EN
L 276/54
Official Journal of the European Union
26.10.2022
(c) they shall calculate the Spearman correlation coefficient in accordance with the following formula: rs ¼
covðRHPL ,RRTPL Þ σRHPL •σRRTPL
Where: RHPL =
the time series of ranks produced from the time series of hypothetical changes referred to in point (b);
RRTPL =
the time series of ranks produced from the time series of theoretical changes referred to in point (b);
σRHPL =
the standard deviation of the time series of ranks RHPL calculated in accordance with paragraph 3, point (a);
σRRTPL =
the standard deviation of the time series of ranks RRTPL calculated in accordance with paragraph 3, point (b);
cov (RHPL, RRTPL) =
the covariance calculated in accordance with paragraph 3, point (c), between the times series of ranks RHPL and RRTPL.
2.
Institutions shall produce the time series of ranks referred to in paragraph 1, point (b), from an originating time series by performing the following steps in the following order: (a) for each observation within the originating time series, institutions shall count the number of observations with a lower value than that observation within that time series; (b) institutions shall label each observation with the number resulting from the calculation set out in point (a) increased by one; (c) where, as a result of the labelling in accordance with point (b), two or more observations are labelled with the same number, institutions shall in addition increase the numbers of those labels with the following fraction: ðN – 1Þ 2 where N equals the quantity of the labels with the same number; (d) institutions shall consider as time series of ranks, the time series of the labels obtained in accordance with points (b) and (c). 3.
Institutions shall calculate the standard deviation of the time series of ranks RHPL in accordance with the formula laid down in point (a), the standard deviation of the time series of ranks RRTPL in accordance with the formula laid down in point (b), and the covariance between those time series in accordance with the formula laid down in point (c) as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 250 ∑i1⁄41 ðRHPLi – μRHPL Þ2 (a) σRHPL 1⁄4 ; 249 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 250 ∑i1⁄41 ðRRTPLi – μRRTPL Þ2 (b) σRRTPL 1⁄4 ; 249 250
(c) cov ðRHPL ,RRTPL Þ ¼
∑i¼1 ðRHPL  – μR i
Þ•ðRRTPLi  – μRRTPL Þ ; 249 HPL
Where: i=
the index that denotes the observation in the time series of ranks;
RHPL i =
the ‘i-th’ observation of the time series of ranks RHPL;
μRHPL =
the mean of the time series of ranks RHPL;
RRTPLi =
the ‘i-th’ observation of the time series of ranks RRTPL;
μRRTPL =
the mean of the time series of ranks RRTPL.