msst {ASSA}

Multivariate Singular Spectrum Trendlines

Description

Computes trendlines for multivariate time series data using multivariate singular spectrum analysis.

Usage

msst(y, l = "automatic", m = "automatic", vertical = TRUE)

Arguments

y

mtsframe object containing raw data.

l

window length; the string "automatic" sets the default option
l = ceiling((y$n + 1) / y$D) for vertical and ceiling(y$D * (y$n + 1) / (y$D + 1)) in the case of horizontal binding.

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 "automatic", see details.

vertical

logical; if TRUE the trajectory matrices are stacked vertically, otherwise the bind is horizontal.

Details

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.

Value

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 m).

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 m).

svd

the Singular Value Decomposition of the trajectory matrix.

erc

list with elementary reconstructed components.

observations

mtsframe object with the observations y.

Author(s)

Gabriel Martos and Miguel de Carvalho

References

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 Also

See msstc for a similar routine yielding trendlines for multivariate time series of compositional data.

Examples

## 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))