Designing Linear Price Indicators with Normalized Weights and Window Functions
Summary
This article develops a framework for constructing linear technical indicators as weighted sums of recent prices. It normalizes the coefficients so they sum to one, then uses the coefficient-weighted index positions to locate the indicator's center. Examples derive weights from simple and shifted moving averages, triangular windows, Fibonacci-like sequences, and other integer series. It also discusses negative weights and a stability condition, along with finite geometric, arithmetic, and mixed progression filters that can approximate familiar moving averages.
The later sections apply digital signal processing window functions, including cosine-based windows, and show how shifting a window's center changes its behavior. Indicator variants and oscillator combinations are explored in trading examples, with reported outcomes that vary across configurations. Those results are limited to the article's examples and do not establish general profitability; the author notes that the strategies need further study. The central contribution is a reusable way to think about indicator design through coefficient shape, normalization, center, and stability, rather than a validated trading system.
Key ideas
- A linear price indicator is a weighted sum whose coefficients can be normalized to sum to one.
- The coefficients determine the indicator's effective center and response to price changes.
- Moving-average combinations produce triangular and other structured weight sequences.
- Negative weights can make an indicator unstable unless their magnitudes are constrained.
- Window functions can be shifted to create smoothing, trend-oriented, or countertrend responses.
- Reported strategy outcomes differ by configuration and require further testing.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.