Description Usage Arguments Details Value Author(s) References See Also Examples
PVC (Principal Volatility Component) estimator for the blind source separation (BSS) problem. This method is a modified version of PVC by Hu and Tsay (2014).
1 2 3 4 5 6 7 8 9 10 |
X |
A numeric matrix or a multivariate time series object of class |
k |
A vector of lags. It can be any non-zero positive integer, or a vector consisting of them. Default is |
ordered |
Whether to order components according to their volatility. Default is |
acfk |
A vector of lags to be used in testing the presence of serial autocorrelation. Applicable only if |
original |
Whether to return the original components or their residuals based on ARMA fit. Default is |
alpha |
Alpha level for linear correlation detection. Default is 0.05. |
... |
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. Then for each lag k we calculate
Cov(Y_t Y_t', Y_(ij, t-k)) = (1/T) * sum_t [{Y_t Y_t' - (1/(T-k))*sum_t [Y_t Y_t']}*{Y_(ij, t - k) - (1/(T-k))*sum_t [Y_(ij, t-k)]}],
where t = k + 1, …, T and Y_(ij, t-k) = Y_(i, t-k) Y_(j, t-k), i, j = 1, …, p. Then
g_k(Y) = sum_i [sum_j[{Cov(Y_t Y_t', Y_(ij, t-k))}^2]],
where i,j = 1, …, p. Thus the generalized kurtosis matrix is
G_K(Y) = sum_k [g_k(Y)],
where k = 1, …, K is the set of chosen lags. Then U is the matrix with eigenvectors of G_K(Y) as its rows. The final unmixing matrix is then W = U S^(-1/2), where the average value of each row is set to be positive.
For ordered = TRUE
the function orders the sources according to their volatility. First a possible linear autocorrelation is removed using auto.arima
. Then a squared autocorrelation test is performed for the sources (or for their residuals, when linear correlation is present). The sources are then put in a decreasing order according to the value of the test statistic of the squared autocorrelation test. For more information, see lbtest
.
A list of class 'bssvol', inheriting from class 'bss', containing the following components:
W |
The estimated unmixing matrix. If |
k |
The vector of the used lags. |
S |
The estimated sources as time series object standardized to have mean 0 and unit variances. If |
MU |
The mean vector of |
If ordered = TRUE
, then also the following components included in the list:
Sraw |
The ordered original estimated sources as time series object standardized to have mean 0 and unit variances. Returned only if |
fits |
The ARMA fits for the components with linear autocorrelation. |
armaeff |
A logical vector. Is TRUE if ARMA fit was done to the corresponding component. |
linTS |
The value of the modified Ljung-Box test statistic for each component. |
linP |
p-value based on the modified Ljung-Box test statistic for each component. |
volTS |
The value of the volatility clustering test statistic. |
volP |
p-value based on the volatility clustering test statistic. |
Jari Miettinen, Markus Matilainen
Miettinen, M., Matilainen, M., Nordhausen, K. and Taskinen, S. (2020), Extracting Conditionally Heteroskedastic Components Using Independent Component Analysis, Journal of Time Series Analysis,41, 293–311.
Hu, Y.-P. and Tsay, R. S. (2014), Principal Volatility Component Analysis, Journal of Business & Economic Statistics, 32(2), 153–164.
comVol
, gSOBI
, lbtest
, auto.arima
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | if(require("stochvol")) {
n <- 10000
A <- matrix(rnorm(9), 3, 3)
# Simulate SV models
s1 <- svsim(n, mu = -10, phi = 0.8, sigma = 0.1)$y
s2 <- svsim(n, mu = -10, phi = 0.9, sigma = 0.2)$y
s3 <- svsim(n, mu = -10, phi = 0.95, sigma = 0.4)$y
# Create a daily time series
X <- ts(cbind(s1, s2, s3) %*% t(A), end = c(2015, 338), frequency = 365.25)
res <- PVC(X)
res
coef(res)
plot(res)
head(bss.components(res))
MD(res$W, A) # Minimum Distance Index, should be close to zero
}
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