Counts N_ij of obligors in grade i at the first date and grade j
at the second, the row probabilities p_ij, the upper and lower matrix
weighted bandwidths
$$MWB_{up} = \frac{\sum_{i<j} |i-j|\, N_i\, p_{ij}}{\sum_i \max(|i-K|, |i-1|)\, N_i \sum_{j>i} p_{ij}},$$
(and the mirror image for downgrades), the z statistic of every
off-diagonal cell against its neighbor closer to the diagonal (a
significantly positive value means the probability does not decay away
from the diagonal) and the mobility summary. Values of grade_t1
outside 1..K count as default, NA as closed; both stay out of
the bandwidths.
Value
An object of class scr_migration: matrix (counts, K rows,
K + 2 columns), p (row probabilities), n (row totals),
mwb_upper, mwb_lower, z (K x K), n_significant (cells with
z > 1.645), mobility (share_stable, share_up, share_down,
mean_distance, share_default, share_closed).
Also K, the number of grades.
Examples
set.seed(2)
g0 <- sample(1:5, 500, TRUE)
g1 <- pmin(5, pmax(1, g0 + sample(c(-1, 0, 0, 0, 1), 500, TRUE)))
g1[sample(500, 10)] <- NA
scr_migration(g0, g1, K = 5)
#> <scr_migration> 5 grades | 500 obligors | stable 69.4% | up 17.6% | down 13.1% | default 0.0% | closed 2.0%
#> MWB upper 0.3308 | MWB lower 0.3422 | mean distance 0.306 | 0 cell(s) not decaying from the diagonal (z > 1.645)
#> from 1 2 3 4 5 default closed
#> 1 73.3% 22.8% 0.0% 0.0% 0.0% 0.0% 4.0%
#> 2 10.5% 64.2% 24.2% 0.0% 0.0% 0.0% 1.1%
#> 3 0.0% 22.9% 53.1% 21.9% 0.0% 0.0% 2.1%
#> 4 0.0% 0.0% 15.3% 62.2% 19.4% 0.0% 3.1%
#> 5 0.0% 0.0% 0.0% 15.5% 84.5% 0.0% 0.0%