by means of the argument sFUN. The default is sFUN = min, i.e. the function min is applied to select the optimal orders.

The function returns a vector with two elements. The first element is the optimal order p, whereas the second element is the selected optimal order q.

Sebastian Letmathe (Scientific Employee) (Department of Economics, Paderborn University),

## Not run: 
set.seed(21)
Xt <- arima.sim(model = list(ar = c(1.2, -0.5), ma = 0.7), n = 1000) + 7
mat <- smoots::critMatrix(Xt)
optOrd(mat)  # without restrictions
optOrd(mat, p <= q)  # with one restriction
optOrd(mat, p >= 1 & q >= 4)  # with two restrictions

## End(Not run)