| Title: | Applied Singular Spectrum Analysis (ASSA) |
|---|---|
| Description: | Functions to model and decompose time series into principal components using singular spectrum analysis (de Carvalho and Rua (2017) <doi:10.1016/j.ijforecast.2015.09.004>; de Carvalho et al (2012) <doi:10.1016/j.econlet.2011.09.007>). |
| Authors: | Miguel de Carvalho [aut, cre], Gabriel Martos [aut] |
| Maintainer: | Miguel de Carvalho <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 2.0 |
| Built: | 2024-11-19 05:10:36 UTC |
| Source: | https://github.com/cran/ASSA |
The package ASSA is an add-on tool for R that implements time series decomposition and modeling methods based on singular spectrum analysis (SSA) and multivariate singular spectrum analysis (MSSA). The current version of the package includes tools tailored for extracting business cycles, and for computing trendlines.
For a complete list of functions, data sets and documentation, type
help.start() and follow the link to ASSA on the
Package Index.
Funding from the project INTERSTATA (Interdisciplinary Statistics in Action), by the International Research and Partnership Fund, is gratefully acknowledged.
Computes a business cycle indicator using multivariate singular spectrum analysis.
bmssa(y, l = 32)bmssa(y, l = 32)
y |
multivariate time series of economic activity data from which the cycle is to be extracted; the first column is reserved to Gross Domestic Product (GDP). |
l |
window length; by default, |
The business cycle indicator produced using this routine is based on
methods proposed in de Carvalho and Rua (2017). A quick summary of the
method is as follows. Multivariate singular spectrum analysis is used
to decompose a multivariate time series (y) into principal
components, and a Fisher statistic automatically selects
elementary reconstructed components (erc) within business cycle
frequencies. The indicator results from adding elementary
reconstructed components within business cycle frequencies. The
plot method depicts the resulting business cycle indicator,
and the print method reports the business cycle indicator
along with the components selected by the Fisher statistic.
cycle |
time series with the business cycle indicator. |
sfisher |
vector with indices of elementary reconstructed
components selected with Fisher |
erc |
time series with elementary reconstructed components
resulting from targeted grouping based on a Fisher |
l |
window length. |
Miguel de Carvalho.
de Carvalho, M., Rodrigues, P., and Rua, A. (2012). Tracking the US business cycle with a singular spectrum analysis. Economics Letters, 114, 32–35.
de Carvalho, M. and Rua, A. (2017). Real-time nowcasting the US output gap: Singular spectrum analysis at work. International Journal of Forecasting, 33, 185–198.
See combplot for a chart of the selected elementary
reconstructed components from which the business cycle indicator
results. See bssa for a univariate version of the
method.
## Tracking the US Business Cycle (de Carvalho et al, 2017; Fig. 6) data(GDPIP) fit <- bmssa(log(GDPIP)) plot(fit) print(fit)## Tracking the US Business Cycle (de Carvalho et al, 2017; Fig. 6) data(GDPIP) fit <- bmssa(log(GDPIP)) plot(fit) print(fit)
The data consist of 267 polls conducted before the June 23 2016 EU referendum, which took place in the UK.
brexitbrexit
A dataframe with 272 observations on six variables. The object
is of class list.
Financial Times (FT) Brexit poll tracker.
de Carvalho, M. and Martos, G. (2020). Brexit: Tracking and disentangling the sentiment towards leaving the EU. International Journal of Forecasting, 36, 1128–1137.
## Leave--stay plot (de Carvalho and Martos, 2018; Fig. 1) data(brexit) attach(brexit) par(pty = "s") plot(leave[(leave > stay)], stay[(leave > stay)], xlim = c(22, 66), ylim = c(22, 66), pch = 16, col = "red", xlab = "Leave", ylab = "Stay") points(leave[(stay > leave)], stay[(stay > leave)], pch = 16, col = "blue") points(leave[(stay == leave)], stay[(stay == leave)], pch = 24) abline(a = 0, b = 1, lwd = 3)## Leave--stay plot (de Carvalho and Martos, 2018; Fig. 1) data(brexit) attach(brexit) par(pty = "s") plot(leave[(leave > stay)], stay[(leave > stay)], xlim = c(22, 66), ylim = c(22, 66), pch = 16, col = "red", xlab = "Leave", ylab = "Stay") points(leave[(stay > leave)], stay[(stay > leave)], pch = 16, col = "blue") points(leave[(stay == leave)], stay[(stay == leave)], pch = 24) abline(a = 0, b = 1, lwd = 3)
Computes a business cycle indicator using singular spectrum analysis.
bssa(y, l = 32)bssa(y, l = 32)
y |
time series of economic activity data from which the cycle is to be extracted. |
l |
window length; by default, |
The business cycle indicator produced using this routine is based on
methods proposed in de Carvalho et al (2012) and de Carvalho and Rua
(2017). A quick summary of the method is as follows: Singular
spectrum analysis is used to decompose a GDP time series (y)
into principal components, and a Fisher statistic
automatically selects elementary reconstructed components
(erc) within business cycle frequencies. The indicator
results from adding principal components within business cycle
frequencies. The plot method depicts the resulting business
cycle indicator, and the print method reports the business
cycle indicator along with the components selected by the Fisher
statistic.
cycle |
time series with the business cycle indicator. |
sfisher |
vector with indices of principal components selected
with Fisher |
erc |
time series with elementary reconstructed components
resulting from targeted grouping based on a Fisher |
l |
window length. |
Miguel de Carvalho.
de Carvalho, M., Rodrigues, P., and Rua, A. (2012) Tracking the US business cycle with a singular spectrum analysis. Economics Letters, 114, 32–35.
de Carvalho, M. and Rua, A. (2017) Real-time nowcasting the US output gap: Singular spectrum analysis at work. International Journal of Forecasting, 33, 185–198.
See combplot for a chart of the selected elementary
reconstructed components from which the business cycle indicator
results. See bmssa for a multivariate version of the
method.
## Tracking the US Business Cycle (de Carvalho et al, 2017; Fig. 6) data(GDPIP) fit <- bssa(log(GDPIP[, 1])) plot(fit) print(fit)## Tracking the US Business Cycle (de Carvalho et al, 2017; Fig. 6) data(GDPIP) fit <- bssa(log(GDPIP[, 1])) plot(fit) print(fit)
Produces a comb-plot for visualizing what principal components are used for producing the (multivariate) singular spectrum business cycle indicator.
combplot(fit)combplot(fit)
fit |
a |
combplot yields a comb-plot indentifying the indices
of the components selected according to the Fisher statistic,
along with the corresponding principal components; see de Carvalho and
Rua (2017, p. 190) for a definition.
Miguel de Carvalho.
de Carvalho, M. and Rua, A. (2017). Real-time nowcasting the US output gap: Singular spectrum analysis at work. International Journal of Forecasting, 33, 185–198.
bssa.
## Tracking the US Business Cycle (de Carvalho and Rua, 2017; Fig. 5) data(GDPIP) fit <- bssa(log(GDPIP[, 1])) combplot(fit)## Tracking the US Business Cycle (de Carvalho and Rua, 2017; Fig. 5) data(GDPIP) fit <- bssa(log(GDPIP[, 1])) combplot(fit)
US GDP (Gross Domestic Product) and IP (Industrial Production) ranging from from 1947 (Q1) to 2013 (Q4); the data correspond to a real-time vintage.
GDPIPGDPIP
A bivariate time series with 268 observations on two
variables. The object is of class mts.
Federal Reserve Bank of Philadelphia.
de Carvalho, M. and Rua, A. (2017). Real-time nowcasting the US output gap: Singular spectrum analysis at work. International Journal of Forecasting, 33, 185–198.
## Plotting GDP and IP (de Carvalho and Rua, 2017; Fig. 4) data(GDPIP) par(mar = c(5, 4, 4, 5) + .1) plot(GDPIP[, 1], type = "l", xlab = "Time", ylab = "Gross Domestic Product (GDP)", lwd = 3, col = "red", cex.lab = 1.4, cex.axis = 1.4) par(new = TRUE) plot(GDPIP[, 2], type = "l", xaxt = "n", yaxt = "n", xlab = "", ylab = "", lwd = 3, col = "blue", cex.axis = 1.4) axis(4) mtext("Industrial Production (IP)", side = 4, line = 3, cex = 1.4) legend("topleft", col = c("red", "blue"), lty = 1, lwd = 3, legend = c("GDP", "IP"))## Plotting GDP and IP (de Carvalho and Rua, 2017; Fig. 4) data(GDPIP) par(mar = c(5, 4, 4, 5) + .1) plot(GDPIP[, 1], type = "l", xlab = "Time", ylab = "Gross Domestic Product (GDP)", lwd = 3, col = "red", cex.lab = 1.4, cex.axis = 1.4) par(new = TRUE) plot(GDPIP[, 2], type = "l", xaxt = "n", yaxt = "n", xlab = "", ylab = "", lwd = 3, col = "blue", cex.axis = 1.4) axis(4) mtext("Industrial Production (IP)", side = 4, line = 3, cex = 1.4) legend("topleft", col = c("red", "blue"), lty = 1, lwd = 3, legend = c("GDP", "IP"))
Computes the trendline estimation for interval time series data using singular spectrum analysis.
isst(y, l= 'automatic' , m = 'automatic')isst(y, l= 'automatic' , m = 'automatic')
y |
|
l |
window length; the string |
m |
number of leading eigentriples; the string |
Singular spectrum analysis decompose time series data (y)
into principal components, and a cumulative periodogram-based
criterion learn about elementary reconstructed components
(erc) that contribute to the signal. The trendline results
from adding principal components selected by a cumulative
periodogram-based criteria; see de Carvalho and Martos (2018,
Section 4.1). The plot method yields the resulting trendlines
along with the data; options for the plot method are give by
a list including the strings "trendline",
"components", "cpgram", and "screeplot",
along with a set of values (ncomp) indicating the components
on which these diagnostics are to be depicted (e.g. plot(fit,
options = list(type = "components", ncomp = 1:3)).
trendline |
itsframe object with interval trendline estimation from
targeted grouping based on a cumulative periodogram criterion (or
according to the number of components specified in |
l |
window length. |
m |
number of leading eigentriples. An automatic
criterion based on the cumulative periodogram of the residuals is
provided by default by using the string |
residuals |
itsframe object with the residuals from targeted
grouping based on a cumulative periodogram criterion (or according
to the number of components specified in |
svd |
Singular value decomposition corresponding to the trajectory matrix. |
erc |
elementary reconstructed components. |
observations |
itsframe object with the raw data. |
de Carvalho, M. and Martos, G. (2020). Modeling Interval Trendlines: Symbolic Singular Spectrum Analysis for Interval Time Series. Submitted (available on arXiv).
See misst for a version of the routine for multivariate
interval value time series.
# Merval data example: data(merval) id.data <- rev(which(merval[,1]>'2015-12-31' & merval[,1]<'2020-10-01') ) y <- itsframe(date=merval[id.data,1], a=merval[id.data,2], b=merval[id.data,3]); isst_output <- isst(y ,l = 'automatic', m = 'automatic') print(isst_output) # Estimated trendlines plot(isst_output) ## Scree-plot plot(isst_output, options = list(type = "screeplot", ncomp = 1:10), type = "b", pch = 20, lwd = 2) # Elementary reconstructed components plot(isst_output, options=list(type='components',ncomp=1:3), xlab='Time') # cpgram's ('a=low' and 'b=high') plot(isst_output, options = list(type='cpgram')) # Setting m = 'automatic' (default option) to obtain cpgrams inside the bandwiths. ################################## ### Forecasting with isst ### ################################## pred <- predict(isst_output, p = 5) head(pred$forecast,3) # Forecasted interval data. attributes(pred) pred$coefficients[1:5] # linear recurrence parameters. # End# Merval data example: data(merval) id.data <- rev(which(merval[,1]>'2015-12-31' & merval[,1]<'2020-10-01') ) y <- itsframe(date=merval[id.data,1], a=merval[id.data,2], b=merval[id.data,3]); isst_output <- isst(y ,l = 'automatic', m = 'automatic') print(isst_output) # Estimated trendlines plot(isst_output) ## Scree-plot plot(isst_output, options = list(type = "screeplot", ncomp = 1:10), type = "b", pch = 20, lwd = 2) # Elementary reconstructed components plot(isst_output, options=list(type='components',ncomp=1:3), xlab='Time') # cpgram's ('a=low' and 'b=high') plot(isst_output, options = list(type='cpgram')) # Setting m = 'automatic' (default option) to obtain cpgrams inside the bandwiths. ################################## ### Forecasting with isst ### ################################## pred <- predict(isst_output, p = 5) head(pred$forecast,3) # Forecasted interval data. attributes(pred) pred$coefficients[1:5] # linear recurrence parameters. # End
The function itsframe creates a univariate interval time series
object to be used in combination with the functions in the package
ASSA.
itsframe(dates, a, b)itsframe(dates, a, b)
dates |
dates at which observations took place. |
a |
vector with lower interval time-series values sorted in ascendant way (first element in 'a' corresponds to the oldest value of the interval series and last element in 'a' corresponds to the newest value). |
b |
vector with upper interval time-series values sorted in ascendant way (first element in 'b' corresponds to the oldest value of the interval series and last element in 'b' corresponds to the newest value). |
de Carvalho, M. and Martos, G. (2020). Modeling Interval Trendlines: Symbolic Singular Spectrum Analysis for Interval Time Series. Submitted (available on arXiv).
data(merval) id.data <- rev(which(merval[,1]>'2015-12-31' & merval[,1]<'2020-10-01') ) y <- itsframe(date=merval[id.data,1], a=merval[id.data,2], b=merval[id.data,3]); plot(y, main = 'MERVAL')data(merval) id.data <- rev(which(merval[,1]>'2015-12-31' & merval[,1]<'2020-10-01') ) y <- itsframe(date=merval[id.data,1], a=merval[id.data,2], b=merval[id.data,3]); plot(y, main = 'MERVAL')
Raw interval data series corresponding to weekly minimum and maximum values of MERVAL index ranging from January 1st 2016 to September 30th 2020.
mervalmerval
A dataframe with 353 observations. The object
is of class list.
Yahoo Finance.
de Carvalho, M. and Martos, G. (2020). Modeling Interval Trendlines: Symbolic Singular Spectrum Analysis for Interval Time Series. Submitted (available on arXiv).
data(merval) head(merval,3)data(merval) head(merval,3)
Computes a trendline for multivariate interval data using singular spectrum analysis.
misst(y, l= 'automatic' , m = 'automatic', vertical = TRUE)misst(y, l= 'automatic' , m = 'automatic', vertical = TRUE)
y |
object of class |
l |
window length; the string |
m |
number of leading eigentriples. An automatic
criterion based on the cumulative periodogram of the residuals is
provided by default by using the string |
vertical |
logical; if |
Multivariate singular spectrum analysis is used to decompose interval time
series data (y) into principal components, and a cumulative
periodogram-based criterion automatically learns about what elementary
reconstructed components (erc) contribute to the signal; see de
Carvalho and Martos (2018) for details. The trendline results from
adding elementary reconstructed components selected by the cumulative
periodogram of the residuals. The plot method depicts the
trendlines, and the print method reports the trendlines along
with the components selected by the cumulative periodogram-based
criterion.
trendline |
mitsframe object with interval trendline estimation from targeted grouping based on a cumulative periodogram criterion (or according to the number of components specified in vector |
l |
window length. |
m |
vector with number of components selected on each dimension. |
vertical |
flag indicating if the trajectory matrices where stacked vertically. |
residuals |
mitsframe object with the interval residuals from targeted grouping based on a cumulative periodogram criterion (or according to the number of components specified in vector |
svd |
the Singular Value Decomposition of the trajectory matrix. |
erc |
list with elementary reconstructed components. |
observations |
mitsframe object with the raw data |
de Carvalho, M. and Martos, G. (2020). Modeling Interval Trendlines: Symbolic Singular Spectrum Analysis for Interval Time Series. Submitted (available on arXiv).
See msst for a similar routine yielding trendlines for
standard multivariate time series of data.
muX.a = function(t){ 8 + t + sin(pi*t) } ; muX.b = function(t){ muX.a(t) + 2 } muY.a = function(t){sqrt(t) + cos(pi*t/2) } ; muY.b = function(t){ 2*muY.a(t) + 2 } N = 100; t=seq(0.1,2*pi,length = N); set.seed(1) e.x = rnorm(100); e.y = rnorm(100); a.X = muX.a(t) + e.x; b.X = a.X + 2 a.Y = muY.a(t) + e.y ; b.Y = 2*a.Y + 2 A <- cbind(a.X, a.Y); B <- cbind(b.X, b.Y) y <- mitsframe(dates=t, A=A, B = B) fit <- misst(y) fit$l; fit$m; fit$vertical # Estimated trendlines: head(fit$trendlines$A,5) head(fit$trendlines$B,5) ## Estimated interval trendlines plot(fit) ## Scree-plot plot(fit, options = list(type = "screeplots")) ## Per plot(fit, options = list(type = "cpgrams")) ## ERC plot(fit, options=list(type='components',ncomp=1:3)) ################################## ### Forecasting with misst ### ################################## pred = predict(fit, p = 5) pred$forecasts # Forecast organized in an array. # EndmuX.a = function(t){ 8 + t + sin(pi*t) } ; muX.b = function(t){ muX.a(t) + 2 } muY.a = function(t){sqrt(t) + cos(pi*t/2) } ; muY.b = function(t){ 2*muY.a(t) + 2 } N = 100; t=seq(0.1,2*pi,length = N); set.seed(1) e.x = rnorm(100); e.y = rnorm(100); a.X = muX.a(t) + e.x; b.X = a.X + 2 a.Y = muY.a(t) + e.y ; b.Y = 2*a.Y + 2 A <- cbind(a.X, a.Y); B <- cbind(b.X, b.Y) y <- mitsframe(dates=t, A=A, B = B) fit <- misst(y) fit$l; fit$m; fit$vertical # Estimated trendlines: head(fit$trendlines$A,5) head(fit$trendlines$B,5) ## Estimated interval trendlines plot(fit) ## Scree-plot plot(fit, options = list(type = "screeplots")) ## Per plot(fit, options = list(type = "cpgrams")) ## ERC plot(fit, options=list(type='components',ncomp=1:3)) ################################## ### Forecasting with misst ### ################################## pred = predict(fit, p = 5) pred$forecasts # Forecast organized in an array. # End
The function mitsframe is used to create interval-valued multivariate time series objects.
mitsframe(dates, A, B)mitsframe(dates, A, B)
dates |
a vector of dates at which observations took place. |
A |
matrix with time series in columns (dimensions) and observations in rows corresponding to the lowest values. Data must be sorted in ascendant way (first row in 'A' corresponds to the oldest values of the series and last row in 'A' corresponds to the newest values). |
B |
matrix with time series in columns (dimensions) and observations in rows corresponding to the lowest values. Data must be sorted in ascendant way (first row in 'A' corresponds to the oldest values of the series and last row in 'A' corresponds to the newest values). |
Gabriel Martos and Miguel de Carvalho.
de Carvalho, M. and Martos, G. (2020). Modeling Interval Trendlines: Symbolic Singular Spectrum Analysis for Interval Time Series. Submitted (available on arXiv).
muX.a = function(t){ 8 + t + sin(pi*t) } ; muX.b = function(t){ muX.a(t) + 2 } muY.a = function(t){sqrt(t) + cos(pi*t/2) } ; muY.b = function(t){ 2*muY.a(t) + 2 } N = 100; t=seq(0.1,2*pi,length = N); set.seed(1) e.x = rnorm(100); e.y = rnorm(100); a.X = muX.a(t) + e.x; b.X = a.X + 2 a.Y = muY.a(t) + e.y ; b.Y = 2*a.Y + 2 A <- cbind(a.X, a.Y); B <- cbind(b.X, b.Y) y <- mitsframe(dates=t, A=A, B = B) plot(y) # standard plot.muX.a = function(t){ 8 + t + sin(pi*t) } ; muX.b = function(t){ muX.a(t) + 2 } muY.a = function(t){sqrt(t) + cos(pi*t/2) } ; muY.b = function(t){ 2*muY.a(t) + 2 } N = 100; t=seq(0.1,2*pi,length = N); set.seed(1) e.x = rnorm(100); e.y = rnorm(100); a.X = muX.a(t) + e.x; b.X = a.X + 2 a.Y = muY.a(t) + e.y ; b.Y = 2*a.Y + 2 A <- cbind(a.X, a.Y); B <- cbind(b.X, b.Y) y <- mitsframe(dates=t, A=A, B = B) plot(y) # standard plot.
Computes trendlines for multivariate time series data using multivariate singular spectrum analysis.
msst(y, l = "automatic", m = "automatic", vertical = TRUE)msst(y, l = "automatic", m = "automatic", vertical = TRUE)
y |
mtsframe object containing raw data. |
l |
window length; the string |
m |
vector with the number of leading eigentriples on each dimension. An automatic
criterion based on the cumulative periodogram of the residuals is
provided by default by using the string |
vertical |
logical; if |
Multivariate singular spectrum analysis is used to decompose time
series data (y) into principal components, and a cumulative
periodogram-based criterion automatically learns about what elementary
reconstructed components (erc) contribute to the signal; see de
Carvalho and Martos (2018) for details. The trendline results from
adding elementary reconstructed components selected by the cumulative
periodogram of the residuals. The plot method depicts the
trendlines, and the print method reports the trendlines along
with the components selected by the cumulative periodogram-based
criterion.
trendline |
mtsframe object with trendline estimation from targeted grouping based on a cumulative periodogram criterion (or according to the number of components specified in vector |
l |
window length. |
m |
vector with number of components selected on each dimension. |
vertical |
flag indicating if the trajectory matrices where stacked vertically. |
residuals |
mtsframe object with the residuals from targeted grouping based on a cumulative periodogram criterion (or according to the number of components specified in vector |
svd |
the Singular Value Decomposition of the trajectory matrix. |
erc |
list with elementary reconstructed components. |
observations |
mtsframe object with the observations |
Gabriel Martos and Miguel de Carvalho
de Carvalho, M. and Martos, G. (2020). Brexit: Tracking and disentangling the sentiment towards leaving the EU. International Journal of Forecasting, 36, 1128–1137.
See msstc for a similar routine yielding trendlines for
multivariate time series of compositional data.
## SIMULATED EXAMPLE t <- seq(0.05, 5, by = 0.05) t2 <- seq(0.05, 6, by = 0.05) p = length(t2)-length(t) # Forecasting horizon parameter: n = length(t) Y <- cbind(t^3 - 9 * t^2 + 23 * t + rnorm(n, 0, 1), 10 * sin(3 * t) / t + rnorm(n, 0, 1)) y <- mtsframe(dates = t, Y) fit.vertical <- msst(y) pred.vertical <- predict(fit.vertical, p = p) print(pred.vertical$forecast) ## BREXIT DATA EXAMPLE ## (de Carvalho and Martos, 2018; Fig. 1) data(brexit) attach(brexit) y <- mtsframe(date, brexit[, 1:3] / 100) fit <- msst(y) ## Window length and components automatically selected fit$l; fit$m ## Plot trendlines (de Carvalho and Martos, 2018; Fig. 1) plot(fit, options = list(type = "trendlines"), xlab="time", col=c("blue", "red", "black"), lwd = 2, lty = c(1, 2, 3)) ## Plot cumulative periodograms (with 95% confidence bands) par(mfrow = c(1, 3)) plot(fit, options = list(type = "cpgrams", series.names = c('Leave','Stay','Undecided')) ) ## Scree-plot par(mfrow = c(1, 1)) plot(fit, options = list(type = "screeplot", ncomp.scree = 1:10), type = "b", pch = 20, lwd = 2, main='Scree plot') ## Plot elementary reconstructed components plot(fit, options = list(type = "components", ncomp = 1:2))## SIMULATED EXAMPLE t <- seq(0.05, 5, by = 0.05) t2 <- seq(0.05, 6, by = 0.05) p = length(t2)-length(t) # Forecasting horizon parameter: n = length(t) Y <- cbind(t^3 - 9 * t^2 + 23 * t + rnorm(n, 0, 1), 10 * sin(3 * t) / t + rnorm(n, 0, 1)) y <- mtsframe(dates = t, Y) fit.vertical <- msst(y) pred.vertical <- predict(fit.vertical, p = p) print(pred.vertical$forecast) ## BREXIT DATA EXAMPLE ## (de Carvalho and Martos, 2018; Fig. 1) data(brexit) attach(brexit) y <- mtsframe(date, brexit[, 1:3] / 100) fit <- msst(y) ## Window length and components automatically selected fit$l; fit$m ## Plot trendlines (de Carvalho and Martos, 2018; Fig. 1) plot(fit, options = list(type = "trendlines"), xlab="time", col=c("blue", "red", "black"), lwd = 2, lty = c(1, 2, 3)) ## Plot cumulative periodograms (with 95% confidence bands) par(mfrow = c(1, 3)) plot(fit, options = list(type = "cpgrams", series.names = c('Leave','Stay','Undecided')) ) ## Scree-plot par(mfrow = c(1, 1)) plot(fit, options = list(type = "screeplot", ncomp.scree = 1:10), type = "b", pch = 20, lwd = 2, main='Scree plot') ## Plot elementary reconstructed components plot(fit, options = list(type = "components", ncomp = 1:2))
Computes trendlines on the unit simplex for multivariate time series data using multivariate singular spectrum analysis.
msstc(y, l = 'automatic', m = 'automatic', vertical = TRUE)msstc(y, l = 'automatic', m = 'automatic', vertical = TRUE)
y |
mtsframe object containing data. |
l |
window length; the string |
m |
vector with the number of leading eigentriples on each dimension. An automatic
criterion based on the cumulative periodogram of the residuals is
provided by default by using the string |
vertical |
logical; if |
The trendline produced using this routine is based on the methods
proposed in de Carvalho and Martos (2018). A quick summary of the
method is as follows. Multivariate singular spectrum analysis is
used to decompose time series data (y) into principal
components, and a cumulative periodogram-based criterion
automatically learns about what elementary reconstructed components
(erc) contribute to the signal; see de Carvalho and Martos
(2018) for details. The trendline results from adding elementary
reconstructed components selected by the cumulative periodogram, and
after projecting into the unit simplex. The plot method
depicts the trendlines, and the print method reports the
trendlines along with the components selected by the cumulative
periodogram-based criterion.
trendline |
mtsframe object with trendline estimation from targeted grouping based on a cumulative periodogram criterion (or according to the number of components specified in vector |
l |
window length. |
m |
vector with number of components selected on each dimension. |
vertical |
flag indicating if the trajectory matrices where stacked vertically. |
residuals |
mtsframe object with the residuals from targeted grouping based on a cumulative periodogram criterion (or according to the number of components specified in vector |
svd |
the Singular Value Decomposition of the trajectory matrix. |
erc |
list with elementary reconstructed components. |
observations |
mtsframe object with the observations |
Gabriel Martos and Miguel de Carvalho
de Carvalho, M. and Martos, G. (2020). Brexit: Tracking and disentangling the sentiment towards leaving the EU. International Journal of Forecasting, 36, 1128–1137.
See msst for a similar routine yielding trendlines for
multivariate time series, but which does not project the pointwise
estimates to the unit simplex.
## BREXIT DATA EXAMPLE ## (de Carvalho and Martos, 2018; Fig. 1) data(brexit) attach(brexit) y <- mtsframe(date, brexit[, 1:3] / 100) fit <- msstc(y) # Estimations on the simplex rowSums(fit$trendlines$Y) # Forecast also in the simplex rowSums(predict(fit, p = 5)$forecast) ## Window length and components automatically selected fit$l; fit$m ## Plot trendlines (de Carvalho and Martos, 2018; Fig. 1) plot(fit, options = list(type = "trendlines"), xlab="time", col=c("blue", "red", "black"), lwd = 2, lty = c(1, 2, 3)) ## Plot cumulative periodograms (with 95% confidence bands) par(mfrow = c(1, 3)) plot(fit, options = list(type = "cpgrams") ) ## Scree-plot (with 95% confidence bands) par(mfrow = c(1, 1)) plot(fit, options = list(type = "screeplot", ncomp.scree = 1:10), type = "b", pch = 20, lwd = 2, main='Scree plot') ## Plot elementary reconstructed components ## (de Carvalho and Martos, 2020; Fig. 5) plot(fit, options = list(type = "components", ncomp = 1:2))## BREXIT DATA EXAMPLE ## (de Carvalho and Martos, 2018; Fig. 1) data(brexit) attach(brexit) y <- mtsframe(date, brexit[, 1:3] / 100) fit <- msstc(y) # Estimations on the simplex rowSums(fit$trendlines$Y) # Forecast also in the simplex rowSums(predict(fit, p = 5)$forecast) ## Window length and components automatically selected fit$l; fit$m ## Plot trendlines (de Carvalho and Martos, 2018; Fig. 1) plot(fit, options = list(type = "trendlines"), xlab="time", col=c("blue", "red", "black"), lwd = 2, lty = c(1, 2, 3)) ## Plot cumulative periodograms (with 95% confidence bands) par(mfrow = c(1, 3)) plot(fit, options = list(type = "cpgrams") ) ## Scree-plot (with 95% confidence bands) par(mfrow = c(1, 1)) plot(fit, options = list(type = "screeplot", ncomp.scree = 1:10), type = "b", pch = 20, lwd = 2, main='Scree plot') ## Plot elementary reconstructed components ## (de Carvalho and Martos, 2020; Fig. 5) plot(fit, options = list(type = "components", ncomp = 1:2))
The function mtsframe create a mutivariate time series object to be used in combination with the functions in the package ASSA.
mtsframe(dates, Y)mtsframe(dates, Y)
dates |
dates at which observations took place. |
Y |
matrix with different time-series in columns (dimensions) and observations in rows. Values must be be sorted in ascendant way (first row in 'Y' corresponds to the oldest values of the series and last row in 'Y' corresponds to the newest values). |
data(brexit); attach(brexit) head(brexit, 3) y <- mtsframe(date, Y = brexit[, 1:3]) print(y) # A 'list' with 4 elements: dates, series data matrix, and series length. head(y$Y, 3) y$n y$D plot(y) # standard plot. # Customized plot (time.format is an additional feature to use when y$date is in 'date' format) plot(y, time.format = '%Y' , col = c('blue','red','black'), lty = 2, type = 'p', pch = 20, main = 'Brexit data', xlab = 'Year', ylab ='Trendline estimations')data(brexit); attach(brexit) head(brexit, 3) y <- mtsframe(date, Y = brexit[, 1:3]) print(y) # A 'list' with 4 elements: dates, series data matrix, and series length. head(y$Y, 3) y$n y$D plot(y) # standard plot. # Customized plot (time.format is an additional feature to use when y$date is in 'date' format) plot(y, time.format = '%Y' , col = c('blue','red','black'), lty = 2, type = 'p', pch = 20, main = 'Brexit data', xlab = 'Year', ylab ='Trendline estimations')
Computes a forcasted trendline for time series data using singular spectrum analysis.
predict(fitted.model, p = 1)predict(fitted.model, p = 1)
fitted.model |
estimated model using the functions in the package. |
p |
the horizon to produce forecasts. |
predict is a wrapper function for predictions from the results of various singular spectrum model fitting functions on the package. The function invokes particular methods which depend on the class of the first argument (i.e. sst,msst, msstc, isst, misst, etc) .
forecast |
Matrix containing in columns the dimensions and in rows the forecasts. |
a |
Parameters corresponding to the linear recurrence formula. |
Gabriel Martos and Miguel de Carvalho
de Carvalho, M. and Martos, G. (2020). Brexit: Tracking and disentangling the sentiment towards leaving the EU. International Journal of Forecasting, 36, 1128–1137. de Carvalho, M. and Martos, G. (2020). Modeling Interval Trendlines: Symbolic Singular Spectrum Analysis for Interval Time Series. Submitted (available on arXiv).
See sst,msst, msstc, isst, misst
for a version of different models.
## SIMULATED DATA EXAMPLE set.seed(1) N <- 500 t <- seq(.01, 5, length = N) Y <- cbind(t^3 - 9 * t^2 + 23 * t + rnorm(N, 0, 1), 10 * sin(3 * t) / t + rnorm(N, 0, 1)) y <- mtsframe(date = t, Y) fit <- msst(y) # Forecasting: predict(fit, p = 5)$forecast## SIMULATED DATA EXAMPLE set.seed(1) N <- 500 t <- seq(.01, 5, length = N) Y <- cbind(t^3 - 9 * t^2 + 23 * t + rnorm(N, 0, 1), 10 * sin(3 * t) / t + rnorm(N, 0, 1)) y <- mtsframe(date = t, Y) fit <- msst(y) # Forecasting: predict(fit, p = 5)$forecast
Computes a trendline for univariate time series data using singular spectrum analysis.
sst(y, l = "automatic", m = "automatic")sst(y, l = "automatic", m = "automatic")
y |
tsframe format data containing univariate time series data.
More appropriate method for multivariate time series is |
l |
window length; the string |
m |
number of leading eigentriples; the string |
Singular spectrum analysis decompose time series data (y)
into principal components, and a cumulative periodogram-based
criterion learn about elementary reconstructed components
(erc) that contribute to the signal. The trendline results
from adding principal components selected by a cumulative
periodogram-based criteria; see de Carvalho and Martos (2018,
Section 4.1). The plot method yields the resulting trendlines
along with the data; options for the plot method are give by
a list including the strings "trendline",
"components", "cpgram", and "screeplot",
along with a set of values (ncomp) indicating the components
on which these diagnostics are to be depicted (e.g. plot(fit,
options = list(type = "components", ncomp = 1:3)).
trendline |
tsframe object with trendline estimation from
targeted grouping based on a cumulative periodogram criterion (or
according to the number of components specified in |
l |
window length. |
m |
number of leading eigentriples. An automatic
criterion based on the cumulative periodogram of the residuals is
provided by default by using the string |
residuals |
tsframe object with the residuals from targeted
grouping based on a cumulative periodogram criterion (or according
to the number of components specified in |
svd |
Singular value decomposition corresponding to the trajectory matrix. |
erc |
elementary reconstructed components. |
observations |
tsframe object with the raw data. |
Gabriel Martos and Miguel de Carvalho
de Carvalho, M. and Martos, G. (2020). Brexit: Tracking and disentangling the sentiment towards leaving the EU. International Journal of Forecasting, 36, 1128–1137.
See msst for a version of the routine for multivariate
time series, and see msstc for a version of the routine
for multivariate time series of compositional data.
## BREXIT DATA EXAMPLE data(brexit); attach(brexit) l <- tsframe(date, brexit[, 1] / 100) # l = leave fit <- sst(l); fit$m; fit$l # Number of ERC and parameter l in the model. plot(fit, col = "red", lwd = 3, xlab = 'Time', ylab = 'Leave') points(date, brexit[, 1] / 100, pch = 20) ## Scree-plot plot(fit, options = list(type = "screeplot", ncomp = 1:10, series.names = c('Leave')), type = "b", pch = 20, lwd = 2) ## Plot cumulative periodogram par(mfrow=c(1,1), mar=c(4,2,1,1)) plot(fit, options = list(type = "cpgram", series.names = c('Leave')) ) ## Elementary Reconstructed Components (ERC) plot: plot(fit, options = list(type = "components", ncomp = 1:2))## BREXIT DATA EXAMPLE data(brexit); attach(brexit) l <- tsframe(date, brexit[, 1] / 100) # l = leave fit <- sst(l); fit$m; fit$l # Number of ERC and parameter l in the model. plot(fit, col = "red", lwd = 3, xlab = 'Time', ylab = 'Leave') points(date, brexit[, 1] / 100, pch = 20) ## Scree-plot plot(fit, options = list(type = "screeplot", ncomp = 1:10, series.names = c('Leave')), type = "b", pch = 20, lwd = 2) ## Plot cumulative periodogram par(mfrow=c(1,1), mar=c(4,2,1,1)) plot(fit, options = list(type = "cpgram", series.names = c('Leave')) ) ## Elementary Reconstructed Components (ERC) plot: plot(fit, options = list(type = "components", ncomp = 1:2))
The function tsframe creates a univariate time series
object to be used in combination with the functions in the package
ASSA.
tsframe(dates, y)tsframe(dates, y)
dates |
dates at which observations took place. |
y |
vector with time-series values sorted in ascendant way (first element in 'y' corresponds to the oldest value of the series and last element in 'y' corresponds to the newest value). |
data(brexit); attach(brexit) head(brexit, 3) y <- tsframe(date, y = brexit[, 1]) # data is print(y) # 'list' with 4 elements: dates, the series data, and serie length. plot(y, col = 'blue' , lwd = 2, lty = 1)data(brexit); attach(brexit) head(brexit, 3) y <- tsframe(date, y = brexit[, 1]) # data is print(y) # 'list' with 4 elements: dates, the series data, and serie length. plot(y, col = 'blue' , lwd = 2, lty = 1)