Direct answer
A worked example of SMMA (Smoothed Moving Average) shows how one new SMMA value is computed from a previous SMMA value and the next price observation. Because SMMA is recursive, you start with an initial SMMA value (an assumption), then apply the same calculation rule repeatedly.
Mechanism and definition
SMMA is a type of moving average designed to smooth a time series. “Smoothed” means each new output value partly reflects new data while still carrying forward memory from earlier data.
A common way to express the SMMA update is:
- Let the smoothing period be N.
- Let Price[t] be the next input (for example, a close price) at time t.
- Let SMMA[t] be the SMMA after processing Price[t].
- Then:
- SMMA[t] = (SMMA[t−1] × (N−1) + Price[t]) / N
Key variables and assumptions you must make in any example:
- N (period length) is chosen before the calculation.
- You must define the input series (e.g., close prices). Different inputs give different results.
- You must define the initial value SMMA[0]. Many explanations set it equal to an average of the first N observations; others set it to the first price. Here, we will state our choice explicitly.
Evidence or worked example (fully numeric)
Assume these fixed conditions (so the math can be independently checked):
- Smoothing period: N = 4.
- Input series: Price[t] are assumed close values.
- Initial assumption for the example: SMMA[3] equals the simple average of the first 4 prices (this is one standard initialization choice).
Assumed prices (time 0 to 4):
- Price[0] = 10
- Price[1] = 12
- Price[2] = 11
- Price[3] = 13
- Price[4] = 14
Step 1: Initialize SMMA at t = 3
Simple average of Price[0]..Price[3]:
- (10 + 12 + 11 + 13) / 4 = 46 / 4 = 11.5
So:
- SMMA[3] = 11.5
Step 2: Compute the next SMMA value at t = 4
Use the update rule with N = 4:
- SMMA[4] = (SMMA[3] × (N−1) + Price[4]) / N
- SMMA[4] = (11.5 × 3 + 14) / 4
- SMMA[4] = (34.5 + 14) / 4
- SMMA[4] = 48.5 / 4 = 12.125
Result of the worked example:
- With N = 4 and the stated initialization, the SMMA moves from 11.5 to 12.125 after the next price update.
How to read this mechanically (without treating it as a standalone trading signal):
- The new price (14) increases the average, but it does not fully replace history because 3/4 of the previous SMMA’s weight is carried forward.
Limitations and risks (material failure modes)
- Initialization choice changes early values. If you initialize SMMA differently (for example, set SMMA[3] to Price[3] instead of an average), the early path of SMMA will differ even with the same N and inputs.
- Input definition matters. Using close versus another price series changes Price[t], so the SMMA output changes.
- Slow responsiveness. Because the formula retains (N−1)/N of the prior SMMA, sudden changes affect SMMA gradually. This can lag behind fast moves.
- No automatic predictive accuracy. A moving average is a smoothing operation on past data; it does not inherently confirm future direction.
Verification and next question
To verify the worked example independently, recompute:
- The initial average (46/4 = 11.5)
- The next update (11.5×3 + 14, then divide by 4)
If you want a different worked example, specify the assumptions you prefer (the value of N, the input series, and how to initialize SMMA), and you can reproduce the same calculation steps.