Reorganize files

assets/01_common.R

@@ -0,0 +1,90 @@
+text_size <- 16
+linesize <- 1
+width <- 12
+height <- 6
+
+# col_lightgray <- "#e7e7e7"
+# col_blue <- "#F24159"
+# col_b_smooth <- "#F7CE14"
+# col_p_smooth <- "#58A64A"
+# col_pointwise <- "#772395"
+# col_b_constant <- "#BF236D"
+# col_p_constant <- "#F6912E"
+# col_optimum <- "#666666"
+
+# https://www.schemecolor.com/retro-rainbow-pastels.php
+col_lightgray <- "#e7e7e7"
+col_blue <- "#F24159"
+col_b_smooth <- "#5391AE"
+col_p_smooth <- "#85B464"
+col_pointwise <- "#E2D269"
+col_b_constant <- "#7A4E8A"
+col_p_constant <- "#BC677B"
+col_optimum <- "#666666"
+col_auto <- "#EA915E"
+
+T_selection <- c(32, 128, 512)
+
+# Lambda grid
+lamgrid <- c(-Inf, 2^(-15:25))
+
+# Gamma grid
+gammagrid <- sort(1 - sqrt(seq(0, 0.99, .05)))
+
+material_pals <- c(
+  "red", "pink", "purple", "deep-purple", "indigo",
+  "blue", "light-blue", "cyan", "teal", "green", "light-green", "lime",
+  "yellow", "amber", "orange", "deep-orange", "brown", "grey", "blue-grey"
+)
+cols <- purrr::map(material_pals, ~ ggsci::pal_material(.x)(10)) %>%
+  purrr::reduce(cbind)
+colnames(cols) <- material_pals
+
+cols %>%
+  as_tibble() %>%
+  mutate(idx = as.factor(1:10)) %>%
+  pivot_longer(-idx, names_to = "var", values_to = "val") %>%
+  mutate(var = factor(var, levels = material_pals[19:1])) %>%
+  ggplot() +
+  xlab(NULL) +
+  ylab(NULL) +
+  geom_tile(aes(x = idx, y = var, fill = val)) +
+  scale_fill_identity() +
+  scale_x_discrete(expand = c(0, 0)) +
+  scale_y_discrete(expand = c(0, 0)) +
+  theme_minimal() -> plot_cols
+
+col_gas <- "blue"
+col_eua <- "green"
+col_oil <- "amber"
+col_coal <- "brown"
+
+col_scale2 <- function(x, rng_t) {
+  ret <- x
+  for (i in seq_along(x)) {
+    if (x[i] < rng_t[1]) {
+      ret[i] <- col_scale(rng_t[1])
+    } else if (x[i] > rng_t[2]) {
+      ret[i] <- col_scale(rng_t[2])
+    } else {
+      ret[i] <- col_scale(x[i])
+    }
+  }
+  return(ret)
+}
+
+rng_t <- c(-5, 5)
+h_sub <- c(1, 5, 30)
+
+col_scale <- scales::gradient_n_pal(
+  c(
+    cols[5, "green"],
+    cols[5, "light-green"],
+    cols[5, "yellow"],
+    # cols[5, "amber"],
+    cols[5, "orange"],
+    # cols[5, "deep-orange"],
+    cols[5, "red"]
+  ),
+  values = seq(rng_t[1], rng_t[2], length.out = 5)
+)

assets/library.bib

@@ -0,0 +1,558 @@
+@article{aastveit2014nowcasting,
+  title     = {Nowcasting GDP in real time: A density combination approach},
+  author    = {Aastveit, Knut Are and Gerdrup, Karsten R and Jore, Anne Sofie and Thorsrud, Leif Anders},
+  journal   = {Journal of Business \& Economic Statistics},
+  volume    = {32},
+  number    = {1},
+  pages     = {48--68},
+  year      = {2014},
+  publisher = {Taylor \& Francis}
+}
+@article{berrisch2023modeling,
+  title     = {Modeling volatility and dependence of European carbon and energy prices},
+  author    = {Berrisch, Jonathan and Pappert, Sven and Ziel, Florian and Arsova, Antonia},
+  journal   = {Finance Research Letters},
+  volume    = {52},
+  pages     = {103503},
+  year      = {2023},
+  publisher = {Elsevier}
+}
+@incollection{aastveit2019evolution,
+  title     = {The Evolution of Forecast Density Combinations in Economics},
+  author    = {Aastveit, Knut Are and Mitchell, James and Ravazzolo, Francesco and van Dijk, Herman K},
+  booktitle = {Oxford Research Encyclopedia of Economics and Finance},
+  year      = {2019}
+}
+@article{marcjasz2022distributional,
+  title     = {Distributional neural networks for electricity price forecasting},
+  author    = {Marcjasz, Grzegorz and Narajewski, Micha{\l} and Weron, Rafa{\l} and Ziel, Florian},
+  journal   = {Energy Economics},
+  volume    = {125},
+  pages     = {106843},
+  year      = {2023},
+  doi       = {10.1016/j.eneco.2023.106843},
+  publisher = {Elsevier}
+}
+@article{atiya2020does,
+  title     = {Why does forecast combination work so well?},
+  author    = {Atiya, Amir F},
+  journal   = {International Journal of Forecasting},
+  volume    = {36},
+  number    = {1},
+  pages     = {197--200},
+  year      = {2020},
+  publisher = {Elsevier}
+}
+@article{atsalakis2016using,
+  title     = {Using computational intelligence to forecast carbon prices},
+  author    = {Atsalakis, George S},
+  journal   = {Applied Soft Computing},
+  volume    = {43},
+  pages     = {107--116},
+  year      = {2016},
+  publisher = {Elsevier}
+}
+@article{bai2020does,
+  title     = {Does crude oil futures price really help to predict spot oil price? New evidence from density forecasting},
+  author    = {Bai, Lan and Li, Xiafei and Wei, Yu and Wei, Guiwu},
+  journal   = {International Journal of Finance \& Economics},
+  year      = {2020},
+  publisher = {Wiley Online Library}
+}
+@article{benz2009modeling,
+  title     = {Modeling the price dynamics of CO2 emission allowances},
+  author    = {Benz, Eva and Tr{\"u}ck, Stefan},
+  journal   = {Energy Economics},
+  volume    = {31},
+  number    = {1},
+  pages     = {4--15},
+  year      = {2009},
+  publisher = {Elsevier}
+}
+@article{biau2011sequential,
+  title     = {Sequential quantile prediction of time series},
+  author    = {Biau, G{\'e}rard and Patra, Beno{\^\i}t},
+  journal   = {IEEE Transactions on Information Theory},
+  volume    = {57},
+  number    = {3},
+  pages     = {1664--1674},
+  year      = {2011},
+  publisher = {IEEE}
+}
+@inproceedings{bousquet2001tracking,
+  title        = {Tracking a small set of experts by mixing past posteriors},
+  author       = {Bousquet, Olivier and Warmuth, Manfred K},
+  booktitle    = {International Conference on Computational Learning Theory},
+  pages        = {31--47},
+  year         = {2001},
+  organization = {Springer}
+}
+@article{bregere2020online,
+  title   = {Online hierarchical forecasting for power consumption data},
+  author  = {Br{\'e}g{\`e}re, Margaux and Huard, Malo},
+  journal = {arXiv preprint arXiv:2003.00585},
+  year    = {2020}
+}
+@article{busetti2017quantile,
+  title     = {Quantile aggregation of density forecasts},
+  author    = {Busetti, Fabio},
+  journal   = {Oxford Bulletin of Economics and Statistics},
+  volume    = {79},
+  number    = {4},
+  pages     = {495--512},
+  year      = {2017},
+  publisher = {Wiley Online Library}
+}
+@book{cesa2006prediction,
+  title     = {Prediction, learning, and games},
+  author    = {Cesa-Bianchi, Nicolo and Lugosi, G{\'a}bor},
+  year      = {2006},
+  publisher = {Cambridge university press}
+}
+@article{cesa2012mirror,
+  title   = {Mirror descent meets fixed share (and feels no regret)},
+  author  = {Cesa-Bianchi, Nicolo and Gaillard, Pierre and Lugosi, G{\'a}bor and Stoltz, Gilles},
+  journal = {Advances in Neural Information Processing Systems},
+  volume  = {25},
+  pages   = {980--988},
+  year    = {2012}
+}
+@article{cheng2015forecasting,
+  title     = {Forecasting with factor-augmented regression: A frequentist model averaging approach},
+  author    = {Cheng, Xu and Hansen, Bruce E},
+  journal   = {Journal of Econometrics},
+  volume    = {186},
+  number    = {2},
+  pages     = {280--293},
+  year      = {2015},
+  publisher = {Elsevier}
+}
+@article{chernozhukov2010quantile,
+  title     = {Quantile and probability curves without crossing},
+  author    = {Chernozhukov, Victor and Fern{\'a}ndez-Val, Iv{\'a}n and Galichon, Alfred},
+  journal   = {Econometrica},
+  volume    = {78},
+  number    = {3},
+  pages     = {1093--1125},
+  year      = {2010},
+  publisher = {Wiley Online Library}
+}
+@article{devaine2013forecasting,
+  title     = {Forecasting electricity consumption by aggregating specialized experts},
+  author    = {Devaine, Marie and Gaillard, Pierre and Goude, Yannig and Stoltz, Gilles},
+  journal   = {Machine Learning},
+  volume    = {90},
+  number    = {2},
+  pages     = {231--260},
+  year      = {2013},
+  publisher = {Springer}
+}
+@article{dutta2018modeling,
+  title     = {Modeling and forecasting the volatility of carbon emission market: The role of outliers, time-varying jumps and oil price risk},
+  author    = {Dutta, Anupam},
+  journal   = {Journal of Cleaner Production},
+  volume    = {172},
+  pages     = {2773--2781},
+  year      = {2018},
+  publisher = {Elsevier}
+}
+@article{eddelbuettel2014rcpparmadillo,
+  title     = {RcppArmadillo: Accelerating R with high-performance C++ linear algebra},
+  author    = {Eddelbuettel, Dirk and Sanderson, Conrad},
+  journal   = {Computational Statistics \& Data Analysis},
+  volume    = {71},
+  pages     = {1054--1063},
+  year      = {2014},
+  publisher = {Elsevier}
+}
+@article{fragoso2018bayesian,
+  title     = {Bayesian model averaging: A systematic review and conceptual classification},
+  author    = {Fragoso, Tiago M and Bertoli, Wesley and Louzada, Francisco},
+  journal   = {International Statistical Review},
+  volume    = {86},
+  number    = {1},
+  pages     = {1--28},
+  year      = {2018},
+  publisher = {Wiley Online Library}
+}
+@inproceedings{gaillard2014second,
+  title        = {A second-order bound with excess losses},
+  author       = {Gaillard, Pierre and Stoltz, Gilles and Van Erven, Tim},
+  booktitle    = {Conference on Learning Theory},
+  pages        = {176--196},
+  year         = {2014},
+  organization = {PMLR}
+}
+@incollection{gaillard2015forecasting,
+  title     = {Forecasting electricity consumption by aggregating experts; how to design a good set of experts},
+  author    = {Gaillard, Pierre and Goude, Yannig},
+  booktitle = {Modeling and stochastic learning for forecasting in high dimensions},
+  pages     = {95--115},
+  year      = {2015},
+  publisher = {Springer}
+}
+@inproceedings{gaillard2018efficient,
+  title     = {Efficient online algorithms for fast-rate regret bounds under sparsity},
+  author    = {Gaillard, Pierre and Wintenberger, Olivier},
+  booktitle = {Advances in Neural Information Processing Systems},
+  pages     = {7026--7036},
+  year      = {2018}
+}
+@article{garcia2020short,
+  title   = {Short-term European Union Allowance price forecasting with artificial neural networks},
+  author  = {Garc{\'\i}a, Agust{\'\i}n and Jaramillo-Mor{\'a}n, Miguel A},
+  journal = {Entrepreneurship and Sustainability Issues},
+  volume  = {8},
+  number  = {1},
+  pages   = {261},
+  year    = {2020}
+}
+@article{gneiting2007strictly,
+  title     = {Strictly proper scoring rules, prediction, and estimation},
+  author    = {Gneiting, Tilmann and Raftery, Adrian E},
+  journal   = {Journal of the American statistical Association},
+  volume    = {102},
+  number    = {477},
+  pages     = {359--378},
+  year      = {2007},
+  publisher = {Taylor \& Francis}
+}
+@article{gneiting2011comparing,
+  title     = {Comparing density forecasts using threshold-and quantile-weighted scoring rules},
+  author    = {Gneiting, Tilmann and Ranjan, Roopesh},
+  journal   = {Journal of Business \& Economic Statistics},
+  volume    = {29},
+  number    = {3},
+  pages     = {411--422},
+  year      = {2011},
+  publisher = {Taylor \& Francis}
+}
+@article{gneiting2011making,
+  title     = {Making and evaluating point forecasts},
+  author    = {Gneiting, Tilmann},
+  journal   = {Journal of the American Statistical Association},
+  volume    = {106},
+  number    = {494},
+  pages     = {746--762},
+  year      = {2011},
+  publisher = {Taylor \& Francis}
+}
+@article{gneiting2011quantiles,
+  title     = {Quantiles as optimal point forecasts},
+  author    = {Gneiting, Tilmann},
+  journal   = {International Journal of forecasting},
+  volume    = {27},
+  number    = {2},
+  pages     = {197--207},
+  year      = {2011},
+  publisher = {Elsevier}
+}
+@article{hansen2008least,
+  title     = {Least-squares forecast averaging},
+  author    = {Hansen, Bruce E},
+  journal   = {Journal of Econometrics},
+  volume    = {146},
+  number    = {2},
+  pages     = {342--350},
+  year      = {2008},
+  publisher = {Elsevier}
+}
+@article{hao2020modelling,
+  title     = {Modelling of carbon price in two real carbon trading markets},
+  author    = {Hao, Yan and Tian, Chengshi and Wu, Chunying},
+  journal   = {Journal of Cleaner Production},
+  volume    = {244},
+  pages     = {118556},
+  year      = {2020},
+  publisher = {Elsevier}
+}
+@article{he1997quantile,
+  title     = {Quantile curves without crossing},
+  author    = {He, Xuming},
+  journal   = {The American Statistician},
+  volume    = {51},
+  number    = {2},
+  pages     = {186--192},
+  year      = {1997},
+  publisher = {Taylor \& Francis}
+}
+@article{herbster1998tracking,
+  title     = {Tracking the best expert},
+  author    = {Herbster, Mark and Warmuth, Manfred K},
+  journal   = {Machine learning},
+  volume    = {32},
+  number    = {2},
+  pages     = {151--178},
+  year      = {1998},
+  publisher = {Springer}
+}
+@article{hsiao2014there,
+  title     = {Is there an optimal forecast combination?},
+  author    = {Hsiao, Cheng and Wan, Shui Ki},
+  journal   = {Journal of Econometrics},
+  volume    = {178},
+  pages     = {294--309},
+  year      = {2014},
+  publisher = {Elsevier}
+}
+@book{hyndman2018forecasting,
+  title     = {Forecasting: principles and practice},
+  author    = {Hyndman, Rob J and Athanasopoulos, George},
+  year      = {2018},
+  publisher = {OTexts}
+}
+@article{jore2010combining,
+  title     = {Combining forecast densities from VARs with uncertain instabilities},
+  author    = {Jore, Anne Sofie and Mitchell, James and Vahey, Shaun P},
+  journal   = {Journal of Applied Econometrics},
+  volume    = {25},
+  number    = {4},
+  pages     = {621--634},
+  year      = {2010},
+  publisher = {Wiley Online Library}
+}
+@inproceedings{kakade2008generalization,
+  title     = {On the Generalization Ability of Online Strongly Convex Programming Algorithms.},
+  author    = {Kakade, Sham M and Tewari, Ambuj},
+  booktitle = {NIPS},
+  pages     = {801--808},
+  year      = {2008}
+}
+@article{kapetanios2015generalised,
+  title     = {Generalised density forecast combinations},
+  author    = {Kapetanios, G and Mitchell, James and Price, Simon and Fawcett, Nicholas},
+  journal   = {Journal of Econometrics},
+  volume    = {188},
+  number    = {1},
+  pages     = {150--165},
+  year      = {2015},
+  publisher = {Elsevier}
+}
+@inproceedings{koolen2015second,
+  title     = {Second-order quantile methods for experts and combinatorial games},
+  author    = {Koolen, Wouter M and Van Erven, Tim},
+  booktitle = {Conference on Learning Theory},
+  pages     = {1155--1175},
+  year      = {2015}
+}
+@article{koop2013forecasting,
+  title     = {Forecasting the European carbon market},
+  author    = {Koop, Gary and Tole, Lise},
+  journal   = {Journal of the Royal Statistical Society: Series A (Statistics in Society)},
+  volume    = {176},
+  number    = {3},
+  pages     = {723--741},
+  year      = {2013},
+  publisher = {Wiley Online Library}
+}
+@article{korotin2019integral,
+  title   = {Integral Mixabilty: a Tool for Efficient Online Aggregation of Functional and Probabilistic Forecasts},
+  author  = {Korotin, Alexander and V'yugin, Vladimir and Burnaev, Evgeny},
+  journal = {arXiv preprint arXiv:1912.07048},
+  year    = {2019}
+}
+@inproceedings{korotin2020mixing,
+  title        = {Mixing past predictions},
+  author       = {Korotin, Alexander and V’yugin, Vladimir and Burnaev, Evgeny},
+  booktitle    = {Conformal and Probabilistic Prediction and Applications},
+  pages        = {171--188},
+  year         = {2020},
+  organization = {PMLR}
+}
+@article{lichtendahl2013better,
+  title     = {Is it better to average probabilities or quantiles?},
+  author    = {Lichtendahl Jr, Kenneth C and Grushka-Cockayne, Yael and Winkler, Robert L},
+  journal   = {Management Science},
+  volume    = {59},
+  number    = {7},
+  pages     = {1594--1611},
+  year      = {2013},
+  publisher = {INFORMS}
+}
+@article{lin2018multi,
+  title     = {A multi-model combination approach for probabilistic wind power forecasting},
+  author    = {Lin, You and Yang, Ming and Wan, Can and Wang, Jianhui and Song, Yonghua},
+  journal   = {IEEE Transactions on Sustainable Energy},
+  volume    = {10},
+  number    = {1},
+  pages     = {226--237},
+  year      = {2018},
+  publisher = {IEEE}
+}
+@article{littlestone1994weighted,
+  title     = {The weighted majority algorithm},
+  author    = {Littlestone, Nick and Warmuth, Manfred K},
+  journal   = {Information and computation},
+  volume    = {108},
+  number    = {2},
+  pages     = {212--261},
+  year      = {1994},
+  publisher = {Elsevier}
+}
+@article{lu2015jackknife,
+  title     = {Jackknife model averaging for quantile regressions},
+  author    = {Lu, Xun and Su, Liangjun},
+  journal   = {Journal of Econometrics},
+  volume    = {188},
+  number    = {1},
+  pages     = {40--58},
+  year      = {2015},
+  publisher = {Elsevier}
+}
+@article{maciejowska2020pca,
+  title     = {PCA Forecast Averaging—Predicting Day-Ahead and Intraday Electricity Prices},
+  author    = {Maciejowska, Katarzyna and Uniejewski, Bartosz and Serafin, Tomasz},
+  journal   = {Energies},
+  volume    = {13},
+  number    = {14},
+  pages     = {3530},
+  year      = {2020},
+  publisher = {Multidisciplinary Digital Publishing Institute}
+}
+@article{mhammedi2019lipschitz,
+  title   = {Lipschitz adaptivity with multiple learning rates in online learning},
+  author  = {Mhammedi, Zakaria and Koolen, Wouter M and Van Erven, Tim},
+  journal = {arXiv preprint arXiv:1902.10797},
+  year    = {2019}
+}
+@article{nowotarski2018recent,
+  title     = {Recent advances in electricity price forecasting: A review of probabilistic forecasting},
+  author    = {Nowotarski, Jakub and Weron, Rafa{\l}},
+  journal   = {Renewable and Sustainable Energy Reviews},
+  volume    = {81},
+  pages     = {1548--1568},
+  year      = {2018},
+  publisher = {Elsevier}
+}
+@article{opschoor2017combining,
+  title     = {Combining density forecasts using focused scoring rules},
+  author    = {Opschoor, Anne and Van Dijk, Dick and van der Wel, Michel},
+  journal   = {Journal of Applied Econometrics},
+  volume    = {32},
+  number    = {7},
+  pages     = {1298--1313},
+  year      = {2017},
+  publisher = {Wiley Online Library}
+}
+@article{petropoulos2020forecasting,
+  title   = {Forecasting: theory and practice},
+  author  = {Petropoulos, Fotios and Apiletti, Daniele and Assimakopoulos, Vassilios and Babai, Mohamed Zied and Barrow, Devon K and Bergmeir, Christoph and Bessa, Ricardo J and Boylan, John E and Browell, Jethro and Carnevale, Claudio and others},
+  journal = {arXiv preprint arXiv:2012.03854},
+  year    = {2020}
+}
+@article{raftery2005using,
+  title   = {Using Bayesian model averaging to calibrate forecast ensembles},
+  author  = {Raftery, Adrian E and Gneiting, Tilmann and Balabdaoui, Fadoua and Polakowski, Michael},
+  journal = {Monthly weather review},
+  volume  = {133},
+  number  = {5},
+  pages   = {1155--1174},
+  year    = {2005}
+}
+@article{segnon2017modeling,
+  title     = {Modeling and forecasting the volatility of carbon dioxide emission allowance prices: A review and comparison of modern volatility models},
+  author    = {Segnon, Mawuli and Lux, Thomas and Gupta, Rangan},
+  journal   = {Renewable and Sustainable Energy Reviews},
+  volume    = {69},
+  pages     = {692--704},
+  year      = {2017},
+  publisher = {Elsevier}
+}
+@article{thorey2017online,
+  title     = {Online learning with the Continuous Ranked Probability Score for ensemble forecasting},
+  author    = {Thorey, Jean and Mallet, Vivien and Baudin, Paul},
+  journal   = {Quarterly Journal of the Royal Meteorological Society},
+  volume    = {143},
+  number    = {702},
+  pages     = {521--529},
+  year      = {2017},
+  publisher = {Wiley Online Library}
+}
+@article{thorey2018ensemble,
+  title     = {Ensemble forecast of photovoltaic power with online CRPS learning},
+  author    = {Thorey, Jean and Chaussin, Christophe and Mallet, Vivien},
+  journal   = {International Journal of Forecasting},
+  volume    = {34},
+  number    = {4},
+  pages     = {762--773},
+  year      = {2018},
+  publisher = {Elsevier}
+}
+@article{tu2011markowitz,
+  title     = {Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies},
+  author    = {Tu, Jun and Zhou, Guofu},
+  journal   = {Journal of Financial Economics},
+  volume    = {99},
+  number    = {1},
+  pages     = {204--215},
+  year      = {2011},
+  publisher = {Elsevier}
+}
+@article{v2020online,
+  title     = {Online Aggregation of Probabilistic Forecasts Based on the Continuous Ranked Probability Score},
+  author    = {V’yugin, VV and Trunov, VG},
+  journal   = {Journal of Communications Technology and Electronics},
+  volume    = {65},
+  number    = {6},
+  pages     = {662--676},
+  year      = {2020},
+  publisher = {Springer}
+}
+@article{van2018probabilistic,
+  title     = {Probabilistic forecasting of solar power, electricity consumption and net load: Investigating the effect of seasons, aggregation and penetration on prediction intervals},
+  author    = {Van der Meer, DW and Munkhammar, Joakim and Wid{\'e}n, Joakim},
+  journal   = {Solar Energy},
+  volume    = {171},
+  pages     = {397--413},
+  year      = {2018},
+  publisher = {Elsevier}
+}
+@article{vovk1990aggregating,
+  title   = {Aggregating strategies},
+  author  = {Vovk, Volodimir G},
+  journal = {Proc. of Computational Learning Theory, 1990},
+  year    = {1990}
+}
+@book{wahba1990spline,
+  title     = {Spline models for observational data},
+  author    = {Wahba, Grace},
+  year      = {1990},
+  publisher = {SIAM}
+}
+@book{wang2011smoothing,
+  title     = {Smoothing splines: methods and applications},
+  author    = {Wang, Yuedong},
+  year      = {2011},
+  publisher = {CRC Press}
+}
+@article{wang2019jackknife,
+  title   = {Jackknife Model Averaging for Composite Quantile Regression},
+  author  = {Wang, Miaomiao and Zou, Guohua},
+  journal = {arXiv preprint arXiv:1910.12209},
+  year    = {2019}
+}
+@article{wintenberger2017optimal,
+  title     = {Optimal learning with Bernstein online aggregation},
+  author    = {Wintenberger, Olivier},
+  journal   = {Machine Learning},
+  volume    = {106},
+  number    = {1},
+  pages     = {119--141},
+  year      = {2017},
+  publisher = {Springer}
+}
+@article{zamo2020sequential,
+  title   = {Sequential Aggregation of Probabilistic Forecasts--Applicaton to Wind Speed Ensemble Forecasts},
+  author  = {Zamo, Micha{\"e}l and Bel, Liliane and Mestre, Olivier},
+  journal = {arXiv preprint arXiv:2005.03540},
+  year    = {2020}
+}
+@article{zhang2020load,
+  title     = {Load probability density forecasting by transforming and combining quantile forecasts},
+  author    = {Zhang, Shu and Wang, Yi and Zhang, Yutian and Wang, Dan and Zhang, Ning},
+  journal   = {Applied Energy},
+  volume    = {277},
+  pages     = {115600},
+  year      = {2020},
+  publisher = {Elsevier}
+}

assets/make_knots_data.R

@@ -0,0 +1,82 @@
+# %%
+library(profoc)
+library(ggplot2)
+library(tidyr)
+library(dplyr)
+library(readr)
+
+# Creating faceted plots for different knot values and mu values
+# Create a function to generate the data for a given number of knots and mu value
+generate_basis_data <- function(num_knots, mu_value, sig_value, nonc_value, tailw_value, deg_value) {
+  grid <- seq(from = 0, to = 1, length.out = 26)
+  # Use provided degree
+  B <- profoc:::make_basis_matrix(grid,
+    profoc::make_knots(
+      n = num_knots,
+      mu = mu_value,
+      sig = sig_value,
+      nonc = nonc_value,
+      tailw = tailw_value,
+      deg = deg_value
+    ),
+    deg = deg_value
+  )
+  B_mat <- round(as.matrix(B), 5)
+  df <- as.data.frame(B_mat)
+  df$x <- grid
+  df_long <- pivot_longer(df,
+    cols = -x,
+    names_to = "b",
+    values_to = "y"
+  )
+  df_long$knots <- num_knots
+  df_long$mu <- mu_value
+  df_long$sig <- sig_value
+  df_long$nonc <- nonc_value
+  df_long$tailw <- tailw_value
+  df_long$deg <- deg_value
+  return(df_long)
+}
+
+# Generate data for each combination of knot, mu, sig, nonc, tailw, and deg
+mu_values <- seq(0.1, 0.9, by = 0.2)
+sig_values <- 2^(-2:2)
+nonc_values <- c(-4, -2, 0, 2, 4)
+tailw_values <- 2^(-2:2)
+
+# Create an empty list to store all combinations
+all_data <- list()
+counter <- 1
+
+# Nested loops to cover all parameter combinations
+for (m in mu_values) {
+  print(paste("Processing mu:", m))
+  for (s in sig_values) {
+    for (nc in nonc_values) {
+      for (tw in tailw_values) {
+        all_data[[counter]] <- generate_basis_data(5, m, s, nc, tw, 2)
+        counter <- counter + 1
+      }
+    }
+  }
+}
+
+# Combine all data frames
+all_data <- bind_rows(all_data)
+
+write_csv(all_data, "25_07_phd_defense/assets/mcrps_learning/basis_functions.csv")
+
+# %%
+all_data %>%
+  filter(mu == 0.1) %>%
+  filter(sig == 0.25) %>%
+  filter(nonc == -4) %>%
+  filter(tailw == 0.25) %>%
+  ggplot(aes(x = x, y = y, col = b)) +
+  geom_line(size = 2) +
+  labs(
+    title = "Basis Functions for Different Knot Values",
+    x = "x",
+    y = "y"
+  ) +
+  theme_minimal()