Parabolic Weighted Moving Average

The Parabolic Weighted Moving Average (PWMA) tool provides a customizable trend-following filter that assigns non-linear weights to price data, offering greater responsiveness or smoothness compared to standard moving averages.

Usage

The PWMA is used to identify market trends and potential reversal points by emphasizing recent price action through exponential weighting. Unlike a standard Linear Weighted Moving Average (WMA), the PWMA allows users to adjust the "Power" of the weights, which changes how aggressively the indicator reacts to recent price changes.

Users can observe the color of the plot to determine trend direction:

• Green: Indicates the PWMA is sloping upwards, signaling a bullish trend.
• Red: Indicates the PWMA is sloping downwards, signaling a bearish trend.
• Blue: Indicates a neutral or flat slope.

This indicator is particularly useful for traders who want to fine-tune the balance between lag and noise reduction. A higher power setting will make the average more sensitive to the most recent bars, while a lower power setting provides a more balanced distribution.

Details

The calculation behind the Parabolic Weighted Moving Average is based on the summation of price multiplied by a weight factor, divided by the sum of those weights. The weight for each period is determined by taking the position of the data point within the lookback window (starting from the oldest to the newest) and raising it to the user-defined Power.

The formula for the weight at index $i$ is: $Weight = (Length - i)^{Power}$

By adjusting the Power parameter, the script transforms its mathematical behavior:

• At Power = 0, the weights for all bars become 1, resulting in a Simple Moving Average (SMA).
• At Power = 1, the weights increase linearly, resulting in a Weighted Moving Average (WMA).
• At Power > 1, the weights increase parabolically, placing significantly more importance on the most recent price data and increasing responsiveness.

Settings

• Length: The lookback period used for the calculation. Higher values result in a smoother line with more lag, while lower values are more reactive.
• Power: The exponent applied to the weight of each data point. This determines the "curvature" of the weighting distribution.
• Highlight Movements: A toggle to enable or disable color changes based on whether the PWMA is rising or falling.
• Source: The price data used for the calculation (e.g., Close, Open, High, Low).

FAQ

What is the difference between PWMA and a standard WMA? A standard WMA uses a linear weighting scale, whereas the PWMA uses a power-based weighting scale. This allows the PWMA to become much more sensitive to recent price action than a standard WMA when the power setting is increased above 1.

How do I use the PWMA for trend reversals? Traders often look for the color change of the indicator. When the line changes from red to green, it indicates the average has begun to slope upwards, suggesting a potential bullish reversal.

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