addSeason2formula | R Documentation |

This function helps to construct a `formula`

object that
can be used in a call to `hhh4`

to model
seasonal variation via a sum of sine and cosine terms.

```
addSeason2formula(f = ~1, S = 1, period = 52, timevar = "t")
```

`f` |
formula that the seasonal terms should be added to,
defaults to an intercept |

`S` |
number of sine and cosine terms. If |

`period` |
period of the season, defaults to 52 for weekly data. |

`timevar` |
the time variable in the model. Defaults to |

The function adds the seasonal terms

```
\sin( s \cdot 2\pi \cdot \code{timevar}/\code{period} ),\;
\cos( s \cdot 2\pi \cdot \code{timevar}/\code{period} ),
```

for `s = 1,\dots,\code{S}`

to an existing formula `f`

.

Note the following equivalence when interpreting the coefficients of the seasonal terms:

```
\gamma \sin(\omega t) + \delta \cos(\omega t) =
A \sin(\omega t + \epsilon)
```

with amplitude `A = \sqrt{\gamma^2 + \delta^2}`

and phase shift `\epsilon = \arctan(\delta / \gamma)`

.
The amplitude and phase shift can be obtained from a fitted
`hhh4`

model via `coef(..., amplitudeShift = TRUE)`

,
see `coef.hhh4`

.

Returns a `formula`

with the seasonal terms added and
its environment set to `.GlobalEnv`

.
Note that to use the resulting formula in `hhh4`

,
a time variable named as specified by the argument `timevar`

must
be available.

M. Paul, with contributions by S. Meyer

`hhh4`

, `fe`

, `ri`

```
# add 2 sine/cosine terms to a model with intercept and linear trend
addSeason2formula(f = ~ 1 + t, S = 2)
# the same for monthly data
addSeason2formula(f = ~ 1 + t, S = 2, period = 12)
# different number of seasons for a bivariate time series
addSeason2formula(f = ~ 1, S = c(3, 1), period = 52)
```

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