fix(outliers): spikes and dips in one segment no longer mask each other

[dgnaglo]

Problem

With preprocessing: {"outliers": true}, several spikes or dips in the same series mask each other. Seen on agent-dev (engine 0.1.5) with 24 months of trend (100 -> 184), spikes at 950 and 900 and a dip at 5: only the 900 was corrected, and it was brought to 212 while the trend is at ~169 there.

outliers_detection(method_ls = "cpt") tests |x - mean| > 3 sd inside each changepoint segment, with the mean and sd computed with the spikes in them. Recomputed on that series (cut at 11): segment 1-11 has sd 257, so 950 sits at 2.99 sd and 5 at 0.69 sd; segment 11-24 catches 900 at 3.46 sd and replaces it with the segment mean, 212.4 (the API returned 212).

Fix

• Inside each segment, a point is an outlier when it is more than 3 sd from the segment mean (unchanged rule), or more than 5 sd from the mean of the other points, sd of the other points too, the farthest point first, until none is left (.segment_outliers()). Leave-one-out scores are computed in O(n) per pass (.deleted_z()), so long segments stay cheap.
• Outliers are replaced by a linear interpolation of their non-outlier neighbours, instead of the segment mean, which the spike pulled up and which ignored the trend.
• docs/API.md and NEWS.md updated. .merge_short_segments() is unchanged.

On the series above: 3 corrections, 950 -> 114, 5 -> 132, 900 -> 166.

Bench

timetk::m4_monthly, defects injected at random positions, 100 draws per case, same script and seed before/after (absolute numbers differ from #26's table, which used another script; the deltas are comparable). "corrected" = the point ends up at less than half of its injected deviation from the true value; "error" = median |corrected - true| / true over corrected points; "other changed" = points changed that were not injected, per series. multi = a x3 spike, a -80 % dip and a x2 spike in the same series.

Window	Case	Corrected before	Corrected after	Error before	Error after	Other changed before	Other changed after
36 months	spike x3	93 %	95 %	11.6 %	6.4 %	0.03	0.08
36 months	spike x2	75 %	82 %	8.9 %	4.2 %	0.02	0.06
36 months	dip -80 %	73 %	76 %	5.7 %	4.9 %	0.04	0.05
36 months	multi	43 %	63 %	11.3 %	3.6 %	0.01	0.06
36 months	clean series					0.04	0.07
60 months	spike x3	91 %	95 %	10.8 %	3.6 %	0.06	0.11
60 months	spike x2	82 %	86 %	7.3 %	5.1 %	0.06	0.07
60 months	dip -80 %	78 %	79 %	7.7 %	4.3 %	0.07	0.08
60 months	multi	52 %	69 %	8.2 %	5.3 %	0.05	0.07
60 months	clean series					0.11	0.12
full series	spike x3	97 %	97 %	11.2 %	4.5 %	0.83	1.07
full series	spike x2	79 %	80 %	10.9 %	4.5 %	0.90	1.18
full series	dip -80 %	78 %	79 %	9.0 %	6.1 %	0.90	1.14
full series	multi	78 %	83 %	9.5 %	6.0 %	0.73	1.02
full series	clean series					0.95	1.20

Detection never goes down; false corrections go up by 0.03 per clean 36-month series and 0.25 per full series.

Variants tried and dropped (same bench):

• robust STL + super smoother residuals, 3 IQR (the forecast::tsoutliers() approach, base stats only): 1.36 false corrections per clean 36-month series;
• leave-one-out only, without the 3 sd rule: at 3 sd, 1.2 false corrections per series; at 5 sd, below the current rule on single spikes and dips (73 % / 69 % vs 75 % / 73 %); at 6 sd and above, the multi gain is gone.
• The 5 sd threshold of the combined rule: 4 sd doubles false corrections (0.18 per clean 36-month series), 6 sd loses 7 points on multi.

Tests

• tests/testthat/test-outliers-spikes.R: the 24-month series above (3 points changed, replacements close to the neighbours), the API report lists the 3 dates, and .deleted_z() matches a direct leave-one-out computation. Against main (0.1.5 image, pkgload::load_all()): 7 failures/errors; after: all pass.
• Full suite against this branch installed in a private library of the apowerb/th2forecast:0.1.5 image, as CI tests the installed package: test_dir(..., stop_on_failure = TRUE) exit 0.

Not changed

• The trend is still not removed before the test (a spike smaller than the seasonal swing can still be missed; anomalies is the step for that).
• preprocessing_data() also calls outliers_detection(method_ls = "cpt") and gets the same new behaviour.