PDF Smoothed Moving Average

The PDF Smoothed Moving Average indicator applies Probability Density Function (PDF) weighting to price data to create an adaptive trend-following tool that reduces market noise while maintaining responsiveness. By blending probabilistic smoothing with traditional moving averages, this tool provides traders with a clearer view of trend direction and strength for improved technical analysis.

Usage

The Usage section describes how the script can be used, particularly in identifying market regimes and potential entry or exit points. The indicator outputs a smoothed line on the chart and optionally modifies candle colors to reflect the current trend state.

• Trend Following: Traders can use the color-coded system to stay on the right side of a move. When the PDF-MA is rising, the trend is bullish (green); when it is falling, the trend is bearish (red).
• Mean Reversion and Breakouts: The adaptive nature of the PDF weighting allows the average to hug price action during tight consolidations and expand during volatile breakouts.
• Signal Confirmation: Use the PDF-MA as a filter for other strategies. For example, only take long positions when the candles are green and the price is above the PDF-MA line.

Details

The indicator utilizes a mathematical Probability Density Function to assign weights to historical price points over a specific lookback period. Unlike a simple moving average where all data points have equal weight, the PDF weighting is controlled by variance and mean parameters to focus the smoothing effect on specific parts of the distribution.

To balance the adaptive PDF weighting with structural stability, the final output is a blend of the PDF-weighted average and a standard moving average (SMA or EMA). The PDF function calculates weights based on a Gaussian-like distribution, which is then normalized and applied to the price source. This hybrid approach helps mitigate the lag often found in standard smoothing techniques.

Settings

User Inputs

• Price Source: Determines which price data (Close, Open, High, Low, HLC3, etc.) is used for the calculation.
• Smoothing Method: Selects between an Exponential Moving Average (EMA) or a Simple Moving Average (SMA) to be blended with the PDF-weighted value.
• Smoothing Period: Sets the lookback length for both the PDF calculation and the traditional moving average.
• PDF Variance: Adjusts the spread of the weighting distribution; higher values result in broader smoothing.
• PDF Mean: Centers the weighting distribution, influencing the sensitivity and directionality of the trend detection.

UI Settings

• Show PDF MA on chart?: Toggles the visibility of the smoothed moving average line.
• Paint candles according to Trend?: Enables or disables the dynamic coloring of candles (green for uptrends, red for downtrends).

FAQ

How do I adjust the indicator to be more responsive to price changes? You can decrease the Smoothing Period or lower the PDF Variance to make the indicator react faster to recent price movements.

What is the difference between selecting SMA or EMA in the settings? The EMA option will prioritize recent price data more heavily in the blended calculation, making the PDF-MA more reactive, while the SMA option provides a more stable and balanced average.

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