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89. Moving average forecast
GeneralCompute a simple moving average (SMA) forecast for a time series, where each forecasted value is the average of the previous (k) observed values. The SMA at time (t) is defined as:
Requirements
Implement the function
Rules:
- Return a NumPy array of length
len(series) - k, aligned so the first forecast corresponds to indexkinseries. - Use NumPy for computation (e.g., cumulative sums or convolution); no pandas.
- Do not use any prebuilt moving-average helpers (e.g.,
np.convolveis allowed, butpandas.Series.rollingis not). - Keep it efficient: aim for (O(n)) time, not (O(nk)).
- Output values should be NumPy float array.
Example
Output:
| Argument | Type |
|---|---|
| k | int |
| series | np.ndarray |
| Return Name | Type |
|---|---|
| value | np.ndarray |
Constraints
Use NumPy only; no pandas rolling.
Runtime must be O(n), not O(nk).
Return NumPy array.
Hint 1
Start by thinking about what the first forecast should use: it averages series[0:k], and the output length must be len(series) - k (first output aligns to index k).
Hint 2
Avoid an O(n*k) loop by reusing work between windows. A prefix-sum (cumulative sum) lets you get any window sum via subtraction in O(1).
Hint 3
With NumPy: arr = series.astype(float); build csum with a leading 0; then window_sums = csum[k:] - csum[:-k] and divide by k. Return the result as a NumPy array.
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Python Editor