Momentum Scan

RSI(14), J. Welles Wilder Jr. (1978). Per-period gain and loss are magnitudes: g_t = max(C_t - C_{t-1}, 0) and l_t = max(C_{t-1} - C_t, 0). The seed is an arithmetic mean of the first 14 of each, which needs 15 closes: G_14 = (1/14) * sum(g_1..g_14), L_14 likewise. Thereafter each is smoothed RECURSIVELY and SEPARATELY: G_t = (13*G_{t-1} + g_t)/14, L_t = (13*L_{t-1} + l_t)/14. Then RS = G_t / L_t and RSI = 100 - 100/(1 + RS). Wilder's recursion is not a rolling arithmetic mean - substituting one gives a different, jumpier indicator, and it is the most common reimplementation error. Boundary cases matter: if L = 0 and G > 0 the ratio diverges and RSI is taken as 100; if G = 0 and L > 0, RSI is 0; if both are 0 - a completely flat window - the expression is 0/0 and there is no universal convention, so implementations differ. This analysis reads that window as 100, the same as gains with no losses, so a 100 beside a price that never moved records no movement rather than strength.

MACD(12,26,9), Gerald Appel (late 1970s); the histogram is Thomas Aspray's (1986) addition. MACD line = EMA(12) - EMA(26) of closes; signal line = EMA(9) of the MACD line; histogram = MACD line - signal line. EMA uses alpha = 2/(N+1). Initialisation differs between libraries (SMA seed versus first value), which changes early observations - a reproducibility trap when comparing implementations.

Bollinger Bands, John Bollinger (early 1980s): a 20-period SMA of closes with bands at +/- 2 standard deviations of those closes. This is the dispersion of price LEVELS over the window, not volatility in the financial sense, which is the dispersion of RETURNS and is usually annualised. The +/- 2 figure does not imply ~95% coverage - that would need IID normal observations with stable parameters, and prices are none of those. Whether the standard deviation uses divisor N or N-1 is an implementation choice that shifts the bands slightly.

SMA-20/50/200: unweighted means of the last N closes. 14, 12/26/9, 20/2 and 20/50/200 are CONVENTIONS inherited from practice, not optimised or theoretically derived. Longer windows lag more and respond less to any single observation; shorter windows respond more strongly to each new observation and may produce more frequent changes in the resulting label. That is a central trade-off, though not the only one - horizon, turnover, transaction costs and the multiple-testing problem all bear on parameter choice too.

The output label is a DETERMINISTIC HEURISTIC produced by a rules engine from these inputs. It is not a probability, an expected return, or four independent votes; read the run's published combination rule for the vote boundaries and how conflicting readings are resolved.

One implementation detail changes the mathematics: the most recent daily close is overridden with a 5-minute spot observation, mixing sampling conventions, which can make a reading non-reproducible or flip it intraday. And crypto trades continuously, so a 'daily' window inherited from equity markets does not carry the same calendar meaning.