hA_calc {deseats} | R Documentation |
Calculation of Theoretically Optimal Bandwidth and Its Components
Description
Allows to calculate the theoretically optimal bandwidth for estimating the trend and the seasonality in an equidistant time series with short-range dependence using locally weighted regression, if the trend function and the exact ARMA dependence structure of the errors are known.
Usage
hA_calc(
m,
arma = list(ar = NULL, ma = NULL, sd_e = 1),
p = c(1, 3),
mu = c(0, 1, 2, 3),
frequ = c(4, 12),
n = 300,
cb = 0.1
)
Arguments
m |
an expression that defines the trend function in terms of |
arma |
a list with the elements |
p |
the order of polynomial to use locally for the trend estimation. |
mu |
the smoothness parameter of the second-order kernel function used in the weighting process. |
frequ |
the frequency of the theoretical time series (4 for quarterly and 12 for monthly time series). |
n |
the number of observations. |
cb |
the part of observations to drop at each boundary. |
Details
For simulation studies of the function deseats
one may be
interested in obtaining the theoretically optimal bandwidth for local
regression first for a given theoretical process (from which realizations
will be drawn in the simulation). This function assists in obtaining this
theoretical bandwidth.
Value
This function returns a list with various elements. See the documentation of
deseats
to understand, what each quantity signifies.
b
This is the theoretical quantity
\beta_{(k)}
.hA
The theoretically asymptotically optimal global bandwidth for locally weighted regression applied to the theoretical time series under consideration.
Imk
This is the theoretical quantity
I[m^{(k)}]
.RK
This is the theoretical quantity
R(K)
.RW
This is the theoretical quantity
R(W)
.sum_autocov
This is the theoretical quantity
2\pi c_f
.
Author(s)
Dominik Schulz (Research Assistant) (Department of Economics, Paderborn University),
Author and Package Creator
Examples
arma <- list(ar = 0.8, sd_e = 0.01)
m_f <- expression(13.1 + 3.1 * x + (dnorm(x / 0.15 - 0.5 / 0.15) / 0.15) / 4)
n <- 500
p <- 1
mu <- 1
frequ <- 4
cb <- 0.05
hA_calc(
m = m_f,
arma = arma,
p = p,
mu = mu,
frequ = frequ,
n = n,
cb = cb
)
t <- 1:n
xt <- t / n
mxt <- 13.1 + 3.1 * xt + dnorm(xt, mean = 0.5, sd = 0.15) / 4
S2 <- rep(c(0, 1, 0, 0), length.out = n)
S3 <- rep(c(0, 0, 1, 0), length.out = n)
S4 <- rep(c(0, 0, 0, 1), length.out = n)
sxt <- -0.5 + 0.25 * S2 + 0.5 * S3 + 1.25 * S4
set.seed(123)
et <- arima.sim(model = list(ar = 0.8), sd = 0.01, n = n)
yt <- ts(mxt + sxt + et, frequency = frequ)
plot(yt)
est <- deseats(yt)
est@bwidth
est@sum_autocov