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86fe32a682
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com> Co-authored-by: aider (openrouter/anthropic/claude-sonnet-4) <aider@aider.chat> Co-authored-by: Warp <agent@warp.dev>
4.2 KiB
4.2 KiB
Trends (FIR)
"FIR filters are always stable. The question is how many coefficients you need." Digital Signal Processing folklore
Finite Impulse Response (FIR) trend indicators. These use fixed-length windows with explicit coefficients. No feedback loops, no recursion. Output depends only on current and past inputs. Always stable. Linear phase possible. SIMD-friendly batch computation.
Indicator Status
| Indicator | Full Name | Status | Description |
|---|---|---|---|
| ALMA | Arnaud Legoux MA | Gaussian window with offset parameter. Smooth with configurable lag. | |
| BLMA | Blackman MA | Blackman window. Excellent side-lobe suppression (-58 dB). | |
| BWMA | Bessel-Weighted MA | Bessel window function. Good frequency resolution. | |
| Conv | Convolution MA | Generic convolution with custom kernel. Building block for others. | |
| DWMA | Double Weighted MA | WMA of WMA. Smoother than single WMA. Triangular-like response. | |
| GWMA | Gaussian Weighted MA | Centered Gaussian bell curve. No overshoot. � controls width. | |
| HAMMA | Hamming MA | Hamming window. -43 dB side lobes. Good general purpose. | |
| HANMA | Hanning MA | Hanning (raised cosine). Zero at edges. Smooth roll-off. | |
| HMA | Hull MA | Reduced lag via weighted average differencing. Can overshoot. | |
| HWMA | Holt-Winters MA | Triple exponential smoothing. Tracks level, velocity, acceleration. | |
| LSMA | Least Squares MA | Linear regression endpoint. Extrapolates trend. | |
| PWMA | Pascal Weighted MA | Pascal's triangle coefficients. Binomial distribution weights. | |
| SGMA | Savitzky-Golay MA | Polynomial fit. Preserves higher moments. Shape-preserving. | |
| SINEMA | Sine-Weighted MA | Sine wave weighting. Smooth bell-shaped emphasis. | |
| SMA | Simple MA | Equal weights. Baseline reference. Lag = (N-1)/2. | |
| TRIMA | Triangular MA | Triangular weights. SMA of SMA. Emphasizes middle. | |
| WMA | Weighted MA | Linear weights. Recent prices weighted more. Lag < SMA. |
Status Key: Implemented | =� Planned
Selection Guide
| Use Case | Recommended | Why |
|---|---|---|
| Baseline comparison | SMA | Simple, well-understood. Reference for lag/smoothness. |
| Reduced lag | HMA, WMA, LSMA | HMA aggressive. WMA moderate. LSMA extrapolates. |
| Minimal overshoot | GWMA, TRIMA | Gaussian and triangular weights are gentle. |
| Spectral purity | BLMA, HAMMA | Window functions designed for frequency analysis. |
| Shape preservation | SGMA | Polynomial fit preserves peaks and valleys. |
| Configurable response | ALMA, Conv | ALMA has offset/sigma. Conv accepts any kernel. |
| Trend extrapolation | LSMA, HWMA | LSMA extends regression. HWMA tracks velocity. |
FIR vs IIR Comparison
| Aspect | FIR (This Category) | IIR (trends_IIR) |
|---|---|---|
| Stability | Always stable | Can be unstable if poorly designed |
| Phase | Linear phase possible | Nonlinear phase (causes distortion) |
| Coefficients | Many (N = period) | Few (2-4 typically) |
| Memory | Higher | Lower |
| Computation | O(N) per sample, SIMD-friendly | O(1) per sample, recursive |
| Lag | Fixed for given N | Can be lower for same smoothness |
| Overshoot | Generally low | Can overshoot (especially JMA, HMA) |
Window Function Characteristics
| Window | Main Lobe Width | Side Lobe (dB) | Best For |
|---|---|---|---|
| Rectangular (SMA) | Narrow | -13 | Frequency resolution |
| Hanning | Medium | -31 | General purpose |
| Hamming | Medium | -43 | Better side-lobe rejection |
| Blackman | Wide | -58 | Excellent side-lobe rejection |
| Gaussian | Configurable | Configurable | Tunable trade-off |
Narrower main lobe = better frequency resolution. Lower side lobes = less spectral leakage.