misst {ASSA} R Documentation

## Multivariate Interval Singular Spectrum Trendlines

### Description

Computes a trendline for multivariate interval data using singular spectrum analysis.

### Usage

```misst(y, l= 'automatic' , m = 'automatic', vertical = TRUE)
```

### Arguments

 `y` object of class `mitsframe` (multivariate interval time series data). `l` window length; the string `"automatic"` sets the default option `l = ceiling(y\$n + 1) / (y\$D+1)` for `vertical` and `ceiling(D * (y\$n + 1) / (y\$D + 1))`. `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"`. `vertical` logical; if `TRUE` the trajectory matrices are stacked vertically, otherwise the bind is horizontal.

### Details

Multivariate singular spectrum analysis is used to decompose interval 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` mitsframe object with interval 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` mitsframe object with the interval 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` mitsframe object with the raw data `y`.

### References

de Carvalho, M. and Martos, G. (2020). Modeling Interval Trendlines: Symbolic Singular Spectrum Analysis for Interval Time Series. Submitted (available on arXiv).

See `msst` for a similar routine yielding trendlines for standard multivariate time series of data.

### Examples

```muX.a = function(t){ 8 + t + sin(pi*t) }    ;    muX.b = function(t){ muX.a(t) + 2 }
muY.a = function(t){sqrt(t) + cos(pi*t/2) }    ;  muY.b = function(t){ 2*muY.a(t) + 2 }
N = 100; t=seq(0.1,2*pi,length = N);
set.seed(1)
e.x = rnorm(100); e.y = rnorm(100);
a.X = muX.a(t) + e.x; b.X = a.X + 2
a.Y = muY.a(t) + e.y        ; b.Y = 2*a.Y + 2

A <- cbind(a.X, a.Y); B <- cbind(b.X, b.Y)
y <- mitsframe(dates=t, A=A, B = B)

fit <- misst(y)
fit\$l;
fit\$m;
fit\$vertical

# Estimated trendlines:

## Estimated interval trendlines
plot(fit)

## Scree-plot
plot(fit, options = list(type = "screeplots"))

## Per
plot(fit, options = list(type = "cpgrams"))

## ERC
plot(fit, options=list(type='components',ncomp=1:3))

##################################
### Forecasting with misst     ###
##################################
pred = predict(fit, p = 5)
pred\$forecasts # Forecast organized in an array.
# End
```

[Package ASSA version 2.0 Index]