Moving Average

Smooth a series with a simple moving average.

Each output value is the mean of window consecutive input values. Only full windows count, so a series of length n gives n - window + 1 values. Output j is the mean of x[j], x[j + 1], ..., x[j + window - 1].

A moving average removes short, random wiggles and keeps the slower trend. It is also the "MA" smoothing step behind many classical forecasting methods.

Function signature

def moving_average(x, window):

Example

Input

moving_average(np.array([1.0, 2.0, 3.0, 4.0, 5.0]), window=3)

Output

array([2., 3., 4.])

Reasoning

The three full windows are [1, 2, 3], [2, 3, 4] and [3, 4, 5]. Their means are 2, 3 and 4.

Constraints and notes

• 1 <= window. If window > len(x), return an empty array.
• Try to do it in O(n) with a cumulative sum rather than O(n * window).