Function forceIndex

Elder's Force Index — how hard a move was pushed, as the bar's price change times the volume behind it, smoothed with an EMA:

rawForce[i] = (close[i] − close[i−1]) · volume[i]
force       = EMA(rawForce, period)                       Elder's 13
Copy

Elder's three elements in one number: direction (the sign of the change), extent (its size) and volume. Read against its zero line and for divergence; the 2-bar version is the short-term trading signal and the 13-bar the trend one, which is why period is a knob and not a constant.

period: 1 is the raw force — an EMA of span 1 has α = 1, so it is its own input, bar for bar. That is the unsmoothed series Elder defines first, available without a second study or a smooth: false flag.

Appends one column. The EMA is the K2 engine's array door (movingAverageValues with 'ema') — pond's first-sample seed, the same average ema and elderRay use — so the study owns only the per-bar derivation.

Why no maType

Elder names the EMA, and the elderRay precedent applies: an option whose other nine settings nobody publishes is a speculative knob. A caller who wants a different smoothing has forceIndex({ period: 1, output: 'raw' }) followed by movingAverage({ column: 'raw', … }), which is the composition the package is built for.

Definition, verified

TA-Lib has no Force Index, so the oracle is a pandas replication on pond's EMA seed at period 13 and 2, with the analytic first valid bar (period, not period − 1 — see below) asserted, and separated from a version that drops the volume factor so the weighting is pinned.

Edges

• Warm-up is period rows. The raw force needs a previous close, so bar 0 has none, and the EMA's array door waits for period finite values — one more row than a study whose input is defined from bar 0. Length-preserving.
• A leading gap shifts the seed rather than emptying the column (the array door steps over a non-finite head), so the study runs over another study's output.
• An interior gap costs two bars, then the EMA carries on — the bar itself and the next (whose change reads the missing close). The EMA recursion skips a missing input rather than propagating it, which is the ema-family rule; it is deliberately not the running-sum rule obv and priceVolumeTrend follow, because an average has a local answer where a level does not.
• A missing volume costs one bar — its own.
• Linear in volume and linear in price (an absolute quantity in price × share units, the atr side of the scale pair, not the rsi side), and shift-invariant in price — adding a constant to every close leaves the differences alone. All pinned by property tests.