# averaging

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## Arithmetic Mean Average

An average calculated by adding the value of the points in a data set and dividing the sum by the number of data points. For example, suppose one wishes to calculate the average income of a country with exactly five people in it, and their incomes are \$25,000, \$26,000, \$43,000, \$70,000, and \$72,000. It is calculated as:

(\$25,000 + \$26,000 + \$43,000 + \$70,000 + \$72,000) / 5 = \$47,200.

A limitation to the arithmetic mean average is that it can be overly affected by extremes in either direction. For example, if one of the five persons in the country earns \$100 billion per year, the arithmetic mean average income would be in the billions and would not accurately count the other four citizens. For this reason, many analysts use the median in conjunction with the arithmetic mean average. The arithmetic mean average is also called simply the mean.

## averaging

References in periodicals archive ?
But again, in contrast to the results in the first panel, model averaging across all models consistently improves forecast accuracy relative to model selection when forecasting the unemployment rate.
Tables 1 and 2 show that while model averaging can improve forecast accuracy, it does not always do so relative to our model selection-based benchmark.
Even so, it may be that on average across all these permutations, some simple patterns emerge that could help in identifying the best types of model averaging and the classes of models that should be averaged over.
The [gamma] coefficients are associated with how the weighted forecasts are constructed: Equal takes the value I if either the average or median averaging methods are used and 0 otherwise, Weight takes the value 1 if the models are weighted unequally and 0 otherwise, Top 10% takes the value 1 if the averaging uses only the top 10 percent of forecasts and 0 otherwise, and MSE takes the value 1 if MSE-based weights are used and 0 otherwise.
In each panel, the first six rows relate to the selection of models to average over and the next four rows relate to the type of averaging method.
In the first two rows of panel 1 (those associated with averaging over DMS models, IMS models, or both), there appears to be little statistically significant advantage to any of these particular forecasting methods.
In the next four rows of panel 1, results for the type of averaging method clearly indicate that the simple equally weighted averaging methods perform significantly worse than the benchmark.
In the seventh through ninth rows of panel 2, the results for the type of averaging method are much sharper than those for headline inflation.
A quick glance at the first six rows of panel 1 indicates quite clearly that the preferred model types for averaging are now IMS forecasting models estimated recursively using the full sample--a sharp contrast to the type of models chosen for both headline and core CPI-based inflation.
In particular, we list the 10 best-performing permutations of averaging methods and model classes and their respective relative RMSEs for each variable and each of the 1-, 3-, and 12-month horizons.
In line with the results from Table 1, at the 1- and 3-month horizons there are few, if any, gains to model averaging irrelevant of model class.
The second panel of Table 5 (that associated with core inflation) offers a slightly different picture of the benefits of model averaging relative to model selection.

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