Unroll a stream-wise quantity back to the original time scale

After computing a per-stream cumulative quantity (e.g. e-process values), restores them to the original length T by zero-padding the first k - 1 positions, repeating each stream value h times, then truncating to length T.

Usage

unroll_stream(stream_vals, k, h, T_)

Arguments

stream_vals

Numeric vector. Values for stream k (length ~ T/h).

k

Integer. Stream index (1-based).

h

Integer. Lag.

T_

Integer. Total original sequence length.

Value

Numeric vector of length T_.

Alignment only, not theoretical updating

For lagged forecasts (h >= 2), the returned series is aligned to the evaluated score-difference index after stream splitting. It should not be interpreted as a process that updates at the original forecast-issuance time. The unrolled process is for visualization and alignment only; the theoretical validity argument relies strictly on the streamwise sub-filtrations, not on this unrolled representation.

Examples

unroll_stream(c(1, 2, 3), k = 2, h = 2, T_ = 6)
#> [1] 0 1 1 2 2 3