SSAcomb | R Documentation |
SSAcomb method for identification for non-stationarity in mean, variance and covariance structure.
SSAcomb(X, ...) ## Default S3 method: SSAcomb(X, K, n.cuts = NULL, tau = 1, eps = 1e-6, maxiter = 2000, ...) ## S3 method for class 'ts' SSAcomb(X, ...)
X |
A numeric matrix or a multivariate time series object of class |
K |
Number of intervals the time series is split into. |
n.cuts |
A K+1 vector of values that correspond to the breaks which are used for splitting the data. Default is intervals of equal length. |
tau |
The lag as a scalar or a vector. Default is 1. |
eps |
Convergence tolerance. |
maxiter |
The maximum number of iterations. |
... |
Further arguments to be passed to or from methods. |
Assume that a p-variate Y with T observations is whitened, i.e. Y = S^(-1/2)*(X_t - (1/T)*sum_t(X_t)), for t = 1, …, T, where S is the sample covariance matrix of X.
The values of Y are then split into K disjoint intervals T_i. For all lags j = 1, ..., ntau, algorithm first calculates the M matrices from SSAsir (matrix M_1), SSAsave (matrix M_2) and SSAcor (matrices M_(j+2)).
The algorithm finds an orthogonal matrix U by maximizing
sum(||diag(U M_i U')||^2),
where i = 1, …, ntau + 2. The final unmixing matrix is then W = U S^(-1/2).
Then the pseudo eigenvalues D_i = diag(U M_i U') = (d_i1, ..., d_ip) are obtained and the value of d_ij tells if the jth component is nonstationary with respect to M_i.
A list of class 'ssabss', inheriting from class 'bss', containing the following components:
W |
The estimated unmixing matrix. |
S |
The estimated sources as time series object standardized to have mean 0 and unit variances. |
R |
Used M-matrices as an array. |
K |
Number of intervals the time series is split into. |
D |
The sums of pseudo eigenvalues. |
DTable |
The peudo eigenvalues of size ntau + 2 to see which type of nonstationarity there exists in each component. |
MU |
The mean vector of |
n.cut |
Used K+1 vector of values that correspond to the breaks which are used for splitting the data. |
k |
The used lag. |
method |
Name of the method ("SSAcomb"), to be used in e.g. screeplot. |
Markus Matilainen, Klaus Nordhausen
Flumian L., Matilainen M., Nordhausen K. and Taskinen S. (2021) Stationary subspace analysis based on second-order statistics. Submitted. Available on arXiv: https://arxiv.org/abs/2103.06148
JADE
frjd
n <- 10000 A <- rorth(6) z1 <- arima.sim(n, model = list(ar = 0.7)) + rep(c(-1.52, 1.38), c(floor(n*0.5), n - floor(n*0.5))) z2 <- rtvAR1(n) z3 <- rtvvar(n, alpha = 0.2, beta = 0.5) z4 <- arima.sim(n, model = list(ma = c(0.72, 0.24), ar = c(0.14, 0.45))) z5 <- arima.sim(n, model = list(ma = c(0.34))) z6 <- arima.sim(n, model = list(ma = c(0.72, 0.15))) Z <- cbind(z1, z2, z3, z4, z5, z6) library(xts) X <- tcrossprod(Z, A) X <- xts(X, order.by = as.Date(1:n)) # An xts object res <- SSAcomb(X, K = 12, tau = 1) ggscreeplot(res, type = "lines") # Three non-zero eigenvalues res$DTable # Components have different kind of nonstationarities # Plotting the components as an xts object plot(res, multi.panel = TRUE) # The first three are nonstationary
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.