Understanding Moving Averages & Smoothing
Educational Tool
This calculator demonstrates how moving averages smooth time series data. It is for learning purposes only and should not be used for trading, financial decisions, or professional forecasting.
What Are Moving Averages?
Moving averages smooth out short-term fluctuations in data to reveal underlying trends. By averaging values over a window of time, they reduce the impact of random noise while preserving the general direction of the data.
Think of it like blurring an image slightly — you lose some detail but can see the bigger picture more clearly.
Three Smoothing Methods
Simple Moving Average (SMA)
Formula: SMA = (v₁ + v₂ + ... + vₙ) / n
- • Averages the last n values equally
- • Simple to understand and compute
- • Every point in the window has equal weight
- • Can lag behind sudden changes
Weighted Moving Average (WMA)
Formula: WMA = Σ(wᵢ × vᵢ) / Σwᵢ
- • Assigns different weights to each point
- • Typically, recent values get higher weights
- • More responsive than SMA to recent changes
- • Linear weights (1, 2, 3...) are common defaults
Exponential Moving Average (EMA)
Formula: EMA = α × value + (1-α) × previousEMA
- • Uses exponentially decaying weights
- • α (alpha) controls responsiveness (0 to 1)
- • Higher α = more responsive, lower α = smoother
- • No fixed window — all past values contribute
Choosing the Right Parameters
| Parameter | Lower Value | Higher Value |
|---|---|---|
| Window Size | Less smooth, more responsive | Smoother, more lag |
| Alpha (EMA) | Smoother, less responsive | More responsive, less smooth |
The right settings depend on your data and goals. More noise requires more smoothing, but too much smoothing can hide important patterns.
Understanding Volatility Reduction
We measure "step-to-step volatility" as the standard deviation of differences between consecutive values. A smoothed series should have lower step volatility than the original.
A reduction of 50% means the smoothed series jumps around only half as much as the original from one point to the next.
Critical Warnings
- Not for Trading: Moving averages are commonly discussed in trading contexts, but this tool is purely educational. Do not use it to make actual trading decisions.
- Not a Predictor: Smoothing shows trends in past data. It does NOT predict future values. A smoothed line going up does not mean the real data will continue upward.
- Lag is Inherent: All smoothing methods introduce some lag — they react to changes after they happen, not before.
- No Magic Parameters: There is no universally "best" window size or alpha. The right choice depends entirely on your specific data and what you're trying to understand.
When to Use Each Method
- SMA: Good starting point; use when all recent values should contribute equally to the smooth estimate.
- WMA: When you want to emphasize recent data more than older data within the window.
- EMA: When you want continuous smoothing without a hard window cutoff; popular because it's smooth and responsive.
Frequently Asked Questions
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