msstc {ASSA} | R Documentation |

## 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 |

`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 |

`vertical` |
logical; if |

### 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 |

`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 |

`svd` |
the Singular Value Decomposition of the trajectory matrix. |

`erc` |
list with elementary reconstructed components. |

`observations` |
mtsframe object with the observations |

### 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))
```

*ASSA*version 2.0 Index]