rangemean_tstat: Range-Mean Regression

In palatej/rjd3toolkit: Utility Functions around 'JDemetra+ 3.0'

Range-Mean Regression

Description

Function to perform a range-mean regression, trimmed to avoid outlier distortion. The can be used to select whether the original series will be transformed into log or maintain in level.

Usage

rangemean_tstat(data, period = 0, groupsize = 0, trim = 0)

Arguments

data	data to test.
period	periodicity of the data.
groupsize	number of observations per group (before being trimmed). The default group size (groupsize = 0) is computed as followed: if period = 12 or period = 6, it is equal to 12; if period = 4 it is equal to 12 if the data has at least 166 observations, 8 otherwise; if period = 3 or period = 2 it is equal to 12 if the data has at least 166 observations, 6 otherwise; if period = 1 it is equal to 9 if the data has at least 166 observations, 5 otherwise; it is equal to period otherwise.
trim	number of trimmed observations.

Details

First, the data is divided into n groups of successive observations of length l (groupsize). That is, the first group is formed with the first l observations, the second group is formed with observations 1+l to 2l, etc. Then, for each group i, the observations are sorted and the trim smallest and largest observations are rejected (to avoid outlier distortion). With the other observations, the range (noted y_i) and mean (noted m_i) are computed.

Finally, the following regression is performed :

y_t = \alpha + \beta m_t + u_t.

The function rangemean_tstat returns the T-statistic associated to \beta. If it is significantly higher than 0, log transformation is recommended.

Value

T-Stat of the slope of the range-mean regression.

Examples

y <- ABS$X0.2.09.10.M
# Multiplicative pattern
plot(y)
period <- 12
rm_t <- rangemean_tstat(y, period = period, groupsize = period)
rm_t # higher than 0
# Can be tested:
pt(rm_t, period - 2, lower.tail = FALSE)
# Or :
1 - cdf_t(period - 2, rm_t)

# Close to 0
rm_t_log <- rangemean_tstat(log(y), period = period, groupsize = period)
rm_t_log
pt(rm_t_log, period - 2, lower.tail = FALSE)

palatej/rjd3toolkit documentation built on Oct. 30, 2024, 10:46 p.m.