isst {ASSA} R Documentation

## Interval Singular Spectrum Trendlines

### Description

Computes the trendline estimation for interval time series data using singular spectrum analysis.

### Usage

```isst(y, l= 'automatic' , m = 'automatic')
```

### Arguments

 `y` `itsmframe` data corresponding to univariate interval time series data. `l` window length; the string `'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` itsframe object with interval 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` itsframe 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` itsframe object with the raw data.

### References

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.

### Examples

```# 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)