example.forecast {COST}

example for one-step ahead forecast

Description

Example for one-step ahead forecast for Gaussian Process and our COST method with Gaussian and t copulas, where the data are generated from COST DGP, where the parameters are assumed to be known; the parameters can be obtained by the “optim" function. Assuming that data are observed at d=9 locations, and n+1 time points, where the last time point is for validation.

Usage

example.forecast(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.fore.ECP

a vector of length d, with value 1 or 0, 1 means the verifying value from the corresponding location lies in the 95% forecast interval, 0 means not

COST.t.fore.ML

a vector of length d, each element is the length of forecast interval of the corresponding location

COST.t.fore.rank

multivariate rank of the verifying vector by t copula

COST.G.fore.ECP

same as COST.t.fore.ECP

COST.G.fore.ML

same as COST.t.fore.ML

COST.G.fore.rank

multivariate rank of the verifying vector by Gaussian copula

GP.fore.ECP

same as COST.t.fore.ECP

GP.fore.ML

same as COST.t.fore.ML

GP.fore.rank

multivariate rank of the verifying vector by Gaussian process method

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
seed1 = 2222222
n.total = 101 #number of total time points, including the burning sequence
n = 50 #number of time points we observed
example.forecast(n,n.total,seed1)
#OUTPUTS

# $COST.t.fore.ECP #whether the forecast interval includes the true value at n+1
# [1] 1 1 1 1 1 1 1 1 1
#
# $COST.t.fore.ML #length of the forecast interval
# [1] 0.7036 4.1318 4.8749 2.7615 3.7398 5.8186 4.4532 4.9251 6.3757
#
# $COST.t.fore.rank #multivariate rank
# [1] 162
#
#
# $COST.G.fore.ECP #whether the forecast interval includes the true value at n+1
# [1] 1 1 1 1 1 1 1 1 1
#
# $COST.G.fore.ML #length of the forecast interval
# [1]  0.7035 4.1316 4.8656 2.7611 3.7388 5.7913 4.4458 4.9036 6.3727
#
# $COST.G.fore.rank #multivariate rank
# [1] 186
#

# $GP.fore.ECP #whether the forecast interval includes the true value at n+1
# [1] 1 0 0 1 1 1 1 1 1
#
# $GP.fore.ML #length of the forecast interval
# [1] 0.4879 2.0449 3.4436 2.2107 2.9170 4.4537 4.2169 5.5789 7.3689
#
# $GP.fore.rank #multivariate rank
# [1] 17