tsBSS (version 1.0.0)

summary.tssdr: Summary of an Object of Class tssdr

Description

Gives a summary of an object of class tssdr. It includes different types of methods to select the number of directions (sources) and lags.

Usage

# S3 method for tssdr
summary(object, type = c("rectangle", "alllag", "alldir", "big"), thres = 0.8, ...)
# S3 method for summary.tssdr
print(x, digits = 3, ...)
# S3 method for summary.tssdr
components(x, ...)
# S3 method for summary.tssdr
coef(object, ...)
# S3 method for summary.tssdr
plot(x, main = "The response and the chosen directions", ...)

Arguments

object

An object of class tssdr.

type

Method for choosing the important lags and directions. The choices are "rectangle", "alllag", "alldir" and "big". Default is "rectangle".

thres

The threshold value for choosing the lags and directions. Default is 0.8.

…

Further arguments to be passed to or from methods.

x

An object of class summary.tssdr

digits

The number of digits when printing an object of class summary.tssdr. Default is 3

main

A title for a plot when printing an object of class summary.tssdr.

Value

A list of class 'summary.tssdr' containing the following components:

W

The estimated signal separation matrix

L

The Lambda matrix for choosing lags and directions.

S

The estimated directions as time series object standardized to have mean 0 and unit variances.

type

The method for choosing the important lags and directions.

algorithm

The used algorithm as a character string.

yname

The name for the response time series \(y\).

Xname

The name for the predictor time series \(\bf X\).

k

The chosen number of lags (not for type = "big" ).

p

The chosen number of directions (not for type = "big").

pk

The chosen lag-direction combinations (for type = "big" only).

Details

The sum of values of \(k_0 \times p_0\) matrix \(\bf L\) of object is 1. The values of the matrix are summed together in ways detailed below, until the value is at least \(\pi\) (thres). Let \(\lambda_{ij}\) be the element \((i, j)\) of the matrix \(\bf L\).

For alllag: \(k = k_0\) and \(p\) is the smallest value for which \(\sum_{i = 1}^p \lambda_{ij} \ge \pi.\) where \(i = 1, \ldots, p\). The chosen number of lags and directions are returned.

For alldir: \(p = p_0\) and \(k\) is the smallest value for which \(\sum_{j = 1}^k \lambda_{ij} \ge \pi\) where \(j = 1, \ldots, k\). The chosen number of lags and directions are returned.

For rectangle: \(k\) and \(p\) are values such that their product \(k p\) is the smallest for which \(\sum_{i = 1}^p \sum_{j = 1}^k \lambda_{ij} \ge \pi\) where \(i = 1, \ldots, p\) and \(j = 1, \ldots, k\). The chosen number of lags and directions are returned.

For big: \(r\) is the smallest value of elements \((i_1, j_1), \ldots, (i_r, j_r)\) for which \(\sum_{k = 1}^r \lambda_{i_k,j_k} \ge \pi\) where \(k = 1, \ldots, r\). Thi indices of the matrix corresponding to the chosen values are returned.

Note that when printing a summary.tssdr object, all elements except the component S, which is the matrix of the chosen directions or a vector if there is only one direction, are printed.

References

Matilainen, M., Croux, C., Nordhausen, K. and Oja, H. (2017), Supervised Dimension Reduction for Multivariate Time Series, Econometrics and Statistics, 4, 57--69.

See Also

tssdr

Examples

# NOT RUN {
n <- 10000
A <- matrix(rnorm(9), 3, 3)

x1 <- arima.sim(n = n, list(ar = 0.2))
x2 <- arima.sim(n = n, list(ar = 0.8))
x3 <- arima.sim(n = n, list(ar = 0.3, ma = -0.4))
eps2 <- rnorm(n - 1)
y <- 2*x1[1:(n - 1)] + 3*x2[1:(n - 1)] + eps2
X <- ((cbind(x1, x2, x3))[2:n, ]) %*% t(A)

res2 <- tssdr(y, X, algorithm = "TSIR")
res2
summ2 <- summary(res2, thres = 0.5)
summ2
summary(res2) # Chooses more lags with larger threshold
summary(res2, type = "alllag") # Chooses all lags
summary(res2, type = "alldir", thres = 0.5) # Chooses all directions
summary(res2, type = "big", thres = 0.5) # Same choices than in summ2
# }