Auto-Stabilization

Part of TA-Lib's specification, a reference for AI-agent-driven integration.

Auto-Stabilization is off by default: every unstable period starts at 0, so a caller that never sets an Auto level can skip this page.

An Auto level sets the unstable period by precision instead of by bars: for each function, TA-Lib computes from the call's parameters how many leading bars to discard to reach a target number of significant digits (rZ1, target). It is set like any unstable period and changes no signature: the bars it discards show in the lookback (rL6). How to set a level: Unstable Period. Accepted values: rT3.

The caller must

• Read the bars a level adds from the lookback call, never from the table below (ask). Validate against the release you ship (pin).
• Compare values from different starts with a tolerance, under a level too. Allow the level's digits (target), not 1e-9 (rD3).
• Check the known exceptions for the functions you use.

Bars a level adds

How a level works. A function with an unstable period seeds its state from its first bars, so its values depend on where the series starts until that seed has faded. A level discards those leading bars (rL6): under PREC_4, ATR(14) starts 135 bars later.

rZ1 Under an Auto level, the function that owns an id adds the count of its row to its lookback. Each row is integer arithmetic, except SWAK_BP and MAMA: theirs is the double expression as written, rounded up. X is the level's digit count and K the exponent of its bound: a proof row leaves at most e^-K of the seed's weight in the function's state, for any input. PREC_4 is X = 4, K = 10; PREC_8 is X = 8, K = 19. n is the function's period, isqrt the integer square root, E(n) = ceil(K*n/2), W(n) = ceil(K*(2*n-1)/2) and H = 80 + 50*X.

Id	Bars added	Sized by
EMA	E(n)	proof
RMA, ATR, PLUS_DM, MINUS_DM	W(n)	proof
NATR, RSI, CMO, PLUS_DI, MINUS_DI, DX, RVI	K*n	proof, ratio
ADX	(K+6)*n	proof, ratio
HA	ceil(13*K/9)	proof
SWAK_HP	ceil(K*n/6)	proof
SWAK_GAUSS, SWAK_BUTTER, SWAK_2PHP	ceil((K+3)*(n+2)/9)	proof
SWAK_BP	ceil((K+1)*n/(6*delta))	proof
FISHER	ceil(5*(K+6)/2)	proof, limiter
T3	ceil(11*(X+4)*n/8)	measurement
KAMA	25*X*isqrt(n)	measurement
FRAMA	9*(X+4)*(isqrt(n)+2)/2, at most 99*K	measurement
VIDYA	2*X*(n+1)*isqrt(m), m the CMO period, at most TA_INDEX_MAX	measurement
MCGD	5*X*n	measurement
HT_DCPERIOD, HT_DCPHASE, HT_PHASOR, HT_SINE	H	measurement
HT_TRENDLINE, HT_TRENDMODE	120 + 20*X	measurement
MAMA	H + ceil(2*K/max(fast, slow)), fast and slow its two limits	measurement
STC	ceil(5*K/2) + 3*(s+1), s = max(fast, slow), on top of the E(s) it inherits	measurement

The E, W, K*n, T3, KAMA and VIDYA rows give 0 at a period of 1, where the function does no smoothing.

measurement: the count is a formula sized on measured series, with margin; it is not a bound (a longer count). ratio marks an output that divides by a smoothed value or by a price, limiter a state snapped at a limit (no level).

rZ2 Under a level, a function that owns no id adds these bars of its own to the count it inherits (rL6). CKSP adds its stop period less one to ATR's count. ADOSC adds ceil((15*f + 3*t)/8) to EMA's count at the longer of its two periods, with f the shorter period, s the longer, and t the sum of min(f, s/2^j) for j from 1 to 16, in integer divisions. KVO adds ceil(K'*n/2) - E(n) to EMA's count at the longest n of its three periods, with K' = (4*K + 23)/3 in integer division: 21 at PREC_4, 33 at PREC_8.

What a level targets

A level targets X significant digits: past the count, the first X significant digits of a value no longer depend on where the series starts. Like rD2, it is a target, not a promise.

• An output that stays away from zero is measured against its value: the moving averages and every output on the price scale, ATR, NATR, RSI, the DI and DM pairs, ADX, RVI, STC, the Hilbert period and trendline.
• An output that reaches zero has no leading digit to keep there, and is measured against the size of its swing, two starts differing by about 10^-X of it: CMO, DX, SWAK_HP, SWAK_2PHP, SWAK_BP, HT_PHASOR, HT_SINE, HT_DCPHASE, and the oscillators centred on zero such as MACD, APO, PPO, TRIX and FISHER.

At PREC_8, where the rounding of a function's own arithmetic is larger than the level, the last digits keep moving.

What a proof covers. e^-K is below 10^-X at both levels. EMA, RMA, ATR and the DM pair output their state, so the bound holds on the output, up to rounding, as a fraction of the two starts' difference where the later one begins. The level's digits follow where that difference is no larger than the output, as on prices; an output that decays toward zero, such as a DM line in a one-way market, keeps the bound but can lose the digits. A ratio output, STOCHRSI and CVI, or one that subtracts two averages (APO, PPO, PVO, MACD), can magnify what is left for a few periods past the count. For these the level's digits are a measured result, not a bound.

Known exceptions

Outside the cases below, a level is expected to meet its target. Each exception, the path-dependent one aside, also reaches every function computed through the one it names, directly or as an MA type (rL6). Most of those tied to the market need a condition that persists for many bars: prices that stay flat, hold a narrow range, or climb steadily.

HT_TRENDLINE and HT_TRENDMODE agree exactly or not at all. A level sets how rare a later disagreement is; no tolerance absorbs one.

A longer count covers these. Set a count on the named function's id, in a call after the one that sets the level.

• KAMA, FRAMA and VIDYA are sized for a market that trends or wanders. They slow down by design in a range-bound market and then need several times their count. 99*K bars hold FRAMA's level on any input; VIDYA has no such bound (below).
• T3 can need a fifth more than its count. A count of 20*n covers it at either level.
• MCGD is sized for a line that tracks the price: its rate falls as the line trails. In a steady rise the count runs short once the period times the rise per bar, as a fraction of the price, passes about 0.06: at a period of 100 on daily bars, a year that gains 16%.

No level, and no count, covers these.

• A flat market. RSI, CMO, the DI pair, DX, RVI, TSI, SMI and STC divide one smoothed series by another, and ADX averages such a ratio. When prices stop moving both series shrink together, and the ratio keeps its dependence on the start.
• A limiter. FISHER replaces a smoothed position beyond 0.99 by 0.999. Two starts on either side of 0.99 differ again by a visible amount, at any bar, and the count restarts from there. While the price holds close to the top or the bottom of its channel without resting on it, the two do not meet.
• A Hilbert input that rests on one value for a whole dominant cycle, as an oscillator pinned at 0 or 100 does. The phase is undefined: HT_DCPHASE, HT_SINE and HT_TRENDMODE from two starts can differ by any amount on those bars, and MAMA does not converge. When the input moves again, every Hilbert function starts over.
• A price worth a few thousand ticks or less, for MAMA. On a bar where its in-phase component is zero to rounding, two starts can take different alphas: the difference reopens by up to the distance from the price to the line, and stays open where that keeps happening. A trending series shows none.
• MCGD in a steady rise, once the product above passes about 0.10: in the same example, a year that gains 29%. The line stays 20% under the price, where its rate is zero, and past that it amplifies its start: two starts agree only after the price comes back to the line.
• VIDYA while its CMO rests at 0, as on a balanced range or a flat market. Its coefficient is 0 and it keeps its seed.
• CRSI, while closes keep moving in one direction. Two starts carry different streaks until the first reversal after the later start, so a run longer than the count leaves their difference past it.
• A path-dependent function, which stays path-dependent: no level changes AD, OBV or SAR (metadata). SUPERTREND computes an ATR, so a level lengthens its lookback and promises nothing about its line.