Summary
RollingMedian is RTTA's streaming median of a fixed-length rolling window. For
odd-sized windows it returns the middle order statistic; for even-sized windows
it returns the average of the two central order statistics.
Update API
value = rtta.RollingMedian(window=14, fillna=True).update(value)
With fillna=False, output is NaN until the buffer is full. During warmup
with fillna=True, the median is computed over the samples seen so far.
Theory Of Operation
The median is a robust location estimator: a single spike does not move it as
much as it moves a mean. Streaming medians require order statistics of the
current window. RTTA copies the window into a scratch vector and uses
std::nth_element to find the central element(s) without a full sort.
Recurrence
Let \(x_t\) be the input and \(n\) the constructor window. Maintain a FIFO
buffer of capacity \(n\). After each push, let \(m\) be the current buffer size
and let \(\{y_1 \le \cdots \le y_m\}\) be the sorted buffer contents (conceptually).
(1-based order statistics). Implementation detail: for even \(m\), RTTA finds
the upper middle via nth_element at index \(m/2\), then finds the lower middle
at index \(m/2 - 1\), and averages them — equivalent to the formula above.
Implementation Notes
The recurrence is implemented in src/rtta/indicator.cpp in
class RollingMedian. Scratch storage is resized to the current buffer size
each update.