Technical indicators

Market indicators: trend, momentum, bands, volume, and returns.

Trend

Direction and trend-following: trend-tracking averages, slope fits, ADX, and channels.

Function	Description
Average Directional Index (ADX)	Wilder's ADX with +DI and -DI (3 inputs -> 3 outputs).
Online Bayesian univariate regression (2->4 posterior fit)	Causal one-step-ahead predictive mean and std plus current slope and intercept via Normal-Inverse-Gamma posterior.
Double Exponential MA (DEMA)	Mulloy's Double EMA: 2*EMA - EMA(EMA).
Detrend	x[t] minus its rolling mean.
Donchian Channels	Trend-following envelope: rolling max(high), rolling min(low), and midline.
Expanding slope	Running OLS slope of the series against time over the whole history.
Hull MA	Hull's responsive MA: WMA(2*WMA(n/2) - WMA(n), sqrt(n)).
Kaufman Adaptive MA (KAMA)	Adaptive MA whose smoothing constant responds to the efficiency ratio.
MACD	MACD line, signal line, and histogram (3 outputs).
Rolling Hurst Exponent	Rolling-window Hurst exponent via Anis-Lloyd corrected rescaled-range analysis.
Rolling linear regression (2->4 OLS fit)	Full OLS fit returning (slope, intercept, r_squared, stderr).
Rolling 1st-order polynomial fit	OLS fit y = a + b*t over a trailing window. derivative_order selects value/slope/zero.
Rolling 2nd-order polynomial fit	OLS fit y = a + b*t + c*t^2 over a trailing window.
Rolling Time-Series Forecast (TSF)	Linear regression of y on time, projected one step ahead. TA-Lib's TSF.
Triple Exponential MA (TEMA)	Mulloy's Triple EMA: 3*EMA - 3*EMA(EMA) + EMA(EMA(EMA)).
TRIX (rate of change of triple EMA)	ROC of a triple-smoothed EMA.

Momentum & oscillators

Rate-of-change and overbought/oversold indicators.

Function	Description
Chaikin A/D Oscillator (ADOSC)	Difference of fast and slow EMA of the Accumulation/Distribution line.
Average Directional Index (ADX)	Wilder's ADX with +DI and -DI (3 inputs -> 3 outputs).
Balance of Power (BOP)	(close - open) / (high - low) per bar. No smoothing.
Commodity Channel Index (CCI)	Commodity Channel Index over typical price.
MACD	MACD line, signal line, and histogram (3 outputs).
Money Flow Index (MFI)	Volume-weighted analogue of RSI on the typical price.
Momentum	x[t] - x[t-k], TA-Lib's MOM. Mathematically identical to Diff(k).
Rate of change (ROC)	100 * (x[t] / x[t-k] - 1) - TA-Lib's ROC.
Rolling RSI	Relative Strength Index. Wilder's smoothing by default; Cutler's via method='cutler'.
Stochastic Oscillator	Stochastic oscillator %K and %D (3 inputs -> 2 outputs).
Stochastic RSI	Stochastic applied to RSI (1 input -> 2 outputs).
TRIX (rate of change of triple EMA)	ROC of a triple-smoothed EMA.
Ultimate Oscillator	Three-period weighted oscillator (Williams, 1976).
Williams %R	Inverse stochastic oscillator in [-100, 0].

Bands & channels

Envelopes around price.

Function	Description
Bollinger Bands	Mean +/- num_std rolling standard deviations.
Donchian Channels	Trend-following envelope: rolling max(high), rolling min(low), and midline.
Keltner Channels	Volatility-adapted envelope: EMA midline plus/minus a multiple of ATR.

Volume

Volume-based indicators.

Function	Description
Accumulation/Distribution Line (Chaikin)	Chaikin Accumulation/Distribution Line.
Chaikin A/D Oscillator (ADOSC)	Difference of fast and slow EMA of the Accumulation/Distribution line.
Money Flow Index (MFI)	Volume-weighted analogue of RSI on the typical price.
On-Balance Volume (OBV)	On-Balance Volume: signed cumulative volume by close-direction (Granville, 1963).
Rolling VWAP	Rolling volume-weighted average price (typical-price weighted).

Returns & changes

Differences, returns, rates of change, and lags.

Function	Description
Discrete difference	x[t] - x[t-k] (first difference at lag k).
Second difference	Second-order finite difference (discrete second derivative).
Lag (delay)	Output is the input delayed by k samples.
Log return	log(x[t] / x[t-k]) - log return at lag k.
Momentum	x[t] - x[t-k], TA-Lib's MOM. Mathematically identical to Diff(k).
Simple return	(x[t] - x[t-k]) / x[t-k] - the simple percentage return at lag k.
Rate of change (ROC)	100 * (x[t] / x[t-k] - 1) - TA-Lib's ROC.
Rate of change percent (ROCP)	x[t] / x[t-k] - 1 - TA-Lib's ROCP. Identical to Return.
Rate of change ratio (ROCR)	x[t] / x[t-k] - TA-Lib's ROCR.