Asks whether a series moved to a new level, and where. The step scan
takes every split after period k with at least minseg periods on
each side, and the largest between-segment sum of squares \(T_k = k
(n - k) / n (\bar y_a - \bar y_b)^2\); its p-value comes from the same
maximum over reorderings of the series (every ordering when n! is at
most nperm, giving an exact p-value; otherwise nperm random ones,
(1 + #{T* >= T}) / (1 + nperm)), so it is a test of a step anywhere,
not of the best split alone. Pettitt's rank test takes the split with
the largest \(|U_t|\), \(U_t = \sum_{i \le t < j} sign(y_j -
y_i)\), with its approximate p-value \(2 \exp(-6 K^2 / (n^3 + n^2))\).
Both assume exchangeable periods under no change: a steady trend can
read as a step.
Arguments
- y
The series, in period order: finite numbers.
- x
NULL, or the periods (any vector, one per value):atthen names the last period before each change.- minseg
The fewest periods on either side of a step: one whole number from 1.
- nperm
The reorderings of the step scan's null: one whole number from 1.
- seed
NULLto draw the seed from R's generator, or one whole number from 0.
Value
An object of class stpcp, a list: tab, one row for each
test (test, k, the last period before the change, the means
before and after, the statistic stat (T or K) and p, with at
from x); nperm, the orderings used; exact; and n.
References
Pettitt, A. N. (1979). A non-parametric approach to the change-point problem. Journal of the Royal Statistical Society, Series C, 28(2), 126-135. doi:10.2307/2346729
Examples
stpcp(c(100, 104, 98, 60, 63, 58), x = 2018:2023)
#> stpcp: 6 periods; step p-value exact over 720 orderings
#> test k before after stat p at
#> step 3 100.6667 60.33333 2440.167 0.1000000 2020
#> pettitt 3 100.6667 60.33333 9.000 0.2907114 2020
stpcp(c(100, 104, 98, 101, 97, 60, 63, 58, 61, 59), nperm = 999, seed = 1)
#> stpcp: 10 periods; step p-value from 999 orderings
#> test k before after stat p
#> step 5 100 60.2 3960.1 0.0100000
#> pettitt 5 100 60.2 25.0 0.0661425