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

## Description

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.

## Usage

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

## Arguments

 `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.

## Details

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.

## Value

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.

## Author(s)

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

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## 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) ```

smoots documentation built on Oct. 10, 2021, 1:09 a.m.