Constructing Lower-Lag Trend Filters with Z-Transform Concepts

Summary

This article proposes using discrete-time signal-processing ideas to reduce the lag of moving-average trend indicators. It starts from an exponential moving average, frames the relationship between closing prices and the EMA as a transfer function, and discusses low-pass and high-pass components. The suggested construction smooths the EMA output using current and prior price information; subtracting a low-pass response from one yields a complementary high-pass filter. The author presents a tunable parameter and says its setting depends on the traded instrument.

The discussion is aimed partly at cryptocurrency trading, where the author argues that short intraday intervals are often choppy and can generate repeated moving-average whipsaws, fees, and slippage. It suggests that related filters may also be applied to indicators such as Bollinger Bands or ATR. However, the displayed equations are missing from the supplied text, no code or backtest results are given, and the author notes that the first-order filter has limitations. Higher orders may become complex or produce irregular jumps, so the proposal needs independent derivation and testing.

Key ideas

• The article uses Z-transform and transfer-function concepts to describe filters for price-derived indicators.
• It starts from an EMA and proposes further smoothing to reduce lag while retaining trend information.
• A complementary high-pass response can be formed by subtracting the low-pass response from one.
• The author suggests tuning filter parameters by instrument and extending the idea to other indicators.
• The equations are absent from the text and no code or empirical results are supplied.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.