msstc {ASSA}

Multivariate Singular Spectrum Trendlines for Compositional Data

Description

Computes trendlines on the unit simplex for multivariate time series data using multivariate singular spectrum analysis.

Usage

msstc(y, l = 'automatic', m = 'automatic', vertical = TRUE)

Arguments

y

mtsframe object containing 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

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.

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 msst for a similar routine yielding trendlines for multivariate time series, but which does not project the pointwise estimates to the unit simplex.

Examples

## 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))