moving average

A moving average of time series or sequential data is a new time series where each element is a weighted average of the last N items in the original series. the simplest case is a straight average, that is That is, if x_i is the original series, the new series y_i is just the arithmetic mean of x_i, x_i-1, x_i-2, ... x_i-(N-1). For example, we might use a 7 day moving average to cancel day-of-the-week effects. More generally, y_i is calculated using weights w_k (0≤k<N):

    y_i = w₀x_i + w₁x_i-1 + w₂x_i-2 + ... w_N-1x_i-(N-1)