Package 'sdrt'

Return the distance between two subspaces spanning by column space of matrices.

Description

The function calculates three metrics for measuring the distance between two subspaces spaning by the columns of two matrices.

Usage

dist(A, B)

Arguments

A	Matrix 1 with dimension p-by-d.
B	Matrix 2 with dimension p-by-d.

Value

The outputs include three scales and one d-dimensional vector.

r	One minuse the summation of eiegenvalues of the matrix B^TAA^TB.
q	One minues the product of eiegenvalues of the matrix B^TAA^TB.
rho	rho=sqrt(A^TBB^TA)
m^2	A d-variate vector giving the colum-wise distance between A and B.

References

Samadi S. Y. and De Alwis T. P. (2023). Fourier Method of Estimating Time Series Central Mean Subspace. https://arxiv.org/pdf/2312.02110.

Ye Z. and Weiss R.E. (2003). Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods, Journal of the American Statistical Association, 98,968-978.

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Canadian Lynx Data.

Description

Annual record of the number of the Canadian Lynx ‘trapped’ in the Mackenzie River district of the North-West Canada for the period 1821-1934.

Usage

data(lynx)

Format

A data list with 114 rows containing the count of Canadian Lynx from 1821-1934.

Source

https://www.encyclopediaofmath.org /index.php/Canadian_lynx_data

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Select the model parameters using Fourier transformation method.

Description

‘pd.boots()’ estimates the number of lags in the model and the dimension of the time series central mean subspace.

Usage

pd.boots(y, p_list=seq(2,6,by=1), w1=0.1,  space = "mean",std = FALSE,
                                     density = "kernel", method = "FM", B=50)

Arguments

y	A univariate time series observations.
p_list	(default {2,3,4,5,6}). The candidate list of the number of lags, p.
w1	(default 0.1). The tuning parameter of the estimation.
space	(default “mean”). Specify the SDR subspace needed to be estimated.
std	(default FALSE). If TRUE, then standardizing the time series observations.
density	(default “kernel”). Density function for the estimation (“kernel” or “normal”).
method	(default “FM”). Estimation method (“FM” or “NW”).
B	(default 50). Number of block bootstrap sample.

Value

The output is a p-by-p matrix, estimated p and d.

dis_dp	The average block bootsrap distances.
p_hat	The estimator for p.
d_hat	The estimator for d.

References

Samadi S. Y. and De Alwis T. P. (2023). Fourier Method of Estimating Time Series Central Mean Subspace. https://arxiv.org/pdf/2312.02110.

Examples

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_hat

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Estimate the SDR subspaces for univariate time series data.

Description

‘sdrt()’ is the main function to estimate the SDR subspaces in time series.

Usage

sdrt(y, p, d, w1 = 0.1, space = "mean", std = FALSE,
                                 density = "normal", method = "FM",n.grid=10)

Arguments

y	A univariate time series observations.
p	Integer value. The lag of the time series.
d	Integer value (<p). The dimension of the time series central mean subspace.
w1	(default 0.1). The tuning parameter of the “FM” estimation method.
space	(default “mean”). Specify the SDR subspace needed to be estimated.
std	(default FALSE). If TRUE, then standardize the data.
density	(default “kernel”). Specify the density function for the estimation (“kernel” or “normal”).
method	(default “FM”). Specify the estimation method (“FM” or “NW”).
n.grid	(default 10). Number of searches for the initial value in “NW” method

Value

The output is a p-by-d basis matrix for the TS-CMS.

References

Park J. H., Sriram T. N. and Yin X. (2010). Dimension Reduction in Time Series. Statistica Sinica. 20, 747-770.

Samadi S. Y. and De Alwis T. P. (2023). Fourier Method of Estimating Time Series Central Mean Subspace. https://arxiv.org/pdf/2312.02110.

See Also

pd.boots, sigma_u

Examples

data("lynx")
y <- log10(lynx)
p <- 3
d <- 1
fit.model <- sdrt(y, p, d=1,method="FM",density = "kernel")
fit.model$eta_hat

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The tuning parameter for the estimation of the time series central mean subspace

Description

‘sigma_u()’ estimates the turning parameter needed to estimate time series central mean subspace in Fourier Method.

Usage

sigma_u(y, p, d, w1_list=seq(0.1,0.5,by=0.1),space="mean",
                                 std=FALSE,density="kernel",method="FM",B=20)

Arguments

y	A univariate time series observations.
p	Integer value. The lag of the time series.
d	Integer value. The dimension of the time series central mean subspace.
w1_list	(default {0.1, 0.2,0.3,0.4,0.5}). The sequence of candidate list for the tuning parameter.
space	(default “mean”). Specify the SDR subspace needed to be estimated.
std	(default FALSE). If TRUE, then standardizing the time series observations.
density	(default “kernel”). Specify the density function for the estimation (“kernel” or “normal”).
method	(default “FM”). Specify the estimation method. (“FM” or “NW”).
B	(default 20). Number of block bootstrap samples.

Value

The output is a length(sw2_seq) dimensional vector.

dis_sw2

The average block boostrap distances for each candidate list of values.

References

Samadi S. Y. and De Alwis T. P. (2023). Fourier Method of Estimating Time Series Central Mean Subspace. https://arxiv.org/pdf/2312.02110.

Examples

data("lynx")
y <- log10(lynx)
p <- 3
d <- 1
w1_list=seq(0.1,0.5,by=0.1)
Tuning.model=sigma_u(y, p, d, w1_list=w1_list, std=FALSE, B=10)
Tuning.model$sigma_u_hat

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