Why centred moving average

In naive forecasting, the forecast for time t is the data value at time t — 1. Using moving average procedure with a moving average of length one gives naive forecasting. Mean absolute percentage error MAPE measures the accuracy of fitted time series values.

MAPE expresses accuracy as a percentage. Mean absolute deviation MAD measures the accuracy of fitted time series values. MAD expresses accuracy in the same units as the data, which helps conceptualize the amount of error. Mean squared deviation MSD is always computed using the same denominator, n , regardless of the model.

Methods and formulas for Moving Average Learn more about Minitab. Moving average To calculate a moving average, Minitab averages consecutive groups of observations in a series.

Centered moving average By default, moving average values are placed at the period in which they are calculated. If the moving average length is odd Suppose the moving average length is 3. If the moving average length is even Suppose the moving average length is 4.

Now we can smooth the smoothed values again, and get. The calculator below plots CMA for given time series and period even value. If you want to smooth the edges, it simply adds first and last values to the calculation, as needed.

Let's start with a bit of theory. Centered Moving Average. Calculation precision Digits after the decimal point: 2. The file is very large. Browser slowdown may occur during loading and creation. Everyone who receives the link will be able to view this calculation.

For example, we might take a moving average of order 4, and then apply another moving average of order 2 to the results. In the following table, this has been done for the first few years of the Australian quarterly beer production data.

The values in the last column are obtained by taking a moving average of order 2 of the values in the previous column. For example, the first two values in the 4-MA column are The first value in the 2x4-MA column is the average of these two: Other combinations of moving averages are also possible.

In general, an even order MA should be followed by an even order MA to make it symmetric. Similarly, an odd order MA should be followed by an odd order MA. The most common use of centred moving averages is for estimating the trend-cycle from seasonal data. Other choices for the order of the MA will usually result in trend-cycle estimates being contaminated by the seasonality in the data. Notice that the smooth line shows no seasonality; it is almost the same as the trend-cycle shown in Figure 6.

Any other choice for the order of the moving average except for 24, 36, etc. Combinations of moving averages result in weighted moving averages. A major advantage of weighted moving averages is that they yield a smoother estimate of the trend-cycle.