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)

Arguments

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)

Value

Numerical matrix.

Details

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.

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.

See also

seasonaldummy

Examples

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)