Combine forecasts from mvgam models into evenly weighted ensembles
Source:R/ensemble.R
ensemble.mvgam_forecast.RdGenerate evenly weighted ensemble forecast distributions from mvgam_forecast objects
Usage
ensemble(object, ...)
# S3 method for class 'mvgam_forecast'
ensemble(object, ..., ndraws = 5000)Arguments
- object
listobject of classmvgam_forecast. Seeforecast.mvgam()- ...
More
mvgam_forecastobjects.- ndraws
Positive integer specifying the number of draws to use from each forecast distribution for creating the ensemble. If some of the ensemble members have fewer draws than
ndraws, their forecast distributions will be resampled with replacement to achieve the correct number of draws
Value
An object of class mvgam_forecast containing the ensemble predictions. This
object can be readily used with the supplied S3 functions plot and score
Details
It is widely recognised in the forecasting literature that combining forecasts
from different models often results in improved forecast accuracy. The simplest way to create
an ensemble is to use evenly weighted combinations of forecasts from the different models.
This is straightforward to do in a Bayesian setting with mvgam as the posterior MCMC draws
contained in each mvgam_forecast object will already implicitly capture correlations among
the temporal posterior predictions.
Examples
# \donttest{
# Simulate some series and fit a few competing dynamic models
set.seed(1)
simdat <- sim_mvgam(n_series = 1,
prop_trend = 0.6,
mu = 1)
plot_mvgam_series(data = simdat$data_train,
newdata = simdat$data_test)
m1 <- mvgam(y ~ 1,
trend_formula = ~ time +
s(season, bs = 'cc', k = 9),
trend_model = AR(p = 1),
noncentred = TRUE,
data = simdat$data_train,
newdata = simdat$data_test,
chains = 2,
silent = 2)
#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
#> from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
#> from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
#> from stan/lib/stan_math/stan/math/prim.hpp:16,
#> from stan/lib/stan_math/stan/math/rev.hpp:16,
#> from stan/lib/stan_math/stan/math.hpp:19,
#> from stan/src/stan/model/model_header.hpp:4,
#> from C:/Users/uqnclar2/AppData/Local/Temp/RtmpotLup8/model-9e8c74e52e4c.hpp:2:
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
#> 194 | if (cdf_n < 0.0)
#> |
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory
m2 <- mvgam(y ~ time,
trend_model = RW(),
noncentred = TRUE,
data = simdat$data_train,
newdata = simdat$data_test,
chains = 2,
silent = 2)
#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
#> from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
#> from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
#> from stan/lib/stan_math/stan/math/prim.hpp:16,
#> from stan/lib/stan_math/stan/math/rev.hpp:16,
#> from stan/lib/stan_math/stan/math.hpp:19,
#> from stan/src/stan/model/model_header.hpp:4,
#> from C:/Users/uqnclar2/AppData/Local/Temp/RtmpotLup8/model-9e8c1777634c.hpp:2:
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
#> 194 | if (cdf_n < 0.0)
#> |
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory
# Calculate forecast distributions for each model
fc1 <- forecast(m1)
fc2 <- forecast(m2)
# Generate the ensemble forecast
ensemble_fc <- ensemble(fc1, fc2)
# Plot forecasts
plot(fc1)
#> Out of sample DRPS:
#> 42.791261
plot(fc2)
#> Out of sample DRPS:
#> 48.658331
plot(ensemble_fc)
#> Out of sample DRPS:
#> 44.3088696
# Score forecasts
score(fc1)
#> $series_1
#> score in_interval interval_width eval_horizon score_type
#> 1 3.433228 1 0.9 1 crps
#> 2 1.105110 1 0.9 2 crps
#> 3 1.995765 1 0.9 3 crps
#> 4 1.447371 1 0.9 4 crps
#> 5 0.977251 1 0.9 5 crps
#> 6 1.419407 1 0.9 6 crps
#> 7 2.022923 1 0.9 7 crps
#> 8 1.727456 1 0.9 8 crps
#> 9 1.147758 1 0.9 9 crps
#> 10 1.200552 1 0.9 10 crps
#> 11 1.318235 1 0.9 11 crps
#> 12 1.700447 1 0.9 12 crps
#> 13 1.018621 1 0.9 13 crps
#> 14 0.988125 1 0.9 14 crps
#> 15 0.896207 1 0.9 15 crps
#> 16 1.007965 1 0.9 16 crps
#> 17 1.042871 1 0.9 17 crps
#> 18 4.183073 1 0.9 18 crps
#> 19 1.335348 1 0.9 19 crps
#> 20 2.246848 1 0.9 20 crps
#> 21 1.614939 1 0.9 21 crps
#> 22 1.568674 1 0.9 22 crps
#> 23 4.672876 1 0.9 23 crps
#> 24 1.362186 1 0.9 24 crps
#> 25 1.358025 1 0.9 25 crps
#>
#> $all_series
#> score eval_horizon score_type
#> 1 3.433228 1 sum_crps
#> 2 1.105110 2 sum_crps
#> 3 1.995765 3 sum_crps
#> 4 1.447371 4 sum_crps
#> 5 0.977251 5 sum_crps
#> 6 1.419407 6 sum_crps
#> 7 2.022923 7 sum_crps
#> 8 1.727456 8 sum_crps
#> 9 1.147758 9 sum_crps
#> 10 1.200552 10 sum_crps
#> 11 1.318235 11 sum_crps
#> 12 1.700447 12 sum_crps
#> 13 1.018621 13 sum_crps
#> 14 0.988125 14 sum_crps
#> 15 0.896207 15 sum_crps
#> 16 1.007965 16 sum_crps
#> 17 1.042871 17 sum_crps
#> 18 4.183073 18 sum_crps
#> 19 1.335348 19 sum_crps
#> 20 2.246848 20 sum_crps
#> 21 1.614939 21 sum_crps
#> 22 1.568674 22 sum_crps
#> 23 4.672876 23 sum_crps
#> 24 1.362186 24 sum_crps
#> 25 1.358025 25 sum_crps
#>
score(fc2)
#> $series_1
#> score in_interval interval_width eval_horizon score_type
#> 1 4.171226 1 0.9 1 crps
#> 2 1.547056 1 0.9 2 crps
#> 3 3.124789 0 0.9 3 crps
#> 4 0.999647 1 0.9 4 crps
#> 5 2.435121 1 0.9 5 crps
#> 6 2.610246 1 0.9 6 crps
#> 7 1.928458 1 0.9 7 crps
#> 8 0.961976 1 0.9 8 crps
#> 9 1.625352 1 0.9 9 crps
#> 10 1.302485 1 0.9 10 crps
#> 11 1.584327 1 0.9 11 crps
#> 12 1.754281 1 0.9 12 crps
#> 13 1.051481 1 0.9 13 crps
#> 14 1.081281 1 0.9 14 crps
#> 15 1.217669 1 0.9 15 crps
#> 16 1.177959 1 0.9 16 crps
#> 17 1.259938 1 0.9 17 crps
#> 18 2.725221 1 0.9 18 crps
#> 19 1.230060 1 0.9 19 crps
#> 20 3.820228 1 0.9 20 crps
#> 21 2.635251 1 0.9 21 crps
#> 22 1.648463 1 0.9 22 crps
#> 23 4.030445 1 0.9 23 crps
#> 24 1.360764 1 0.9 24 crps
#> 25 1.374607 1 0.9 25 crps
#>
#> $all_series
#> score eval_horizon score_type
#> 1 4.171226 1 sum_crps
#> 2 1.547056 2 sum_crps
#> 3 3.124789 3 sum_crps
#> 4 0.999647 4 sum_crps
#> 5 2.435121 5 sum_crps
#> 6 2.610246 6 sum_crps
#> 7 1.928458 7 sum_crps
#> 8 0.961976 8 sum_crps
#> 9 1.625352 9 sum_crps
#> 10 1.302485 10 sum_crps
#> 11 1.584327 11 sum_crps
#> 12 1.754281 12 sum_crps
#> 13 1.051481 13 sum_crps
#> 14 1.081281 14 sum_crps
#> 15 1.217669 15 sum_crps
#> 16 1.177959 16 sum_crps
#> 17 1.259938 17 sum_crps
#> 18 2.725221 18 sum_crps
#> 19 1.230060 19 sum_crps
#> 20 3.820228 20 sum_crps
#> 21 2.635251 21 sum_crps
#> 22 1.648463 22 sum_crps
#> 23 4.030445 23 sum_crps
#> 24 1.360764 24 sum_crps
#> 25 1.374607 25 sum_crps
#>
score(ensemble_fc)
#> $series_1
#> score in_interval interval_width eval_horizon score_type
#> 1 3.8263402 1 0.9 1 crps
#> 2 1.3036929 1 0.9 2 crps
#> 3 2.5519035 1 0.9 3 crps
#> 4 1.0739452 1 0.9 4 crps
#> 5 1.6133805 1 0.9 5 crps
#> 6 1.9180633 1 0.9 6 crps
#> 7 1.9954492 1 0.9 7 crps
#> 8 1.2471014 1 0.9 8 crps
#> 9 1.2738834 1 0.9 9 crps
#> 10 1.1792346 1 0.9 10 crps
#> 11 1.4541516 1 0.9 11 crps
#> 12 1.6823855 1 0.9 12 crps
#> 13 1.0212761 1 0.9 13 crps
#> 14 1.0489788 1 0.9 14 crps
#> 15 0.9839557 1 0.9 15 crps
#> 16 0.9631836 1 0.9 16 crps
#> 17 0.9966610 1 0.9 17 crps
#> 18 3.4294286 1 0.9 18 crps
#> 19 1.2707383 1 0.9 19 crps
#> 20 2.9218745 1 0.9 20 crps
#> 21 2.0465904 1 0.9 21 crps
#> 22 1.4433498 1 0.9 22 crps
#> 23 4.2497062 1 0.9 23 crps
#> 24 1.3876704 1 0.9 24 crps
#> 25 1.4259249 1 0.9 25 crps
#>
#> $all_series
#> score eval_horizon score_type
#> 1 3.8263402 1 sum_crps
#> 2 1.3036929 2 sum_crps
#> 3 2.5519035 3 sum_crps
#> 4 1.0739452 4 sum_crps
#> 5 1.6133805 5 sum_crps
#> 6 1.9180633 6 sum_crps
#> 7 1.9954492 7 sum_crps
#> 8 1.2471014 8 sum_crps
#> 9 1.2738834 9 sum_crps
#> 10 1.1792346 10 sum_crps
#> 11 1.4541516 11 sum_crps
#> 12 1.6823855 12 sum_crps
#> 13 1.0212761 13 sum_crps
#> 14 1.0489788 14 sum_crps
#> 15 0.9839557 15 sum_crps
#> 16 0.9631836 16 sum_crps
#> 17 0.9966610 17 sum_crps
#> 18 3.4294286 18 sum_crps
#> 19 1.2707383 19 sum_crps
#> 20 2.9218745 20 sum_crps
#> 21 2.0465904 21 sum_crps
#> 22 1.4433498 22 sum_crps
#> 23 4.2497062 23 sum_crps
#> 24 1.3876704 24 sum_crps
#> 25 1.4259249 25 sum_crps
#>
# }