Description Usage Arguments Details Value Author(s) References Examples
The BacktestDensity()
function accepts an object of the class uGASRoll, and returns a list
with
two elements: (i) the averages Negative Log Score (NLS) and weighted Continuous Ranked Probability Score (wCRPS)
introduced by Gneiting and Ranjan (2012), and (ii) their values at each point in time. The wCRPS is
evaluated using 5 weight functions, see Details.
1  BacktestDensity(Roll, lower, upper, K = 1000, a = NULL, b = NULL)

Roll 
an object of the class uGASRoll. 
lower 

upper 

K 

a 

b 

The average Negative Log Score (NLS) is computed as the negative of the average of the log scores evaluated
during the outofsample period. The average weighted Continuous Ranked Probability Score (wCRPS) is computed as
the average of the wCRPS evaluated during the outofsample period, see Gneiting and Ranjan (2012).
The wCRPS is evaluated using Equation 16 of Gneiting and Ranjan (2012). The weights functions implemented are:
w(z) = 1: Uniform,
w(z) = φ_{a,b}(z): Center,
w(z) = 1  φ_{a,b}(z): Tails,
w(z) = Φ_{a,b}(z): Right tail,
w(z) = 1  Φ_{a,b}(z): Left tail,
where φ_{a,b}(z) and Φ_{a,b}(z) are the pdf and cdf of a Gaussian distribution with mean a and standard deviation b, respectively. The label "Uniform" represents the case where equal emphasis is given to all the parts of the distribution.
A list
with elements: average
, series
. The element "average
" is a named vector
with the averages NLS and wCRSP. The element "series
" is a list
: the fist element, LS
, contains
the outofsample Log Score (not with the negative sign), the second element, WCRPS
, contains a matrix
with the wCRPS series. The columns of this matrix are named: "uniform
", "center
", "tails
",
"tail_r
", "tail_l
", which are associated with the wCRSP with emphasis on: Uniform, Center, Tails,
Right tail and Left tail, respectively.
Leopoldo Catania
Gneiting T, Ranjan R (2011). "Comparing Density Forecasts using Threshold and QuantileWeighted Scoring Rules." Journal of Business & Economic Statistics, 29(3), 411422. doi: 10.1198/jbes.2010.08110.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  ## Not run:
data("cpichg")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = TRUE, scale = TRUE,
shape = FALSE))
Roll = UniGASRoll(cpichg, GASSpec, ForecastLength = 50,
RefitEvery = 10, RefitWindow = c("moving"))
BackTest = BacktestDensity(Roll, lower = 100, upper = 100)
BackTest$average
## End(Not run)

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