comb_LAD: Least Absolute Deviation Forecast Combination
In ForecastComb: Forecast Combination Methods

Description Usage Arguments Details Value References See Also Examples

Computes forecast combination weights using least absolute deviation (LAD) regression.

1	comb_LAD(x)

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

The function integrates the least absolute deviation (LAD) forecast combination implementation of the ForecastCombinations package into ForecastComb.

The defining property of comb_LAD is that it does not minimize the squared error loss like comb_OLS and comb_CLS, but the absolute values of the errors. This makes the method more robust to outliers – comb_LAD tends to penalize models, which have high errors for some observations, less harshly than the least squares methods would.

Optimal forecast combinations under general loss functions are discussed by Elliott and Timmermann (2004). The LAD method is described in more detail, and used in an empirical context, by Nowotarksi et al. (2014).

The results are stored in an object of class 'foreccomb_res', for which separate plot and summary functions are provided.

Returns an object of class foreccomb_res with the following components:

`Method`	Returns the best-fit 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.
`Intercept`	Returns the intercept of the linear regression.
`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.

Elliott, G., and Timmermann, A. (2004). Optimal Forecast Combinations Under General Loss Functions and Forecast Error Distributions. Journal of Econometrics, 122(1), 47–79.

Nowotarski, J., Raviv, E., Tr\"uck, S., and Weron, R. (2014). An Empirical Comparison of Alternative Schemes for Combining Electricity Spot Price Forecasts. Energy Economics, 46, 395–412.

Forecast_comb, foreccomb, plot.foreccomb_res, summary.foreccomb_res, accuracy

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_LAD(data)