Wilder’s Smoothing Techniques
Wilder’s smoothing techniques refer to the methods of smoothing and filtering financial data developed by J. Welles Wilder, an influential figure in technical analysis. These techniques are used by algorithmic traders and technical analysts to smooth out price data, reduce the impact of short-term fluctuations, and reveal underlying trends in financial markets.
J. Welles Wilder Jr. introduced several key indicators and methods in his seminal work, “New Concepts in Technical Trading Systems” (1978). Among his contributions are popular indicators such as the Relative Strength Index (RSI), Average True Range (ATR), Parabolic SAR (Stop and Reverse), and the Directional Movement Index (DMI). Let’s dive into the specifics of some of these smoothing techniques and their applications in algorithmic trading.
Relative Strength Index (RSI)
The RSI is a momentum oscillator that measures the speed and change of price movements. It oscillates between 0 and 100 and is commonly used to identify overbought or oversold conditions in a market.
Calculation
The RSI is calculated using the following formula:
[ RSI = 100 - \frac{100}{1 + RS} ]
where
[ RS = \frac{\text{Average Gain}}{\text{Average Loss}} ]
The average gain and average loss are typically computed using a 14-period timeframe.
Wilder devised a smoothing technique to calculate these averages using the following steps:
- Compute the first average gain and average loss using simple arithmetic means for the initial 14 periods.
- Use the subsequent periods’ data to smooth these values using an exponential moving average approach:
[ \text{Average Gain}_{\text{New}} = \frac{(\text{Previous Average Gain} \times 13) + \text{Current Gain}}{14} ]
[ \text{Average Loss}_{\text{New}} = \frac{(\text{Previous Average Loss} \times 13) + \text{Current Loss}}{14} ]
This smoothing method significantly reduces the noise in the price data, making RSI a reliable indicator for identifying trends and potential reversal points.
Average True Range (ATR)
ATR is a volatility indicator that measures the degree of price variability. It was originally developed for commodities but can be applied to stocks and other financial instruments as well.
Calculation
The ATR is calculated as follows:
-
True Range (TR) is the greatest of the following:
| [ \text{True Range} = \max(\text{Current High} - \text{Current Low}, | \text{Current High} - \text{Previous Close} | , | \text{Current Low} - \text{Previous Close} | ) ] |
- Average True Range (ATR) is then computed using a 14-period smoothing technique:
[ \text{ATR}_{\text{New}} = \frac{(\text{Previous ATR} \times 13) + \text{Current TR}}{14} ]
The ATR gives traders an idea of the historical price volatility, which can help in setting stop-loss levels, position sizing, and identifying potential breakout points.
Parabolic SAR (Stop and Reverse)
The Parabolic SAR is a trend-following indicator that indicates potential reversal points in the market. It plots points on the chart that define the price trend direction.
Calculation
The Parabolic SAR is computed as:
- For an uptrend:
[ \text{SAR} = \text{Previous SAR} + [alpha](../a/alpha.html) (\text{EP} - \text{Previous SAR}) ]
- For a downtrend:
[ \text{SAR} = \text{Previous SAR} - [alpha](../a/alpha.html) (\text{Previous SAR} - \text{EP}) ]
where EP (Extreme Point) is the highest high or lowest low of the current trend, and ([alpha](../a/alpha.html)) (acceleration factor) starts at 0.02 and increases by 0.02 up to a maximum of 0.20 every time a new EP is reached.
The resulting SAR values create a parabola that moves closer to the price under trending conditions, offering a dynamic system for setting trailing stops.
Directional Movement Index (DMI) and Average Directional Index (ADX)
The DMI is used to identify the presence and strength of a trend. It consists of three components:
- +DI (Positive Directional Indicator) - measures the strength of upward movement
- -DI (Negative Directional Indicator) - measures the strength of downward movement
- ADX (Average Directional Index) - measures the overall strength of the trend without regard to direction
Calculation
-
Calculate Directional Movement (+DM and -DM):
- +DM = Current High - Previous High (if positive and greater than -DM, else 0)
- -DM = Previous Low - Current Low (if positive and greater than +DM, else 0)
-
Calculate Smoothed +DM and -DM using a 14-period smoothing:
[ +DM_{\text{S}} = (+DM_{\text{Prior}} - \frac{+DM_{\text{Prior}}}{14}) + +DM_{\text{Current}} ]
[ -DM_{\text{S}} = (-DM_{\text{Prior}} - \frac{-DM_{\text{Prior}}}{14}) + -DM_{\text{Current}} ]
- Calculate the Directional Indicator values:
[ +DI = 100 \times \frac{+DM_{\text{S}}}{ATR} ]
[ -DI = 100 \times \frac{-DM_{\text{S}}}{ATR} ]
- Calculate the ADX to measure the trend strength:
| [ DX = 100 \times \frac{ | +DI - -DI | }{ +DI + -DI } ] |
[ ADX = \left( \text{Prior ADX} \times 13 + \text{Current DX} \right) / 14 ]
The ADX line helps distinguish trending from non-trending conditions, while the +DI and -DI lines indicate the trend’s direction and strength.
Applications in Algorithmic Trading
Algorithmic traders utilize Wilder’s smoothing techniques in various strategies, including:
- Mean Reversion Strategies: Using RSI to identify overbought or oversold conditions for triggering buy or sell signals.
- Trend Following Strategies: Implementing Parabolic SAR and ADX to determine entry and exit points in line with prevailing trends.
- Volatility-Based Strategies: Leveraging ATR to dynamically set stop-loss levels and adjust position sizing according to market volatility.
These techniques provide a robust framework for systematic trading due to their ability to filter out noise and focus on significant price movements and trends.
For more information about their applications in modern trading systems, consider reviewing resources provided by financial market education services or professional trading firms that specialize in algorithmic trading.