comb_SA() R function from [GeomComb]

Simple Average Forecast Combination

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


comb_SA(x)

Arguments

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

Returns

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.

Details

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

\mathbf{w}^{SA} = \frac{1}{N}w = 1/N

The combined forecast is then obtained by:

\hat{y}_t = {\mathbf{f}_{t}}'\mathbf{w}^{SA}\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).

Examples


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)

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.

comb_SA function