Optimal Bandwidth Estimation for Locally Weighted Regression in Equidistant Time Series under Short Memory
select_bwidth(
y,
smoothing_options = set_options(),
bwidth_start = NULL,
inflation_rate = c("optimal", "naive"),
correction_factor = FALSE,
autocor = TRUE,
drop = NULL,
error_model = c("free", "ARMA"),
nar_lim = c(0, 3),
nma_lim = c(0, 3),
arma_mean = FALSE
)The function returns a list with different components:
boptthe obtained optimal bandwidth.
bwidthsthe obtained bandwidth for each iteration of the IPI-algorithm.
Imkthe final estimate of \(I[m^{(k)}]\).
sum_autocovthe final estimate of the sum of autocovariances.
a numerical vector or a time series object of class ts or
that can be transformed with as.ts to an object of class
ts; for these observations, trend and seasonality will be obtained.
an S4 object of class smoothing_options, which
is returned by the function set_options; it
includes details about the
options to consider in the locally weighted regression such as the order of
polynomial and the bandwidth for smoothing among others.
a single numeric value that is only relevant if the slot
bwidth in smoothing_options is set to NA;
as the bandwidth will then
be selected automatically, bwidth_start sets the initial bandwidth for
the algorithm; the default, bwidth_start = NULL, corresponds to
bwidth_start = 0.1 for a local linear trend and to
bwidth_start = 0.2 for a local cubic trend.
a character vector of length one that indicates, which inflation rate
to use in the bandwidth selection; for a local linear trend, we have
inflation_rate = "optimal" as the default, for a local cubic trend
it is inflation_rate = "naive", which correspond to inflation rates
of 5/7 and 9/13, respectively.
A logical vector of length one; theoretically, a
larger bandwidth to estimate the sum of autocovariances from residuals of
pilot trend and seasonality estimates is advisable than for estimating trend
and seasonality; for correction_factor = TRUE, this is implemented;
the default is correction_factor = FALSE, because it was found
that setting this argument to TRUE often overestimates the
bandwidth.
a logical vector of length one; indicates whether to consider
autocorrelated errors (TRUE) or independent but identically
distributed errors (FALSE); the default is autocor = TRUE.
a numeric vector of length one that indicates the proportion of
the observations to not include at each boundary in the bandwidth estimation
process, if a bandwidth is selected automatically; the default is
drop = NULL, which corresponds to drop = 0.05 for a
local linear trend and to drop = 0.1 for a local cubic trend.
a character vector of length one that indicates whether
for autocor = TRUE the sum of autocovariances of the errors is
obtained purely nonparametrically ("free") or whether an
autoregressive moving-average (ARMA) model is assumed "ARMA"; the
default is error_model = "free".
only valid for error_model = "ARMA"; set the minimum and
maximum AR order to check via the BIC in each iteration of the algorithm via
a two-element vector.
only valid for error_model = "ARMA"; set the minimum and
maximum MA order to check via the BIC in each iteration of the algorithm via
a two-element vector.
only valid for error_model = "ARMA"; decide whether to
include an estimate of the mean in the ARMA fitting for the detrended series.
Dominik Schulz (Research Assistant) (Department of Economics, Paderborn
University),
Author and Package Creator
Yuanhua Feng (Department of Economics, Paderborn
University),
Author
See further details in the documentation of the function
deseats, where this function is applied internally
by default to select an optimal bandwidth.
Feng, Y. (2013). An iterative plug-in algorithm for decomposing seasonal time series using the Berlin Method. Journal of Applied Statistics, 40(2): 266-281. DOI: 10.1080/02664763.2012.740626.
Feng, Y., Gries. T, and Fritz, M. (2020). Data-driven local polynomial for the trend and its derivatives in economic time series. Journal of Nonparametric Statistics, 32(2): 510-533. DOI: 10.1080/10485252.2020.1759598.
Xt <- log(EXPENDITURES)
select_bwidth(Xt)
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