Author: Ivan Svetunkov
Date: 2025-02-03

# legion: Forecasting Using Multivariate Models

#### Ivan Svetunkov

#### 2025-02-03

This vignette explains how to use functions in `legion` package, what they produce, what each field in outputs and what returned values mean.

The package includes the following functions:

1. ves() - Vector Exponential Smoothing;
2. vets() - Vector ETS with PIC taxonomy;
3. oves() - Occurrence part of the vector ETS model.

## Methods for the class `legion`

There are several methods that can be used together with the forecasting functions of the package. When a model is saved to some object `ourModel`, these function will do some magic. Here’s the list of all the available methods with brief explanations:

1. `print(ourModel)` – function prints brief output with explanation of what was fitted, with what parameters, errors etc;
2. `summary(ourModel)` – alias for `print(ourModel)`;
3. `actuals(ourModel)` – returns actual values;
4. `fitted(ourModel)` – fitted values of the model;
5. `residuals(ourModel)` – residuals of constructed model;
6. `AIC(ourModel)`, `BIC(ourModel)`, `AICc(ourModel)` and `BICc(ourModel)` – information criteria of the constructed model. `AICc()` and `BICc()` functions are not standard `stats` functions and are imported from `greybox` package and modified in `legion` for the specific models;
7. `plot(ourModel)` – produces plots for the diagnostics of the constructed model. There are 9 options of what to produce, see `?plot.legion()` for more details. Prepare the canvas via `par(mfcol=...)` before using this function otherwise the plotting might take time.
8. `forecast(ourModel)` – point and interval forecasts;
9. `plot(forecast(ourModel))` – produces graph with actuals, forecast, fitted and prediction interval using `graphmaker()` function from `greybox` package.
10. `simulate(ourModel)` – produces data simulated from provided model. Only works for `ves()`for now;
11. `logLik(ourModel)` – returns log-likelihood of the model;
12. `nobs(ourModel)` – returns number of observations in-sample we had;
13. `nparam(ourModel)` – number of estimated parameters (originally from `greybox` package);
14. `nvariate(ourModel)` – number of variates, time series in the model (originally from `greybox` package);
15. `sigma(ourModel)` – covariance matrix of the residuals of the model;
16. `modelType(ourModel)` – returns the type of the model. Returns something like “MMM” for ETS(MMM). Can be used with `ves()` and `vets()`. In the latter case can also accept `pic=TRUE`, returning the PIC restrictions;
17. `errorType(ourModel)` – the type of the error of a model (additive or multiplicative);
18. `coef(ourModel)` – returns the vector of all the estimated coefficients of the model;