Direct answer
A worked example of a WMA (Weighted Moving Average) shows exactly how you turn a short series of past values into one number by applying weights—most often giving more weight to the most recent value. The key is to state the window size (how many values you use) and the weighting rule (how weights are assigned), then compute the weighted sum and divide by the total weight.
Mechanism or definition
A Weighted Moving Average (WMA) is a moving average where each observation in the lookback window contributes with a different weight. Formally, you choose a window of N values:
- Let the most recent value be (x_1)
- The value before it be (x_2)
- …and the oldest value in the window be (x_N)
You also choose weights (w_1, w_2, …, w_N). A common choice is linearly increasing weights toward the present, so (w_1 = N, w_2 = N-1, …, w_N = 1). The WMA is then:
[ \text{WMA} = \frac{w_1 x_1 + w_2 x_2 + … + w_N x_N}{w_1 + w_2 + … + w_N} ]
Important: different platforms can use different weight conventions, so the same data can yield different WMA values if the weights or window length differ.
Evidence or example (fully worked)
Assumptions for this example (stated so you can verify independently):
- We use a 5-period WMA, so (N = 5).
- Weights increase toward the present: (w_1 = 5, w_2 = 4, w_3 = 3, w_4 = 2, w_5 = 1).
- The most recent-to-oldest values are: (x_1 = 108), (x_2 = 106), (x_3 = 103), (x_4 = 101), (x_5 = 99).
Step 1: Compute the weighted sum:
- (w_1 x_1 = 5 \times 108 = 540)
- (w_2 x_2 = 4 \times 106 = 424)
- (w_3 x_3 = 3 \times 103 = 309)
- (w_4 x_4 = 2 \times 101 = 202)
- (w_5 x_5 = 1 \times 99 = 99)
Total weighted sum = (540 + 424 + 309 + 202 + 99 = 1574).
Step 2: Compute the sum of weights: (5 + 4 + 3 + 2 + 1 = 15).
Step 3: Divide: [ \text{WMA} = \frac{1574}{15} \approx 104.93 ]
So the WMA value for this point in time is about 104.93, based strictly on the assumptions above.
Limitations and risks (material failure modes)
- Choice sensitivity: Changing the window length (N) or the weighting rule changes the result. WMA is not a single universal number—it is defined by its calculation settings.
- Lag and smoothing: WMAs smooth noise but still react with delay relative to sudden changes. If values move quickly, the WMA may trail.
- Regime changes: A relationship observed in historical data does not guarantee similar behavior later, because market conditions can shift.
Verification or next question
To independently verify any WMA you see reported, check these calculation inputs: (1) the window length, (2) the exact weight pattern used, and (3) which point is considered “most recent” in the window. If you share your WMA’s N and weight rule (or the platform’s formula), you can recompute the number the same way as the worked example above.