msst {ASSA} | R Documentation |

## Multivariate Singular Spectrum Trendlines

### Description

Computes trendlines for multivariate time series data using multivariate singular spectrum analysis.

### Usage

```
msst(y, l = "automatic", m = "automatic", vertical = TRUE)
```

### Arguments

`y` |
mtsframe object containing raw 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

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 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` |
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 `msstc`

for a similar routine yielding trendlines for
multivariate time series of compositional data.

### Examples

```
## SIMULATED EXAMPLE
t <- seq(0.05, 5, by = 0.05)
t2 <- seq(0.05, 6, by = 0.05)
p = length(t2)-length(t) # Forecasting horizon parameter:
n = length(t)
Y <- cbind(t^3 - 9 * t^2 + 23 * t + rnorm(n, 0, 1),
10 * sin(3 * t) / t + rnorm(n, 0, 1))
y <- mtsframe(dates = t, Y)
fit.vertical <- msst(y)
pred.vertical <- predict(fit.vertical, p = p)
print(pred.vertical$forecast)
## BREXIT DATA EXAMPLE
## (de Carvalho and Martos, 2018; Fig. 1)
data(brexit)
attach(brexit)
y <- mtsframe(date, brexit[, 1:3] / 100)
fit <- msst(y)
## Window length and components automatically selected
fit$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",
series.names = c('Leave','Stay','Undecided')) )
## Scree-plot
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
plot(fit, options = list(type = "components", ncomp = 1:2))
```

*ASSA*version 2.0 Index]