Numerical Stability

The documentation specifies which of the four categories below applies to each function. They answer a single practical question: does the value at a given bar depend on how much history you passed in?

If Start-Independent, then...

The value at a bar does not depend on where your data starts. Feed the function a year or a decade and the value it reports for a given bar is identical. These functions read a bounded window — a fixed number of bars — and ignore everything older.

If Initial Unstable Period, then...

Early values depend on how much history precedes them, and converge as more bars are supplied. These functions are defined recursively: each value folds in the previous one, so the series never entirely forgets where it began — though the influence decays until it is lost in floating-point rounding.

How many leading values are discarded is tunable with TA_SetUnstablePeriod. Some functions own their setting; others inherit one from a function they compute internally — DEMA has no unstable period of its own, but is built from EMA and responds to EMA's. Each function page names the setting it responds to.

See Unstable Period for what to do about it: when to ignore it, when to supply extra history, and how to have TA-Lib drop the unstable values for you.

If Depends on MA Type, then...

Some functions take an optInMAType parameter selecting how their moving average is computed. That choice decides which of the properties above applies: a recursive MA type gives the function an initial unstable period, a windowed one leaves it start-independent.

MA Type	Value	Numerical Stability	Why
SMA	0	Start-Independent	A windowed average: it reads a fixed number of bars and forgets everything older.
EMA	1	Initial Unstable Period	Recursive: each value folds in the previous one. Tunable via EMA's own unstable period.
WMA	2	Start-Independent	A windowed average: it reads a fixed number of bars and forgets everything older.
DEMA	3	Initial Unstable Period	Built from EMA, and inherits its unstable period.
TEMA	4	Initial Unstable Period	Built from EMA, and inherits its unstable period.
TRIMA	5	Start-Independent	A windowed average: it reads a fixed number of bars and forgets everything older.
KAMA	6	Initial Unstable Period	Recursive: each value folds in the previous one. Tunable via KAMA's own unstable period.
MAMA	7	Initial Unstable Period	Recursive: each value folds in the previous one. Tunable via MAMA's own unstable period.
T3	8	Initial Unstable Period	Recursive: each value folds in the previous one. Tunable via T3's own unstable period.
HMA	9	Start-Independent	A windowed average: it reads a fixed number of bars and forgets everything older.
DISABLED	10	Start-Independent	Not a moving average: the input is copied through unchanged.

If Path-Dependent, then...

The value is built up from the first bar — a running accumulation or a state machine that tracks the path prices took — so it depends on where your data begins and never converges. Unlike an unstable period, there is no warm-up you can discard: the difference persists for the whole series.

Do not compare these values across differently-sized windows, and expect a backtest starting at a different date to produce different numbers.