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 |
p |
optional; a length 1 or 2 integer vector given the order of the AR
polynomial (extract and fit only). Default is |
q |
optional; a length 1 or 2 integer vector given the order of the MA
polynomial (extract and fit only). Default is |
d |
a length 1 or 2 logical vector indicating whether the long memory
parameter |
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
).