GeomComb (version 1.0)

comb_WA: Winsorized Mean Forecast Combination

Description

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

Usage

comb_WA(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 and 0.5.

criterion

If trim_factor is not specified, an optimization criterion for automated trimming needs to be defined. One of "MAE", "MAPE", or "RMSE" (default).

Value

Returns an object of class foreccomb_res with the following components: with the following components:

Details

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

$$\mathbf{f}_t^{ord} = (f_{(1)t}, \ldots, f_{(N)t})'$$

Using a trim factor $\lambda$ (i.e., the top/bottom $\lambda \%$ are winsorized), and setting $K = N\lambda$ , the combined forecast is calculated as (Jose and Winkler, 2008):

$$\hat{y}_t = \frac{1}{N} \left[Kf_{(K+1)t} + \sum_{i=K+1}^{N-K} f_{(i)t} + Kf_{(N-K)t}\right]$$

Like the trimmed mean, the winsorized mean is a robust statistic that is less sensitive to outliers than the simple average. It is less extreme about handling outliers than the trimmed mean and preferred by Jose and Winkler (2008) for this reason.

This method allows the user to select $\lambda$ (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").

References

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.

See Also

winsor.mean, foreccomb, plot.foreccomb_res, summary.foreccomb_res, comb_SA, comb_TA, accuracy

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,]

## 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")