| Title: | Applications of the Qn Estimator to Time Series (Univariate and Multivariate) |
|---|---|
| Description: | Time Series Qn is a package with applications of the Qn estimator of Rousseeuw and Croux (1993) <doi:10.1080/01621459.1993.10476408> to univariate and multivariate Time Series in time and frequency domains. More specifically, the robust estimation of autocorrelation or autocovariance matrix functions from Ma and Genton (2000, 2001) <doi:10.1111/1467-9892.00203>, <doi:10.1006/jmva.2000.1942> and Cotta (2017) <doi:10.13140/RG.2.2.14092.10883> are provided. The robust pseudo-periodogram of Molinares et. al. (2009) <doi:10.1016/j.jspi.2008.12.014> is also given. This packages also provides the M-estimator of the long-memory parameter d based on the robustification of the GPH estimator proposed by Reisen et al. (2017) <doi:10.1016/j.jspi.2017.02.008>. |
| Authors: | Higor Cotta, Valderio Reisen, Pascal Bondon and Céline Lévy-Leduc |
| Maintainer: | Higor Cotta <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.0 |
| Built: | 2025-03-20 02:44:06 UTC |
| Source: | https://github.com/rogih/tsqn |
Computes the robust correlation matrix of the matrix x proposed by Ma and Genton (2001) using the robust scale Qn of Rousseeuw and Croux (1993).
corMatQn(x)corMatQn(x)
x |
a numeric matrix |
a numeric matrix
Ma, Y. and Genton, M. G. (2001) Highly robust estimation of dispersion matrices. Journal of Multivariate Analysis, 78, 11–36.
Rousseeuw, P. J. and Croux, C. (1993) Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273–1283.
dataset <- cbind(rnorm(100),rnorm(100)) corMatQn(dataset)dataset <- cbind(rnorm(100),rnorm(100)) corMatQn(dataset)
x and y
Computes the robust correlation of x and y proposed by Ma and Genton (2001) using the robust scale Qn of Rousseeuw and Croux (1993).
corQn(x, y)corQn(x, y)
x |
a numeric vector |
y |
a numeric vector |
a numerical value with the robust correlation between x and y
Ma, Y. and Genton, M. G. (2001) Highly robust estimation of dispersion matrices. Journal of Multivariate Analysis, 78, 11–36.
Rousseeuw, P. J. and Croux, C. (1993) Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273–1283.
corQn(rnorm(100),rnorm(100))corQn(rnorm(100),rnorm(100))
Computes the robust covariance matrix of the matrix x proposed by Ma and Genton (2001) using the robust scale Qn of Rousseeuw and Croux (1993).
covMatQn(x)covMatQn(x)
x |
a numeric matrix |
a numeric matrix
Ma, Y. and Genton, M. G. (2001) Highly robust estimation of dispersion matrices. Journal of Multivariate Analysis, 78, 11–36.
Rousseeuw, P. J. and Croux, C. (1993) Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273–1283.
dataset <- cbind(rnorm(100),rnorm(100)) covMatQn(dataset)dataset <- cbind(rnorm(100),rnorm(100)) covMatQn(dataset)
x and y
Computes the robust covariance of x and y proposed by Ma and Genton (2001) using the robust scale Qn of Rousseeuw and Croux (1993).
covQn(x, y)covQn(x, y)
x |
a numeric vector |
y |
a numeric vector |
a numerical value with the robust covariance between x and y
Ma, Y. and Genton, M. G. (2001) Highly robust estimation of dispersion matrices. Journal of Multivariate Analysis, 78, 11–36.
Rousseeuw, P. J. and Croux, C. (1993) Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273–1283.
covQn(rnorm(100),rnorm(100))covQn(rnorm(100),rnorm(100))
Estimate the fractional (or “memory”) parameter d of long-range dependent stationary processes by the method of Geweke and Porter-Hudak (GPH). (GPH-M) and (GPH-Qn) correspond to the estimators devised by Reisen et al. (2017) and Molinares (2009), respectively.
GPH_estimate(series, bandw.exp = 0.7, method = "GPH")GPH_estimate(series, bandw.exp = 0.7, method = "GPH")
series |
univariate time series |
bandw.exp |
the bandwidth used in the regression equation |
method |
character string giving the type of GPH to be computed. Allowed values are " |
d GPH estimate
sd.as asymptotic standard deviation
sd.reg standard error deviation
Valderio Reisen, Céline Lévy-Leduc and Higor Cotta.
Reisen, V. A. and Lévy-Leduc, C. and Taqqu, M. (2017) An M-estimator for the long-memory parameter. To appear in Journal of Statistical Planning and Inference.
Molinares, F. F. and Reisen, V. A., and Cribari-Neto, F. (2009) Robust estimation in long-memory processes under additive outliers. Journal of Statistical Planning and Inference, 139, 2511–2525. #' @references Geweke, J. and Porter-Hudak, S. (1983) The estimation and application of long memory time series models. Journal of Time Series Analysis, 4, 221–238.
library(fracdiff) simseries <- fracdiff.sim(1500, d = 0.3) GPH_estimate(simseries$series,method="GPH")$d ## Not run: GPH_estimate(simseries$series,method="GPH-Qn")$d GPH_estimate(simseries$series,method="GPH-M")$d ## End(Not run)library(fracdiff) simseries <- fracdiff.sim(1500, d = 0.3) GPH_estimate(simseries$series,method="GPH")$d ## Not run: GPH_estimate(simseries$series,method="GPH-Qn")$d GPH_estimate(simseries$series,method="GPH-M")$d ## End(Not run)
This function computes the robust M-periodogram proposed by Reisen et al. (2017).
PerioMrob(series)PerioMrob(series)
series |
univariate time series |
a numeric vector containing the robust estimates of the spectral density
Valderio Reisen, Céline Lévy-Leduc and Higor Cotta.
Reisen, V. A. and Lévy-Leduc, C. and Taqqu, M. (2017) An M-estimator for the long-memory parameter. To appear in Journal of Statistical Planning and Inference.
Geweke, J. and Porter-Hudak, S. (1983) The estimation and application of long memory time series models. Journal of Time Series Analysis, 4, 221–238.
PerioMrob(ldeaths)PerioMrob(ldeaths)
Computes the robust pseudo-periodogram of Molinares et al (2009) based on the robust ACF by Ma and Genton (2000).
PerQn(x, window = "truncated", bandw.rob = 0.7)PerQn(x, window = "truncated", bandw.rob = 0.7)
x |
univariate time series |
window |
character string giving the type of the window. Allowed values are "truncated" (the default) or " |
bandw.rob |
is a numeric value giving the truncation point. |
a numeric vector containing the values of the robust periodogram proposed by Molinares (2009).
Valderio Reisen and Higor Cotta
Molinares, F. F. and Reisen, V. A., and Cribari-Neto, F. (2009) Robust estimation in long-memory processes under additive outliers. Journal of Statistical Planning and Inference, 139, 2511–2525.
Ma, Y. and Genton, M. G. (2000) Highly robust estimation of the autocovariance function. Journal of Time Series Analysis, 21, 663–684.
PerQn(ldeaths)PerQn(ldeaths)
Plot method for objects of class "robacf".
## S3 method for class 'robacf' plot(x, type = "h", xlab = "Lag", ylab = NULL, ylim = NULL, main = NULL, max.mfrow = 6, ask = Npgs > 1 && dev.interactive(), mar = if (nser > 2) c(3, 2, 2, 0.8) else par("mar"), oma = if (nser > 2) c(1, 1.2, 1, 1) else par("oma"), mgp = if (nser > 2) c(1.5, 0.6, 0) else par("mgp"), xpd = par("xpd"), cex.main = if (nser > 2) 1 else par("cex.main"), verbose = getOption("verbose"), ...)## S3 method for class 'robacf' plot(x, type = "h", xlab = "Lag", ylab = NULL, ylim = NULL, main = NULL, max.mfrow = 6, ask = Npgs > 1 && dev.interactive(), mar = if (nser > 2) c(3, 2, 2, 0.8) else par("mar"), oma = if (nser > 2) c(1, 1.2, 1, 1) else par("oma"), mgp = if (nser > 2) c(1.5, 0.6, 0) else par("mgp"), xpd = par("xpd"), cex.main = if (nser > 2) 1 else par("cex.main"), verbose = getOption("verbose"), ...)
x |
an object of class "robacf". |
type |
the type of plot to be drawn, default to histogram like vertical lines. |
xlab |
the x label of the plot. |
ylab |
the y label of the plot. |
ylim |
numeric of length 2 giving the y limits for the plot. |
main |
overall title for the plot. |
max.mfrow |
positive integer; for multivariate x indicating how many rows and columns of plots should be put on one page, using par(mfrow = c(m,m))(see |
ask |
logical; if TRUE, the user is asked before a new page is started. |
mar, oma, mgp, xpd, cex.main
|
graphics parameters as in par(*), by default adjusted to use smaller than default margins for multivariate x only. |
verbose |
logical. Should R report extra information on progress? |
... |
graphics parameters to be passed to the plotting routines. |
None
plot.acf (stats) - R Core
robacf(cbind(ldeaths,mdeaths))robacf(cbind(ldeaths,mdeaths))
This function computer and plots(by default) the robust estimates of the autocovariance or the autocorrelation function based on the Qn.
robacf(x, lag.max = NULL, type = c("correlation", "covariance"), plot = TRUE, na.action = na.fail, demean = TRUE, ...)robacf(x, lag.max = NULL, type = c("correlation", "covariance"), plot = TRUE, na.action = na.fail, demean = TRUE, ...)
x |
a numeric vector or matrix. |
lag.max |
maximum lag at which to calculate the acf. Default is 10*log10(N/m) where N is the number of observations and m the number of series. Will be automatically limited to one less than the number of observations in the series. |
type |
character string giving the type of acf to be computed. Allowed values are "correlation" (the default) or "covariance". Accepts parcial names. |
plot |
logical. If TRUE (the default) the acf is plotted. |
na.action |
function to be called to handle missing values. na.pass can be used. |
demean |
logical. Should the covariances be about the sample means? |
... |
further arguments to be passed to plot.acf. |
An object of class "robacf", which is a list with the following elements:
lag A three dimensional array containing the lags at which the acf is estimated.
acf An array with the same dimensions as lag containing the estimated acf.
type The type of correlation (same as the type argument).
n.used The number of observations in the time series.
series The name of the series x.
snames The series names for a multivariate time series.
The result is returned invisibly if plot is TRUE.
Higor Cotta, Valderio Reisen and Pascal Bondon
Cotta, H. and Reisen, V. A. and Bondon, P. and Stummer, W. (2017) Robust Estimation of Covariance and Correlation Functions of a Stationary Multivariate Process. To appear in 2017 25th European Signal Processing Conference (EUSIPCO 2017).
Ma, Y. and Genton, M. G. (2000) Highly robust estimation of the autocovariance function. Journal of Time Series Analysis, 21, 663–684.
Ma, Y. and Genton, M. G. (2001) Highly robust estimation of dispersion matrices. Journal of Multivariate Analysis, 78, 11–36.
Rousseeuw, P. J. and Croux, C. (1993) Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273–1283.
data.set <- cbind(fdeaths,mdeaths) robacf(data.set) robacf(data.set,type="covariance",lag.max=10)data.set <- cbind(fdeaths,mdeaths) robacf(data.set) robacf(data.set,type="covariance",lag.max=10)
This package contains applications of the Qn estimator of Rousseeuw and Croux(1993) to univariate and multivariate Time Series in time and frequency domains. More especifically, the robust estimation of autocorrelation or autocovariance matrix functions from Ma and Genton (2000,2001) and Cotta et. al. (2017). The robust periodogram of Molinares et. al. (2009) and the M-Periodogram of Reisen et. al. (2017). The robust GPH estimator of d considering robust periodogram approach.
| Package: | TimeSeriesQn |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2017-03-08 |
| License: | GPL (>= 2) |
Higor Cotta, Valderio Reisen, Pascal Bondon and Céline Lévy-Leduc
Maintainer: Higor Cotta [email protected]
H. Cotta, V. Reisen, P. Bondon, W. Stummer (2017): Robust Estimation of Covariance and Correlation Functions of a Stationary Multivariate Process. To appear in 2017 25th European Signal Processing Conference (EUSIPCO 2017)
V. Reisen, C. Lévy-Leduc, M. Taqqu (2017): An M-estimator for the long-memory parameter. To appear in Journal of Statistical Planning and Inference.
Y. Ma, M. Genton (2000): Highly robust estimation of the autocovariance function. Journal of Time Series Analysis, 21, 663–684.
Y. Ma, M. Genton (2001): Highly robust estimation of dispersion matrices. Journal of Multivariate Analysis, 78, 11–36.
P. J. Rousseuw, C. Croux (1993): Alternatives to the median absolute deviation.,Journal of the American Statistical Association, Taylor & Francis Group, 88, n. 424, p. 1273–-1283.
x <- rnorm(1000,10,1) y <- rnorm(1000,100,10) xy <- cbind(x,y) covQn(x,y) corQn(x,y) covMatQn(xy) corMatQn(xy) robacf(x) dataset <- cbind(fdeaths,mdeaths) robacf(dataset) robacf(dataset,type="covariance",lag.max=10) PerQn(ldeaths) library(fracdiff) simseries <- fracdiff.sim(1500, d = 0.3) GPH_estimate(simseries$series,method="GPH")$d GPH_estimate(simseries$series,method="GPH-Qn")$dx <- rnorm(1000,10,1) y <- rnorm(1000,100,10) xy <- cbind(x,y) covQn(x,y) corQn(x,y) covMatQn(xy) corMatQn(xy) robacf(x) dataset <- cbind(fdeaths,mdeaths) robacf(dataset) robacf(dataset,type="covariance",lag.max=10) PerQn(ldeaths) library(fracdiff) simseries <- fracdiff.sim(1500, d = 0.3) GPH_estimate(simseries$series,method="GPH")$d GPH_estimate(simseries$series,method="GPH-Qn")$d