The Moving Median for Some Short‐period, Fat‐tailed, or Contaminated Time Series

The moving median method is suggested as an alternative for short‐term forecasting under some of the standard normal; Student t with degrees of freedom 1, 2 and 3; Cauchy; Chi‐square with degrees of freedom 1 and 2; exponential; and standard normal with outliers. When the Mean Absolute Deviation (MAD) and the Mean Square Error (MSE) are used as the criteria for evaluating forecasting accuracy, the moving average technique is superior to the moving median technique only for time series simulated from the standard normal distribution. The moving median technique is superior to the moving average technique for the fat‐tailed distributions; for example, t ‐distributions of degrees 1, 2 and 3, Cauchy distribution, and the contaminated normal cases. An example shows the moving median technique responds to the level changes faster than the moving average technique. An illustrative example is also given for a practical data set.