Generating Outlier regressors

Usage

ao_variable(frequency, start, length, s, pos, date = NULL)

tc_variable(frequency, start, length, s, pos, date = NULL, rate = 0.7)

ls_variable(frequency, start, length, s, pos, date = NULL, zeroended = TRUE)

so_variable(frequency, start, length, s, pos, date = NULL, zeroended = TRUE)

Arguments

frequency: Frequency of the series, number of periods per year (12,4,3,2..)
start, length: First date (array with the first year and the first period) (for instance c(1980, 1)) and number of periods of the output variables. Can also be provided with the s argument
s: time series used to get the dates for the trading days variables. If supplied the parameters frequency, start and length are ignored.
pos, date: the date of the outlier, defined by the position in period compared to the first date (pos parameter) or by a specific date defined in the format "YYYY-MM-DD".
rate: the decay rate of the transitory change regressor (see details).
zeroended: Boolean indicating if the regressor should end by 0 (zeroended = TRUE, default) or 1 (zeroended = FALSE), argument valid only for LS and SO.

Details

An additive outlier (AO, ao_variable) is defined as: $$AO_t = \begin{cases}1 &\text{if } t=t_0 \\ 0 & \text{if }t\ne t_0\end{cases}$$

A level shift (LS, ls_variable) is defined as (if zeroended = TRUE): $$LS_t = \begin{cases}-1 &\text{if } t < t_0 \\ 0 & \text{if }t\geq t_0 \end{cases}$$ A transitory change (TC, tc_variable) is defined as: $$TC_t = \begin{cases} 0 &\text{if }t < t_0 \\ \alpha^{t-t_0} & t\geq t_0 \end{cases}$$ A seasonal outlier (SO, so_variable) is defined as (if zeroended = TRUE): $$SO_t = \begin{cases} 0 &\text{if }t\geq t_0 \\ -1 & \text{if }t < t_0 \text{ and $t$ same periode as }t_0\\ -\frac{1}{s-1} & \text{otherwise }\end{cases}$$

Examples

# Outliers in February 2002
ao <- ao_variable(12, c(2000, 1), length = 12 * 4, date = "2002-02-01")
ls <- ls_variable(12, c(2000, 1), length = 12 * 4, date = "2002-02-01")
tc <- tc_variable(12, c(2000, 1), length = 12 * 4, date = "2002-02-01")
so <- so_variable(12, c(2000, 1), length = 12 * 4, date = "2002-02-01")
plot.ts(ts.union(ao, ls, tc, so),
    plot.type = "single",
    col = c("black", "orange", "green", "gray")
)