Fisher Least Squares Moving Average

The Fisher Least Squares Moving Average (FLSMA) indicator provides a smooth, adaptive trend-following filter that aims to reduce lag and minimize overshoots associated with traditional least-squares estimations. By utilizing the inverse fisher transform on a scaled moving average error, this tool offers an alternative approach to line rescaling that maintains price alignment without the volatility of standard correlation-based methods.

Usage

The Usage section describes how the script can be used, particularly as a replacement for standard moving averages or traditional Least Squares Moving Averages (LSMA).

• Trend Identification: The FLSMA can be used to determine the prevailing market direction. When the price is consistently above the FLSMA, the trend is considered bullish; when below, the trend is considered bearish.
• Dynamic Support and Resistance: Due to its design, the filter often acts as a dynamic level where price may react during trending periods.
• Crossover Signals: Users can monitor for price crossovers with the FLSMA line. A crossover above the line suggests a potential bullish entry, while a crossunder suggests a potential bearish exit or short entry.
• Lag Management: Compared to standard SMA or EMA filters of the same length, the FLSMA aims to track price movements more closely during shifts in momentum, reducing the typical delay found in lagging indicators.

Details

The FLSMA is constructed using a modified line rescaling method. Traditionally, a least-squares moving average fits a polynomial function of degree 1 to the price by reducing the sum of squared differences. The line rescaling technique simplifies this by following these steps:

1. Calculating the z-score of a linear function.
2. Multiplying the z-score by the correlation between price and the line.
3. Multiplying the result by the standard deviation of the price and adding it to a Simple Moving Average (SMA).

The FLSMA differentiates itself by replacing the standard correlation coefficient in step 2 with a value derived from the inverse fisher transform (IFT). It calculates a "scaled smoothed error" (Z) by taking the SMA of the difference between the source price and the previous estimate, divided by the moving average absolute error. Applying the IFT (via the hyperbolic tangent function) to this Z value produces a bounded output between -1 and 1, which serves as a proxy for correlation. This modification helps mitigate significant overshoots, making the filter smoother than a standard LSMA while maintaining responsiveness.

Settings

• Length: The lookback period used for the Simple Moving Average and standard deviation calculations. Higher values result in a smoother, slower filter, while lower values increase responsiveness to price changes.
• Source: The price data point used for the calculation (e.g., Close, Open, High, Low, HL2). "Close" is the default and most common setting for trend analysis.

FAQ

How do I use the FLSMA for trade entries? The FLSMA is typically used for trend confirmation or crossover signals. Traders often look for the price to close above the filter for a bullish signal or below the filter for a bearish signal.

How does this differ from a standard LSMA? While both attempt to minimize squared errors, the FLSMA uses a smoothed error scaled by the inverse fisher transform instead of a raw correlation coefficient. This generally results in fewer overshoots and a smoother output during volatile market conditions.

How can I access the Fisher Least Squares Moving Average? You can get access on the LuxAlgo Library for charting platforms like TradingView, MetaTrader (MT4/MT5), and NinjaTrader for free.