# cs_dispersion: Compute Cross-Sectional Dispersion In GeomComb: (Geometric) Forecast Combination Methods

## Description

Computes (time-varying) dispersion measures for the cross section of individual model forecasts that are the input of forecast combination.

## Usage

 1 cs_dispersion(x, measure = "SD", plot = FALSE) 

## Arguments

 x An object of class foreccomb. Contains training set (actual values + matrix of model forecasts) and optionally a test set. measure Cross-sectional dispersion measure, one of: "SD" = standard deviation (default); "IQR" = interquartile range; or "Range" = range. plot logical. If TRUE, evolution of cross-sectional forecast dispersion is plotted as ggplot.

## Details

The available measures of scale are defined as in Davison (2003). Let y_(i) denote the i-th order statistic of the sample, then:

Range_t = y_{(n), t} - y_{(1), t}

IQR_t = y_{(3n/4),t} - y_{(n/4),t}

SD_t = sqrt(1/(n-1) Σ_{i=1}^n (y_{i,t} - \bar{y}_t))

Previous research in the forecast combination literature has documented that regression-based combination methods tend to have relative advantage when one or more individual model forecasts are better than the rest, while eigenvector-based methods tend to have relative advantage when individual model forecasts are in the same ball park.

## Value

Returns a vector of the evolution of cross-sectional dispersion over the sample period (using the selected dispersion measure)

## References

Davison, A. C. (2003). Statistical Models. Cambridge University Press.

Hsiao, C., and Wan, S. K. (2014). Is There An Optimal Forecast Combination? Journal of Econometrics, 178(2), 294–309.

## See Also

foreccomb, sd, IQR, range

## Examples

 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) cs_dispersion(data, measure = "IQR") 

GeomComb documentation built on May 1, 2019, 8:06 p.m.