arguments.order {BTSR}R Documentation

Shared documentation for models order

Description

This is the common documentation for arguments related to order of polynomials and truncation points for infinite sums, presented in BTSR models.

Arguments

inf

a length 1 or 2 integer vector given the truncation point for infinite sums. Default is inf = 1000. See the Section Model Order for details.

p

optional; a length 1 or 2 integer vector given the order of the AR polynomial (extract and fit only). Default is p = NULL. See the Section Model Order for details.

q

optional; a length 1 or 2 integer vector given the order of the MA polynomial (extract and fit only). Default is q = NULL. See the Section Model Order for details.

d

a length 1 or 2 logical vector indicating whether the long memory parameter d should be included in the model either as a fixed or non-fixed parameter (fit only). If d = FALSE, internally the value of the parameter d is fixed as 0. In this case, if start or fixed.values include d, the value provided by the user is ignored. If \nu is time-varying and a single value is provided it is assumed that d_1 = d_2 = d.

Model Order

The coefficients \{c_{ik}\}_{k\geq 0} are defined through the relation (see the section ‘The BTSR Structure’ in btsr-package)

c_i(z) := (1-L)^{-d_i}\theta_i(z) = \sum_{k = 0}^\infty c_{ik}z^k, \quad i \in \{1,2\}.

where \theta_i(z) = \sum_{k = 0}^{q_i} \theta_{ik}z^k is the moving average characteristic polynomial, with order q_i. For practical purposes, the following approximation is used

c_i(z) \approx \sum_{k = 0}^{K_i} c_{ik}z^k,

for some K_i sufficiently large.

inf corresponds to the truncation point for all infinite sums using the coefficients \{c_{ik}\}_{k\geq 0}, i \in \{1,2\}, including samples generation and derivatives calculation. It can be provided as either a single integer (legacy format) or a length 2 integer vector (new format) specifying the trunction points for part1/part2. If \nu is time-varying and a single value is provided the same value is used for both parts. When d = 0, Fortran automatically sets inf to q (MA order).

By default p and q are set to NULL, in which case their values are computed internally, based on the size of the argument phi and theta, respectively, in the lists of coefficients (or staring values), fixed lags, and fixed values. For fitting purposes, if p (analogously, q) and start are both NULL, an error message is issued. These parameters can be provided as either a single integer (legacy format) or a length 2 integer vector (new format) specifying orders for part1/part2. If \nu is time-varying and a single value of p (analogously, q) is provided it is assumed that p_1 = p_2 = p (analogously, q_1 = q_2 = q).


[Package BTSR version 1.0.0 Index]