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KAISER - Kaiser

Architectural problem

Real-time chart analysis needs deterministic updates per bar and explicit handling of warm-up periods. KAISER addresses this by implementing I0 approximation (modified Bessel, first kind, order 0) via 25-term power series. with parameterized inputs and direct state progression.

Design decision

This implementation favors streaming execution over batch recomputation. The trade-off is more attention to state initialization, but latency stays predictable when charts scale.

API surface

Functions

  • I0 approximation (modified Bessel, first kind, order 0) via 25-term power series.
  • Computes Kaiser Window Moving Average — a symmetric FIR filter using the

Parameters

Parameter Purpose
source Series to smooth
period Lookback window (>= 2)
beta Kaiser shape parameter controlling sidelobe attenuation (default 3.0).

Returns

  • Kaiser-weighted moving average

Input configuration

Input variable Type Configuration
src input.source default: close, label: "Source"
per input.int default: 14, label: "Period"

Runtime profile

  • Declared optimization: O(period) per bar for convolution; weights precomputed once via I0 series
  • Streaming model: single-pass update on each new bar.
  • Warm-up behavior: outputs can be unstable until enough samples satisfy period.
  • Memory model: state is kept in Pine series context rather than external buffers.

Trade-offs

Streaming logic keeps incremental cost stable, but initialization and edge-case handling become first-class concerns. That is a deliberate choice: predictable execution beats opaque recalculation spikes in live charts.

Verification checklist

  1. Open the script in TradingView and confirm it compiles under Pine Script v6.
  2. Validate warm-up behavior on sparse data and short histories.
  3. Compare output against a trusted reference implementation for the same parameters.
  4. Confirm parameter bounds reject invalid values without silent fallback.

References