Linear Weighting
What Is Linear Weighting?
Linear weighting is a mathematical method of calculating averages where data points are assigned weight values that decrease arithmetically (in a straight line) as they get older, giving more importance to recent data.
In technical analysis, "smoothing" data is essential to see the trend. However, standard smoothing (Simple Moving Average) treats a price from 10 days ago as equally important as the price today. This causes lag. Linear Weighting addresses this by assigning a "weight" to each data point based on its age. The most recent day gets the highest weight. The day before gets slightly less, and so on, in a linear step-down fashion (e.g., 10, 9, 8, 7...). The result is a Linearly Weighted Moving Average (LWMA) that hugs the price action much tighter than a simple average. It reacts faster to reversals but still filters out some noise.
Key Takeaways
- Used primarily in the Linearly Weighted Moving Average (LWMA).
- Assigns higher importance to recent prices compared to older prices.
- Reduces lag significantly compared to the Simple Moving Average (SMA).
- Weights drop off in a constant arithmetic progression (e.g., 5, 4, 3, 2, 1).
- Data outside the lookback period has absolutely zero influence (finite memory).
- Contrast with Exponential Weighting (EMA) which drops off geometrically and has infinite memory.
How It Works (The Math)
Let's calculate a 3-day LWMA for a stock with closing prices: $10, $11, $12 (Today).
Linear vs. Exponential Weighting
Two ways to solve the lag problem.
| Feature | Linear Weighting (LWMA) | Exponential Weighting (EMA) |
|---|---|---|
| Drop-off Pattern | Straight Line (Arithmetic) | Curved (Geometric) |
| Memory | Finite (Zero after N days) | Infinite (Never truly hits zero) |
| Responsiveness | High | Very High |
| Calculation | Complex Sum of Digits | Simple Multiplier |
| Popularity | Niche | Standard |
When to Use Linear Weighting
Traders prefer Linear Weighting when they want a specific, hard cutoff for data relevance. With an EMA, a massive price spike 100 days ago technically still affects the average today (minutely) because of the infinite memory math. With a 20-day LWMA, that spike 100 days ago is mathematically gone. It has zero weight. This makes LWMA superior for traders who believe that "what happened 21 days ago is completely irrelevant."
FAQs
For generating trading signals (like crossovers), yes, because it reacts faster, getting you into the trade earlier. For identifying major support/resistance levels, the SMA is often better simply because institutions watch it more.
It is a matter of preference. EMA is smoother and standard. LWMA is more aggressive and has a definitive cutoff. Scalpers often prefer LWMA for its precision in defining the immediate trend.
Most platforms (TradingView, Thinkorswim) have a "Moving Average Weighted" or "WMA" indicator. Note that "WMA" usually refers to Linear Weighted Moving Average, not just any weighting.
The Bottom Line
Linear Weighting is a sophisticated "middle ground" smoothing technique. It offers a faster reaction time than the sluggish Simple Moving Average but avoids the "infinite memory" tail of the Exponential Moving Average. For traders who want their indicators to be responsive to the "now" while completely discarding the "then," the Linearly Weighted Moving Average is the tool of choice. It represents a precise mathematical compromise between noise reduction and lag reduction.
Related Terms
More in Technical Analysis
At a Glance
Key Takeaways
- Used primarily in the Linearly Weighted Moving Average (LWMA).
- Assigns higher importance to recent prices compared to older prices.
- Reduces lag significantly compared to the Simple Moving Average (SMA).
- Weights drop off in a constant arithmetic progression (e.g., 5, 4, 3, 2, 1).