sst {ASSA} R Documentation

## Singular Spectrum Trendline

### Description

Computes a trendline for univariate time series data using singular spectrum analysis.

### Usage

```sst(y, l = "automatic", m = "automatic")
```

### Arguments

 `y` tsframe format data containing univariate time series data. More appropriate method for multivariate time series is `msst`. `l` window length; the string `"automatic"` automatic sets the default option `l = ceiling(y\$n + 1) / 2`. `m` number of leading eigentriples; the string `"automatic"` yields an automatic criterion for choosing m based on the cumulative periodogram of the residuals; see details.

### Details

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))```.

### Value

 `trendline` tsframe object with trendline estimation from targeted grouping based on a cumulative periodogram criterion (or according to the number of components specified in `m`). `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 `"automatic"`. `residuals` tsframe object with the residuals from targeted grouping based on a cumulative periodogram criterion (or according to the number of components specified in `m`). `svd` Singular value decomposition corresponding to the trajectory matrix. `erc` elementary reconstructed components. `observations` tsframe object with the raw data.

### 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 `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.

### Examples

```## 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))
```

[Package ASSA version 2.0 Index]