# comb_SA: Simple Average Forecast Combination In GeomComb: (Geometric) Forecast Combination Methods

## Description

Computes forecast combination weights using simple average and produces forecasts for the test set, if provided.

## Usage

 1 comb_SA(x) 

## Arguments

 x An object of class foreccomb. Contains training set (actual values + matrix of model forecasts) and optionally a test set.

## Details

Suppose y_t is the variable of interest, there are N not perfectly collinear predictors, f_t = (f_{1t}, …, f_{Nt})'. The simple average gives equal weights to all predictors:

w = 1/N

The combined forecast is then obtained by:

\hat{y}_t = (f_t)'w

It is well-documented that simple average is a robust combination method that is hard to beat (e.g., Stock and Watson, 2004; Timmermann, 2006). This is often associated with the importance of parameter estimation error in sophisticated techniques – a problem that simple averaging avoids. However, simple averaging may not be a suitable combination method when some of the predictors are biased (Palm and Zellner, 1992).

## 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. 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

Palm, F. C., and Zellner, A. (1992). To Combine or not to Combine? Issues of Combining Forecasts. Journal of Forecasting, 11(8), 687–701.

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.

Timmermann, A. (2006). Forecast Combinations. In: Elliott, G., Granger, C. W. J., and Timmermann, A. (Eds.), Handbook of Economic Forecasting, 1, 135–196.

foreccomb, plot.foreccomb_res, summary.foreccomb_res, accuracy
 1 2 3 4 5 6 7 8 9 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,] data<-foreccomb(train_o, train_p, test_o, test_p) comb_SA(data)