# PointFore

The goal of PointFore is to estimate specification models for the state-dependent level of an optimal quantile/expectile forecast.

Wald Tests and the test of overidentifying restrictions are implemented. Ploting of the estimated specification model is possible.

Based on â€śInterpretation of Point Forecastsâ€ť by Patrick Schmidt, Matthias Katzfuss, and Tilmann Gneiting, 2018.

## Installation

You can install PointFore from github with:

``````# install.packages("devtools")
devtools::install_github("Schmidtpk/PointFore")``````

## Example

This is a basic example which shows you how to evaluate which quantile is forecasted by the Greenbook GDP forecats:

``````library(PointFore)
#>
#> Attaching package: 'PointFore'
#> The following object is masked from 'package:stats':
#>
#>     lag

res <- estimate.functional(Y=GDP\$observation,X=GDP\$forecast)
#> Drop  1 case(s) because of chosen instruments
#> Choose parameter theta0 automatically.

summary(res)
#> \$call
#> estimate.functional(Y = GDP\$observation, X = GDP\$forecast)
#>
#> \$coefficients
#>           Estimate Std. Error  t value     Pr(>|t|)
#> Theta[1] 0.5980637 0.04429534 13.50173 1.527435e-41
#>
#> \$Jtest
#>
#>  ##  J-Test: degrees of freedom is 2  ##
#>
#>                 J-test    P-value
#> Test E(g)=0:    5.507506  0.063688

#plot(res)``````

On average the forecast is over-optimistic with a forecasted quantile of 0.6. The J-test rejects optimality for this model.

In the next step, we apply a more general model, where the forecasted quantile depends on the current forecast via a linear probit model.

``````res <- estimate.functional(Y=GDP\$observation,X=GDP\$forecast,
model=probit_linear,
stateVariable = GDP\$forecast)
#> Drop  1 case(s) because of chosen instruments
#> Choose parameter theta0 automatically.

summary(res)
#> \$call
#> estimate.functional(model = probit_linear, Y = GDP\$observation,
#>     X = GDP\$forecast, stateVariable = GDP\$forecast)
#>
#> \$coefficients
#>            Estimate Std. Error    t value   Pr(>|t|)
#> Theta[1] -0.1125011 0.16807744 -0.6693408 0.50327812
#> Theta[2]  0.1132529 0.04437854  2.5519745 0.01071144
#>
#> \$Jtest
#>
#>  ##  J-Test: degrees of freedom is 1  ##
#>
#>                 J-test   P-value
#> Test E(g)=0:    1.38747  0.23883
#plot(res)``````

We see that the forecast is overly optimistic in times of high growth. For this model we cannot reject optimality with a p-value of 0.239 in the J-Test of overidentifying restrictions.