Moving Averages

Remove the noise (random fluctuation) and seasonality from time series

• also called smoothing/ filtering

• often means finding a new time series through the moving average

each average os computed by dropping the oldest observation and including the next observation

• average moves through the time series until Tt is computed at each observation for which all elements of the average are available

• transformed time series is shorter than original one

One-sided moving average

• q = 0

• used for smoothing and for forecasting

Two-sided moving average

• q > 0

• smooth a time series in order to find the underlying local trend and to find the turning points