example.prediction {COST}

example for new location prediction

Description

Example for new location prediction, Gaussian process method, and our COST method with Gaussian and t copulas, where the parameters are assumed to be known; the parameters can be obtained by the “optim" function. Data are generated at 13 locations and n time points, and assume that 9 locations are observed, and 4 new locations need prediction at time n, conditional on 9 locations at time points n-1 and n.

Usage

example.prediction(n,n.total,seed1)

Arguments

n

number of time points for parameter estimation

n.total

number of total time points, with a burning sequence

seed1

random seed to generate a data set, for reproducibility

Value

COST.t.pre.ECP

a vector of length K=4 (number of new locations), with value 1 or 0, 1 means the verifying value from the corresponding location lies in the 95% prediction interval, 0 means not

COST.t.pre.ML

a vector of length K=4, each element is the length of prediction interval of the corresponding location

COST.t.pre.med.error

prediction error based on conditional median

COST.G.pre.ECP

same as COST.t.pre.ECP

COST.G.pre.ML

same as COST.t.pre.ML

COST.G.pre.med.error

same as COST.t.pre.med.error

GP.pre.ECP

same as COST.t.pre.ECP

GP.pre.ML

same as COST.t.pre.ML

GP.pre.med.error

same as COST.t.pre.med.error

Author(s)

Yanlin Tang and Huixia Judy Wang

References

Yanlin Tang, Huixia Judy Wang, Ying Sun, Amanda Hering. Copula-based semiparametric models for spatio-temporal data.

Examples

library(COST)
#settings
n.total = 101 #number of total time points, including the burning sequence
n = 50 #number of time points we observed
seed1 = 22222
example.prediction(n,n.total,seed1)

#OUTPUTS

# $COST.t.pre.ECP #whether the prediction interval includes the true value, time point n
# [1] 1 1 1 1
#
# $COST.t.pre.ML #length of the prediction interval
# [1] 1.445576 2.146452 2.260688 2.706681
#
# $COST.t.pre.med.error #point prediction error, using conditional median
# [1]  0.01127162 -0.03222058 -0.22081051  0.57831480
#
# $COST.G.pre.ECP #whether the prediction interval includes the true value, time point n
# [1] 1 1 1 1
#
# $COST.G.pre.ML #length of the prediction interval
# [1] 1.445576 2.432646 2.260688 2.914887
#
# $COST.G.pre.med.error #point prediction error, using conditional median
# [1] 0.01127162 -0.03222058 -0.22081051  0.57831480
#
# $GP.pre.ECP #whether the prediction interval includes the true value, time point n
# [1] 1 1 1 1
#
# $GP.pre.ML #length of the prediction interval
# [1] 0.8345359 1.4096642 1.5948724 2.3419428
#
# $GP.pre.med.error #point prediction error, using conditional median
# [1] 0.09447685 -0.05889409 -0.08923935  0.58494684