`fourier`

returns a matrix containing terms from a Fourier series, up
to order `K`

, suitable for use in `Arima`

,
`auto.arima`

, or `tslm`

.

```
fourier(x, K, h = NULL)
fourierf(x, K, h)
```

- x
Seasonal time series: a

`ts`

or a`msts`

object- K
Maximum order(s) of Fourier terms

- h
Number of periods ahead to forecast (optional)

Numerical matrix.

`fourierf`

is deprecated, instead use the `h`

argument in
`fourier`

.

The period of the Fourier terms is determined from the time series
characteristics of `x`

. When `h`

is missing, the length of
`x`

also determines the number of rows for the matrix returned by
`fourier`

. Otherwise, the value of `h`

determines the number of
rows for the matrix returned by `fourier`

, typically used for
forecasting. The values within `x`

are not used.

Typical use would omit `h`

when generating Fourier terms for training a model
and include `h`

when generating Fourier terms for forecasting.

When `x`

is a `ts`

object, the value of `K`

should be an
integer and specifies the number of sine and cosine terms to return. Thus,
the matrix returned has `2*K`

columns.

When `x`

is a `msts`

object, then `K`

should be a vector of
integers specifying the number of sine and cosine terms for each of the
seasonal periods. Then the matrix returned will have `2*sum(K)`

columns.

```
library(ggplot2)
# Using Fourier series for a "ts" object
# K is chosen to minimize the AICc
deaths.model <- auto.arima(USAccDeaths, xreg=fourier(USAccDeaths,K=5), seasonal=FALSE)
deaths.fcast <- forecast(deaths.model, xreg=fourier(USAccDeaths, K=5, h=36))
autoplot(deaths.fcast) + xlab("Year")
# Using Fourier series for a "msts" object
taylor.lm <- tslm(taylor ~ fourier(taylor, K = c(3, 3)))
taylor.fcast <- forecast(taylor.lm,
data.frame(fourier(taylor, K = c(3, 3), h = 270)))
autoplot(taylor.fcast)
```