The sdrt R package provides powerful capabilities
for estimating a basis for the Time Series Central Mean Subspace
(TS-CMS). This vignette serves as a comprehensive guide to
the functionalities offered by the sdrt package,
utilizing the lynx dataset as an illustrative example.
The itdr R package can be installed in two ways:
The following code chunk demonstrate the installation of the package
using the install.packages() function in R. Then, the
library can be import into the current R session using the
library() function.
The development version of sdrt R package can be installed form GitHub.
In this section, we demonstrate the functions within the sdrt package that utilize the Fourier method to estimate the sufficient dimension reduction (SDR) subspaces in time series.
In Section 2.1 brings the estimation of model parameters. The tuning the hyper parameter in Section 2.2 and the estimation of a basis of the TS-CMS explains in Section 2.3.
The first step is to estimate the model parameters, specifically
p and d. The block bootstrap procedure is
employed to estimate the unknown lags number (p) and the
unknown dimension of the TS-CMS (d). For more details refer
to Samadi and De Alwis (2023). The following R code chunk demonstrate
the use of the pd.boots() function to estimate
p and d.
data("lynx")
y <- log10(lynx)
p_list=seq(2,5,by=1)
fit.model=pd.boots(y,p_list,w1=0.1,B=10)
fit.model$dis_pd
fit.model$p_hat
fit.model$d_hatIn this example, the estimated lag number and the dimension of the
TS-CMS are denoted as p_hat=3 and d_hat=1 for
the lynx dataset.
Within the Fourier method for estimating the TS-CMS, there exists a
hyperparameter σu2.
While a recommended value of σu2 = 0.1
exists, the sdrt package offers users the flexibility
to fine-tune this parameter for each dataset. The following R code chunk
outlines the procedure using the sigma_u() function to tune
this parameter for the lynx dataset.
set.seed(1)
data("lynx")
y <- log10(lynx)
p <- 3
d <- 1
w1_list=seq(0.1,0.5,by=0.1)
Tunning.model=sigma_u(y, p, d, w1_list=w1_list, std=FALSE, B=10)
Tunning.model$sigma_u_hatIn this example, the estimated tuning parameter for the
lynx dataset is σu2 = 0.3.
Users can adapt this process to optimize the hyperparameter for their
specific dataset.
We have described the estimation procedure of model parameters,
p and d in Section 2.1 and the tuning
parameter σu2
in Section 2.2. Now, we are ready to estimate the Time Series Central
Mean Subspace (TS-CMS). The TS-CMS can be estimated using the
sdrt() function by passing the method argument
as "FM". The following R code chunk illustrate the use of
the sdrt() function for this purpose.
library(sdrt)
data("lynx")
y <- log10(lynx)
p <- 3
d <- 1
fit.model <- sdrt(y, p, d=1,method="FM",density = "kernel")
fit.model$eta_hatIn this example, the estimated TS-CMS is obtained using the Fourier method (“FM”). Users can customize the parameters according to their dataset and analysis needs.
In this section, we demonstrate the application of the
sdrt() function within the sdrt R package
to estimate the TS-CMS using the Nadaraya-Watson (NW) method, as
proposed by Park et al. (2009). The following R code chunk illustrates
the utilization of the sdrt() on the lynx
dataset. Here, we specify the method argument as
"NW" to indicate the Nadaraya-Watson estimation method.
library(pracma)
data("lynx")
y <- log10(lynx)
p <- 4
d <- 1
fit.model <- sdrt(y, p, d,method="NW")
fit.model$eta_hatIn this example, the Nadaraya-Watson method is employed to estimate the TS-CMS, and users can adjust parameters based on their specific dataset requirements.