isst {ASSA}

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 Also

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)
head(pred$forecast,3) # Forecasted interval data.

attributes(pred)
pred$coefficients[1:5] # linear recurrence parameters.
# End