Range-Mean Regression — rangemean

Function to perform a range-mean regression, trimmed to avoid outlier distortion. The slope is used in TRAMO 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.

Value

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

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.

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
#> [1] 32.41607
# Can be tested:
pt(rm_t, period - 2, lower.tail = FALSE)
#> [1] 9.196296e-12
# Or :
1-cdf_t(period-2, rm_t)
#> [1] 9.19631e-12

# Close to 0
rm_t_log = rangemean_tstat(log(y), period = period, groupsize = period)
rm_t_log
#> [1] 0.5946804
pt(rm_t_log, period - 2, lower.tail = FALSE)
#> [1] 0.2826345