Indicator Formula

Technical Details — Linear Moving Average (LMA)

Overview

The Linear Moving Average (LMA), also known as Weighted Moving Average (WMA), applies linearly increasing weights to prices. The most recent bar gets weight n, the previous gets n-1, and so on. This produces a more responsive average than SMA but with a different character than EMA.

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Mathematical Derivation

Step 1 — Calculate Weighted Sum

Purpose: Apply linearly increasing weights to each bar.

$$WeightedSum = \sum_{i=0}^{n-1} (n - i) \times Close[t-i]$$

Where:

• $$n$$ = Period
• Weight for most recent bar = n, oldest bar = 1

What This Measures: Linearly weighted sum of prices

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Step 2 — Divide by Weight Total

Purpose: Normalize by the sum of all weights.

$$LMA[t] = \frac{WeightedSum}{\sum_{i=1}^{n} i} = \frac{WeightedSum}{n(n+1)/2}$$

What This Measures: Linearly weighted average price

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Compact Formula Summary

$$LMA[t] = \frac{\sum_{i=0}^{n-1} (n-i) \times Close[t-i]}{n(n+1)/2}$$

Default Parameter: Period (n) = 14

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Complete Calculation Example

With Period = 3 and closes [44, 45, 46] (oldest to newest): $$LMA = \frac{1×44 + 2×45 + 3×46}{1+2+3} = \frac{44+90+138}{6} = \frac{272}{6} = 45.33$$

SMA would give 45.00 — LMA is closer to the newest price.

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Key Takeaways from the Example

1. Linear Weighting: Clear, intuitive weight distribution — recent bars always have more influence
2. Middle Ground: More responsive than SMA, less exponential than EMA
3. No Memory Beyond Window: Like SMA, only considers the last n bars — no infinite memory
4. Drop-Off Effect: When a heavily weighted recent bar drops off the window, LMA can shift noticeably

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Caution

Important: LMA provides a good middle ground between SMA’s equal weighting and EMA’s exponential decay. It’s particularly useful when you want more recent-price emphasis than SMA provides but prefer the clean windowed behavior (no infinite memory) over EMA’s recursive approach.