# comb_TA: Trimmed Mean Forecast Combination In GeomComb: (Geometric) Forecast Combination Methods

## Description

Computes a ‘combined forecast’ from a pool of individual model forecasts using trimmed mean at each point in time.

## Usage

 1 comb_TA(x, trim_factor = NULL, criterion = "RMSE") 

## Arguments

 x An object of class foreccomb. Contains training set (actual values + matrix of model forecasts) and optionally a test set. trim_factor numeric. Must be between 0 (simple average) and 0.5 (median). criterion If trim_factor is not specified, an optimization criterion for automated trimming needs to be defined. One of "MAE", "MAPE", or "RMSE" (default).

## Details

Suppose y_t is the variable of interest, there are N not perfectly collinear predictors, f_t = (f_{1t}, …, f_{Nt})'. For each point in time, the order forecasts are computed:

(f_t)_ord = (f_{(1)t}, …, f_{(N)t})'

Using a trim factor λ (i.e., the top/bottom λ \% are trimmed) the combined forecast is calculated as:

\hat{y}_t = 1/(N*(1-2λ)) ∑_{i = λ N +1}^{(1-λ)N} f_{(i)t}

The trimmed mean is an interpolation between the simple average and the median. It is an appealing simple, rank-based combination method that is less sensitive to outliers than the simple average approach, and has been proposed by authors such as Armstrong (2001), Stock and Watson (2004), and Jose and Winkler (2008).

This method allows the user to select λ (by specifying trim_factor), or to leave the selection to an optimization algorithm – in which case the optimization criterion has to be selected (one of "MAE", "MAPE", or "RMSE").

## Value

Returns an object of class foreccomb_res with the following components:

 Method Returns the used forecast combination method. Models Returns the individual input models that were used for the forecast combinations. Weights Returns the combination weights obtained by applying the combination method to the training set. Trim Factor Returns the trim factor, λ. Fitted Returns the fitted values of the combination method for the training set. Accuracy_Train Returns range of summary measures of the forecast accuracy for the training set. Forecasts_Test Returns forecasts produced by the combination method for the test set. Only returned if input included a forecast matrix for the test set. Accuracy_Test Returns range of summary measures of the forecast accuracy for the test set. Only returned if input included a forecast matrix and a vector of actual values for the test set. Input_Data Returns the data forwarded to the method.

## Author(s)

Christoph E. Weiss and Gernot R. Roetzer

## References

Armstrong, J. S. (2001). Combining Forecasts. In: Armstrong, J. S. (Ed.), Principles of Forecasting. Springer, Boston, MA, 417–439.

Jose, V. R. R., and Winkler, R. L. (2008). Simple Robust Averages of Forecasts: Some Empirical Results. International Journal of Forecasting, 24(1), 163–169.

Stock, J. H., and Watson, M. W. (2004). Combination Forecasts of Output Growth in a Seven-Country Data Set. Journal of Forecasting, 23(6), 405–430.

foreccomb, plot.foreccomb_res, summary.foreccomb_res, comb_SA, comb_MED, accuracy
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 obs <- rnorm(100) preds <- matrix(rnorm(1000, 1), 100, 10) train_o<-obs[1:80] train_p<-preds[1:80,] test_o<-obs[81:100] test_p<-preds[81:100,] ## User-selected trim factor: data<-foreccomb(train_o, train_p, test_o, test_p) comb_TA(data, trim_factor=0.1) ## Algorithm-optimized trim factor: data<-foreccomb(train_o, train_p, test_o, test_p) comb_TA(data, criterion="RMSE")