class: center, middle, inverse, title-slide # Forecasting Model Territories ## 41st International Symposium on Forecasting ### Thiyanga S. Talagala ### 2021 - 06 - 29 --- ## Forecasting competitions .pull-left[   ] .pull-right[ - 100000 time series - Performance measures for point forecasts: **overall weighted average (OWA)** - Mean Absolute Scale Error (MASE) - symmetric Mean Absolute Percentage Error (sMAPE) ] --- .pull-left[ ## Results <img src="m4results.jpg" width="90%" /> Source: Forecasting with high frequency data: M4 competition and beyond, IJF, 2020 ] .pull-right[ ## R Package: `M4comp2018`  ] --- ## Motivation  --- ## Motivation  --- ## Motivation  --- ## Motivation  --- ## Motivation ```r colMeans(yearly_MASE) ``` ``` [1] 2.979908 3.060247 3.130046 3.125675 3.046349 3.081594 3.037880 3.009206 [9] 3.261748 3.184543 3.183715 3.244296 3.075096 3.091125 3.399793 3.406466 [17] 3.293998 3.382097 3.280375 3.401804 3.379866 3.378789 3.444448 3.545371 [25] 3.324425 ``` <img src="index_files/figure-html/unnamed-chunk-4-1.png" width="100%" /> ] --- ## Motivation  --- ## Motivation  --- ## Results: labeled according to the lowest MASE ``` [1] 25 24 10 8 16 13 24 21 24 24 24 18 20 14 1 21 7 24 24 25 16 15 24 24 [25] 23 24 24 24 24 24 17 24 16 16 24 16 24 16 24 9 1 18 18 2 13 18 18 23 [49] 20 18 22 4 18 15 17 4 10 17 25 13 25 24 24 24 18 1 11 11 20 1 15 18 [73] 20 18 24 18 3 1 10 1 13 24 8 14 25 20 15 25 1 24 17 9 21 3 12 25 [97] 25 25 12 25 25 1 25 14 16 20 1 17 25 25 24 25 25 13 25 9 12 25 25 3 [121] 6 25 9 20 9 14 14 20 1 21 14 1 25 25 16 17 25 25 25 25 17 25 25 16 [145] 9 25 25 10 14 25 25 25 25 1 25 25 25 25 25 12 17 10 20 10 16 5 25 1 [169] 17 16 1 15 19 15 20 16 22 2 25 2 21 5 3 11 12 2 7 5 3 25 25 25 [193] 1 25 11 1 25 9 22 15 7 14 9 1 15 25 25 25 1 25 1 12 25 25 1 25 [217] 25 25 25 13 10 21 9 25 15 1 1 12 20 25 19 25 1 25 2 25 25 14 1 8 [241] 15 8 12 25 24 16 17 25 23 11 9 22 2 24 14 24 9 17 20 18 20 25 24 22 [265] 24 16 25 24 21 20 25 25 24 25 25 12 25 25 14 12 2 3 25 4 18 21 25 25 [289] 25 4 16 25 20 18 2 17 25 24 25 4 25 25 25 12 11 12 25 25 20 25 21 25 [313] 14 8 9 10 3 12 25 25 24 24 17 25 25 1 25 5 20 25 24 25 8 25 22 12 [337] 21 25 18 25 1 12 25 9 15 12 18 23 20 15 1 7 17 4 25 23 22 19 25 11 [361] 25 1 16 15 8 21 18 21 24 12 18 23 20 25 17 17 25 13 24 16 1 19 25 14 [385] 15 17 20 7 17 5 25 19 6 25 18 1 19 11 14 19 20 12 25 25 16 18 19 25 [409] 18 25 8 24 8 11 12 25 21 12 23 5 13 1 16 18 17 13 2 25 14 9 14 25 [433] 1 19 16 18 22 15 24 25 19 25 25 22 25 17 12 12 2 22 25 9 14 20 25 6 [457] 7 12 1 25 18 13 25 18 23 19 25 17 16 25 17 15 18 16 17 1 17 1 2 24 [481] 6 17 19 20 25 24 8 1 3 10 15 25 25 25 24 9 24 23 25 2 22 17 17 4 [505] 17 17 17 25 5 22 25 12 4 24 6 22 1 14 20 1 16 6 16 12 12 25 23 6 [529] 18 25 19 25 24 23 16 25 24 25 17 17 8 25 17 16 20 17 12 17 25 4 25 13 [553] 19 18 23 25 12 25 8 7 25 11 24 25 25 12 17 15 24 8 18 24 15 24 13 19 [577] 18 18 8 18 18 25 3 7 20 14 7 24 1 23 13 17 23 8 23 2 2 17 25 18 [601] 10 11 18 25 17 17 23 24 20 9 21 12 2 15 25 1 1 17 20 2 25 24 1 12 [625] 25 10 9 12 24 8 25 6 2 25 18 19 18 16 2 17 7 20 18 6 25 15 21 25 [649] 20 25 18 25 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15 2 18 25 1 15 17 1 1 15 2 2 1 1 24 [1009] 5 20 15 18 5 18 1 11 7 25 21 6 8 17 12 8 1 22 25 25 25 12 19 5 [1033] 1 12 25 8 20 25 21 25 13 21 19 1 21 7 1 9 19 1 24 7 15 8 25 14 [1057] 2 21 12 20 7 20 3 19 24 9 4 2 18 18 4 13 25 25 11 22 15 20 22 17 [1081] 11 15 13 17 2 17 25 20 25 21 25 17 23 15 4 7 9 25 14 15 19 1 9 21 [1105] 17 25 25 20 15 25 24 17 9 15 4 20 25 25 11 12 11 23 23 24 14 15 25 25 [1129] 10 25 25 24 14 24 16 1 15 3 14 2 19 21 25 11 24 12 16 10 1 25 9 19 [1153] 18 11 9 14 25 8 7 20 18 20 21 8 2 24 1 20 14 14 10 7 21 2 17 11 [1177] 17 3 14 21 23 25 25 18 15 12 18 22 25 25 24 25 17 24 8 19 18 3 25 25 [1201] 23 18 2 18 24 23 24 14 24 1 23 21 25 17 8 24 22 17 16 5 24 12 18 25 [1225] 11 18 18 25 15 2 6 17 17 18 22 9 25 14 24 13 18 3 10 18 9 22 16 17 [1249] 1 17 25 7 17 23 21 15 7 14 8 17 20 20 25 20 24 1 19 9 4 21 20 20 [1273] 16 15 20 11 19 14 14 16 25 1 7 17 19 1 10 25 16 25 12 14 1 17 18 18 [1297] 18 17 12 23 1 6 4 9 1 25 17 15 16 25 21 2 24 18 13 16 16 18 17 1 [1321] 4 20 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[19105] 19 22 23 16 19 22 3 20 24 15 18 16 25 17 7 4 9 16 24 18 18 9 1 13 [19129] 13 14 3 21 17 17 1 13 18 22 9 18 24 5 22 24 17 17 25 22 13 19 17 9 [19153] 1 15 6 14 24 19 23 22 8 18 2 21 22 7 17 21 23 14 22 17 23 15 24 12 [19177] 7 18 15 22 8 1 23 18 17 23 8 20 1 21 15 24 22 24 9 24 19 8 18 12 [19201] 10 7 18 21 22 20 7 15 16 5 14 17 19 22 18 14 23 15 15 22 10 19 19 22 [19225] 25 17 19 1 16 25 9 18 8 16 12 14 16 17 2 25 13 15 25 15 11 9 25 7 [19249] 25 24 15 9 18 8 2 22 14 19 25 1 25 15 17 25 25 8 1 15 9 24 13 9 [19273] 22 22 10 7 25 9 20 7 24 5 18 2 1 12 23 17 25 24 24 18 1 25 1 17 [19297] 17 9 18 12 22 1 5 20 21 7 4 20 21 10 22 17 25 20 10 25 25 16 25 25 [19321] 20 23 16 23 17 3 13 6 20 14 20 9 8 25 25 20 18 7 11 18 25 9 16 25 [19345] 10 2 17 25 11 11 9 25 25 1 9 17 1 1 14 8 1 25 18 25 1 25 2 10 [19369] 25 1 9 25 10 22 24 25 13 25 13 25 15 1 8 21 2 18 7 19 17 10 20 5 [19393] 12 4 4 14 2 2 19 2 20 25 25 25 17 25 16 24 10 9 3 2 25 25 9 15 [19417] 24 9 25 19 24 11 24 13 25 19 18 18 21 23 6 24 18 11 15 25 9 9 11 4 [19441] 25 2 18 25 1 1 12 18 25 24 16 25 5 4 16 25 1 25 25 6 20 1 21 17 [19465] 25 20 1 19 23 15 25 25 25 7 9 16 12 14 20 21 24 24 16 15 9 25 25 21 [19489] 13 9 18 25 17 1 23 24 18 23 9 9 20 10 17 19 1 4 1 9 9 25 1 25 [19513] 25 7 15 25 25 23 24 20 20 14 18 9 14 1 23 2 24 6 9 16 7 5 14 17 [19537] 1 1 23 25 22 17 25 12 9 25 23 2 25 25 18 23 18 22 7 25 22 22 1 8 [19561] 25 13 14 6 24 18 24 24 24 18 2 9 3 9 25 1 25 22 16 1 7 1 15 18 [19585] 18 19 25 18 18 19 9 25 21 23 12 21 13 18 25 15 1 10 21 1 12 25 25 25 [19609] 12 7 24 25 17 25 25 20 23 24 3 23 2 24 18 13 2 18 9 25 25 14 1 24 [19633] 17 1 24 14 18 1 20 1 15 7 21 18 19 25 19 17 25 17 10 23 11 22 25 9 [19657] 16 1 16 15 18 24 3 18 12 18 9 14 14 2 9 17 1 25 16 16 11 9 22 9 [19681] 18 22 19 20 19 21 23 2 7 25 18 1 14 19 14 10 23 24 23 2 18 16 21 2 [19705] 25 21 1 16 7 25 25 15 13 12 25 18 17 14 14 18 24 11 22 8 25 23 1 1 [19729] 1 24 25 20 13 2 1 14 8 6 19 16 22 18 25 22 19 15 9 19 25 4 1 25 [19753] 23 20 4 13 4 5 22 25 18 15 25 16 13 16 25 1 15 24 11 21 25 17 1 12 [19777] 14 16 14 1 14 4 24 9 24 19 24 1 25 24 14 25 1 15 9 20 19 10 12 1 [19801] 24 9 14 21 17 20 25 1 4 24 10 1 25 2 24 8 23 3 25 1 2 25 1 22 [19825] 25 15 24 7 17 5 18 18 18 18 14 17 25 25 1 17 25 24 13 2 2 17 9 4 [19849] 22 17 12 16 9 7 25 10 25 18 1 8 14 20 24 11 17 9 1 18 15 1 2 1 [19873] 10 9 1 7 19 15 9 9 17 7 4 10 3 23 17 2 14 11 4 1 18 21 15 22 [19897] 11 18 12 15 7 1 14 24 17 15 18 17 15 6 2 13 1 17 17 24 8 11 1 1 [19921] 1 1 25 8 14 15 15 17 12 20 24 10 18 8 3 18 21 12 15 24 9 11 25 24 [19945] 13 24 15 15 21 16 15 8 1 2 25 24 1 18 12 10 17 17 24 1 2 17 8 11 [19969] 24 9 21 17 17 17 17 4 19 24 11 4 19 11 25 18 8 24 15 15 22 25 17 5 [19993] 17 17 2 25 24 1 22 25 14 14 25 1 14 10 19 3 7 21 17 18 17 17 3 20 [20017] 16 15 11 16 17 16 9 12 11 2 14 6 18 19 4 16 7 16 10 23 17 17 24 22 [20041] 17 21 24 24 23 22 3 10 13 1 7 18 22 9 25 18 20 25 9 15 7 18 18 18 [20065] 1 16 25 11 2 9 11 18 14 4 22 22 20 17 14 20 14 20 2 17 1 13 23 24 [20089] 1 18 20 13 23 23 24 9 20 3 1 25 15 21 1 25 24 20 20 20 18 25 1 14 [20113] 17 25 9 5 1 2 18 20 25 2 15 16 16 14 25 25 25 25 24 1 19 25 2 1 [20137] 12 12 1 25 25 12 1 25 1 25 1 8 22 25 14 23 1 18 8 17 25 19 21 21 [20161] 23 16 24 12 18 23 17 23 6 21 8 16 25 16 24 8 21 15 19 7 18 2 12 13 [20185] 2 12 1 1 11 1 8 23 16 11 13 22 9 18 15 18 25 1 1 20 16 24 14 20 [20209] 18 14 23 8 12 13 19 12 1 12 23 18 23 15 24 12 19 23 1 21 25 20 9 18 [20233] 4 24 4 24 2 1 18 15 15 7 17 14 19 18 13 12 15 15 17 17 17 25 9 15 [20257] 17 6 5 17 25 21 25 25 13 1 18 6 23 25 18 7 15 6 8 25 12 3 2 18 [20281] 15 16 18 21 25 3 13 25 1 14 25 24 24 2 3 8 9 11 17 25 18 9 11 17 [20305] 13 24 17 24 23 4 17 1 2 9 1 11 25 2 17 22 14 18 4 23 23 18 25 8 [20329] 7 12 20 12 5 17 24 25 22 17 1 15 14 19 8 1 22 20 25 24 18 17 9 23 [20353] 13 25 8 20 25 20 16 20 14 7 24 3 21 12 20 10 22 22 9 12 12 9 24 18 [20377] 22 15 6 1 9 23 10 24 9 22 4 1 18 1 17 23 20 13 23 10 19 1 24 11 [20401] 24 25 23 18 5 17 5 24 13 15 24 6 9 8 25 7 25 9 24 8 18 8 5 23 [20425] 15 17 24 22 24 8 2 25 14 25 14 10 11 22 2 25 15 24 21 15 23 18 25 19 [20449] 17 25 1 17 15 3 17 18 2 16 21 23 23 13 10 18 24 2 14 14 18 15 20 15 [20473] 16 1 25 21 9 2 19 22 18 15 11 5 10 6 15 3 23 17 9 17 8 18 25 12 [20497] 25 25 21 14 24 2 21 25 9 24 19 25 25 20 25 24 1 25 2 25 25 18 24 1 [20521] 8 24 15 24 1 1 9 20 12 2 5 24 8 15 16 22 7 16 17 17 22 24 25 17 [20545] 12 1 4 5 23 21 1 12 4 18 7 24 25 24 24 9 9 18 18 18 25 1 24 13 [20569] 17 24 17 20 24 1 7 25 20 25 18 15 23 16 21 22 12 18 20 25 3 1 14 24 [20593] 24 21 9 24 22 14 1 21 19 25 9 9 12 18 18 25 24 9 25 14 25 16 14 16 [20617] 15 25 2 7 25 16 8 15 12 24 11 13 12 17 2 24 18 14 9 1 14 16 16 4 [20641] 24 16 22 22 2 19 18 22 18 20 20 20 21 15 24 14 16 2 21 17 25 18 18 9 [20665] 22 11 1 17 2 25 1 1 14 20 20 18 24 18 4 15 9 10 1 14 19 11 17 24 [20689] 25 21 24 1 16 25 12 9 25 22 22 2 18 22 25 25 25 12 20 9 9 17 16 19 [20713] 10 25 25 24 2 25 24 2 15 17 14 7 7 7 24 15 25 14 1 25 14 13 18 20 [20737] 4 15 13 18 1 25 1 25 20 24 25 25 19 25 2 25 16 11 18 16 20 2 13 20 [20761] 16 22 20 21 8 9 18 18 1 18 18 18 18 9 24 18 1 10 9 17 8 9 22 25 [20785] 19 23 18 25 22 16 25 12 6 18 14 25 1 1 20 9 18 15 15 15 4 1 24 9 [20809] 12 14 22 20 8 8 13 1 8 21 6 9 15 14 25 25 9 17 21 9 18 8 25 17 [20833] 7 4 12 9 14 24 2 17 18 17 10 14 5 18 19 25 11 10 19 1 24 12 14 22 [20857] 2 19 10 13 18 8 8 4 22 14 25 8 4 15 8 14 11 25 12 8 17 25 19 19 [20881] 19 25 25 1 20 22 22 22 9 2 2 9 3 22 8 10 8 3 13 23 24 14 10 21 [20905] 2 25 20 24 23 16 6 14 10 13 16 7 20 11 15 15 9 12 2 15 25 9 21 1 [20929] 9 18 1 10 25 22 1 12 1 19 11 20 16 14 14 1 17 7 19 3 15 4 13 1 [20953] 19 4 8 8 23 24 24 24 9 24 22 9 18 8 8 18 16 13 25 13 19 1 9 1 [20977] 25 21 2 22 25 17 18 4 18 7 12 19 5 18 17 21 25 25 11 24 25 1 21 17 [21001] 13 1 20 21 18 18 22 25 25 1 7 4 11 15 24 14 25 24 25 3 19 24 25 16 [21025] 12 24 25 1 20 1 1 8 21 16 13 22 13 23 25 1 25 22 2 25 16 20 16 1 [21049] 24 20 16 17 25 25 22 17 4 25 17 17 1 25 18 17 3 25 18 12 19 18 15 24 [21073] 23 17 20 23 18 24 14 25 11 20 1 13 17 14 9 16 25 25 20 22 10 16 1 12 [21097] 1 9 1 1 1 25 4 20 23 3 16 10 12 22 22 18 23 14 18 1 17 19 11 12 [21121] 17 14 11 15 18 21 7 18 21 9 15 17 9 25 25 25 1 24 25 11 11 23 16 16 [21145] 17 12 22 16 15 21 25 12 25 1 18 23 23 23 18 18 18 22 18 25 17 18 9 7 [21169] 18 9 1 24 1 25 4 19 15 21 23 9 20 16 20 16 25 8 14 24 14 25 25 23 [21193] 24 18 25 15 24 18 20 19 18 17 15 3 21 16 16 9 24 25 10 25 15 24 18 1 [21217] 17 24 17 17 17 12 18 18 25 5 12 18 5 25 18 5 22 9 23 9 19 3 1 8 [21241] 4 10 16 19 9 20 14 4 18 8 5 24 23 25 18 18 12 22 1 9 1 24 18 25 [21265] 7 19 20 9 9 9 21 14 7 1 5 17 7 3 4 17 24 1 1 11 18 2 17 2 [21289] 23 1 14 25 24 25 1 23 22 14 24 1 25 25 1 9 25 11 15 18 19 12 12 25 [21313] 18 25 25 23 18 15 8 19 6 14 18 2 18 25 24 23 19 19 23 24 22 24 21 25 [21337] 22 25 1 15 20 19 25 25 16 25 16 25 12 25 2 2 1 19 6 20 2 24 9 23 [21361] 9 20 24 20 1 17 16 18 18 9 20 18 18 20 1 14 1 21 24 25 15 24 22 16 [21385] 23 14 25 6 7 6 17 25 14 6 5 15 22 17 1 17 20 25 1 25 17 5 15 1 [21409] 24 9 9 9 9 1 24 25 12 1 4 4 1 8 25 1 9 25 16 20 14 9 9 11 [21433] 25 24 16 15 25 1 24 24 7 20 14 16 24 15 14 5 15 24 7 21 1 1 1 24 [21457] 16 25 20 24 24 11 24 10 18 1 20 22 25 12 24 16 2 20 17 25 24 14 11 15 [21481] 24 24 18 24 17 22 21 11 24 25 15 22 15 18 18 5 24 18 20 21 9 24 3 22 [21505] 20 24 25 24 19 24 18 23 14 21 9 9 17 20 21 9 17 24 12 13 2 18 18 9 [21529] 22 21 10 12 12 15 6 10 20 15 19 24 1 24 12 24 19 8 21 14 5 15 25 24 [21553] 3 1 25 18 24 25 19 13 12 12 3 25 21 22 24 13 20 17 1 2 19 2 24 9 [21577] 1 2 18 24 19 12 8 8 18 8 3 17 18 2 11 14 14 16 1 14 14 12 21 25 [21601] 1 22 6 25 18 15 21 25 1 16 3 9 13 21 10 4 20 19 21 13 17 2 22 17 [21625] 9 9 13 5 18 15 20 9 4 21 24 25 2 16 20 18 9 8 18 24 18 25 3 13 [21649] 22 22 15 24 8 9 4 21 1 14 23 24 4 9 10 22 24 17 13 17 17 20 10 22 [21673] 19 22 22 24 24 24 25 24 4 24 20 15 20 24 21 24 24 16 1 17 24 24 10 24 [21697] 12 24 24 24 24 1 24 16 24 22 1 20 24 25 24 4 24 24 21 1 24 25 10 15 [21721] 20 10 20 12 15 14 21 20 16 16 21 20 21 21 25 11 11 16 15 24 24 24 2 20 [21745] 16 4 10 25 16 25 9 17 8 6 24 25 2 17 24 25 23 14 3 24 17 20 25 1 [21769] 15 20 9 16 17 12 9 24 12 17 24 25 16 20 24 9 25 12 22 25 24 18 24 15 [21793] 4 17 17 20 12 14 12 16 10 24 9 25 14 8 17 16 24 25 6 24 8 14 24 14 [21817] 24 20 16 20 12 14 17 1 13 15 18 14 24 23 25 25 23 24 8 25 12 25 25 24 [21841] 16 9 18 19 25 21 1 25 24 24 25 15 25 15 1 18 8 10 5 19 19 8 20 25 [21865] 13 10 25 25 12 25 1 14 16 1 8 18 25 25 1 25 25 24 25 25 17 25 25 25 [21889] 24 24 20 25 25 25 25 1 9 25 1 18 25 25 5 25 25 1 25 25 13 25 23 25 [21913] 24 9 25 2 25 23 24 19 16 1 1 4 14 4 11 21 23 25 15 3 1 18 24 15 [21937] 4 24 24 20 9 1 24 12 9 17 22 7 2 18 21 2 9 24 15 1 16 16 8 1 [21961] 2 23 17 13 8 18 13 13 18 25 13 8 18 24 1 25 24 25 25 25 1 24 25 18 [21985] 25 25 15 2 9 7 25 17 25 1 21 24 25 22 5 25 25 8 19 3 8 18 17 25 [22009] 8 8 13 19 10 13 11 25 24 24 14 5 18 8 19 13 8 13 1 18 7 19 1 16 [22033] 19 13 24 17 25 13 20 25 10 25 1 21 3 17 17 24 8 9 14 19 22 19 2 21 [22057] 2 9 8 12 3 21 1 5 10 1 25 24 18 25 25 2 25 2 11 23 12 15 14 18 [22081] 19 7 9 18 19 13 22 16 24 20 25 25 25 25 25 2 17 25 25 9 25 14 24 25 [22105] 2 2 24 4 2 11 18 25 11 16 25 24 24 22 25 20 4 25 24 24 25 8 8 11 [22129] 8 9 9 21 6 1 25 10 17 18 25 25 24 1 2 17 17 14 25 14 25 24 23 6 [22153] 25 25 25 15 8 24 24 16 1 16 25 16 18 25 15 19 14 8 16 10 15 14 23 5 [22177] 8 1 8 24 4 9 23 16 1 25 25 20 25 25 20 25 25 23 1 24 25 10 18 10 [22201] 15 9 24 17 10 24 17 18 5 25 16 25 9 17 1 6 3 1 14 21 10 1 22 18 [22225] 7 16 20 1 10 24 7 24 25 18 17 12 12 10 19 24 24 24 22 20 14 11 12 17 [22249] 24 16 19 23 1 2 4 2 1 14 1 16 21 16 17 17 24 24 25 4 10 25 25 25 [22273] 20 16 14 15 16 21 22 21 12 2 12 3 25 15 21 19 24 24 24 24 25 14 16 18 [22297] 13 25 17 11 16 18 14 15 12 21 24 16 9 21 2 4 25 16 24 15 7 16 19 24 [22321] 18 14 4 22 1 25 15 14 24 24 3 15 25 21 8 9 24 16 15 14 18 21 14 18 [22345] 24 20 2 21 12 25 12 24 14 9 14 9 24 16 24 12 25 24 24 11 9 3 18 14 [22369] 24 9 24 25 14 25 24 22 16 20 25 24 11 18 14 2 5 14 2 8 19 16 12 3 [22393] 18 25 9 17 18 20 9 25 12 24 14 24 21 7 14 14 20 8 24 25 2 24 9 17 [22417] 1 7 12 1 22 7 24 24 23 25 7 17 9 12 25 1 9 11 2 16 20 18 13 24 [22441] 25 12 7 16 16 12 17 16 17 17 25 14 10 10 24 7 18 25 24 25 8 25 17 14 [22465] 9 1 18 24 1 8 1 4 2 10 16 16 25 2 1 22 17 13 18 16 15 21 12 4 [22489] 17 24 12 22 25 18 10 25 22 18 25 1 17 19 9 9 20 8 9 17 1 15 15 22 [22513] 1 25 17 25 8 25 25 16 25 15 14 21 13 15 14 8 14 1 15 25 25 21 24 18 [22537] 1 25 20 15 25 10 17 17 1 12 2 24 21 3 4 14 1 1 17 19 3 4 8 24 [22561] 15 2 11 11 13 17 21 17 17 17 1 6 17 8 1 17 14 20 1 1 9 18 25 23 [22585] 14 20 24 16 25 20 24 20 16 19 5 24 16 23 25 16 2 18 8 19 21 18 18 10 [22609] 11 9 17 23 25 3 24 25 25 17 17 17 24 8 23 25 1 15 24 14 15 7 1 17 [22633] 9 13 24 20 17 8 23 9 9 17 17 17 17 17 22 20 15 10 22 19 22 15 11 11 [22657] 24 6 10 25 25 21 14 13 16 19 17 20 25 24 25 14 25 25 14 14 9 1 14 1 [22681] 9 5 24 25 7 25 14 2 25 17 11 25 22 2 25 20 3 9 10 9 10 9 6 11 [22705] 9 9 12 9 9 9 9 9 15 24 9 12 19 9 25 22 3 9 15 22 20 7 1 25 [22729] 19 20 14 25 21 20 17 17 9 21 17 8 25 8 25 21 25 25 19 25 4 19 17 22 [22753] 25 20 25 22 20 20 14 15 9 9 9 9 24 19 2 9 9 9 9 9 13 12 21 25 [22777] 25 25 1 15 25 18 14 14 25 23 25 17 1 8 25 23 2 2 25 21 25 1 25 13 [22801] 14 9 25 19 18 18 1 15 25 1 1 1 18 15 2 25 25 16 22 25 25 25 25 25 [22825] 25 25 25 14 25 1 18 22 13 1 12 15 14 1 16 9 25 25 16 5 12 1 25 2 [22849] 25 1 9 12 19 19 16 9 16 9 7 25 9 16 22 25 16 20 6 9 18 8 18 18 [22873] 24 25 1 25 24 25 9 17 1 25 18 1 22 25 17 20 1 25 25 14 14 9 25 23 [22897] 20 23 16 18 25 12 1 9 18 3 16 20 25 1 1 14 25 25 17 17 22 4 14 9 [22921] 9 22 19 19 1 14 24 23 8 25 25 17 1 25 25 1 25 11 1 9 25 25 5 25 [22945] 12 25 14 25 9 11 25 20 25 22 17 1 15 20 18 25 8 15 18 11 10 25 25 1 [22969] 25 25 1 1 5 18 15 10 25 25 11 24 6 10 15 10 22 19 25 19 13 3 1 25 [22993] 25 1 9 14 18 1 20 17 ``` --- ## Composition of labels ``` yearly_MASE_rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1601 703 366 438 335 275 528 836 1179 562 606 762 672 1069 847 798 17 18 19 20 21 22 23 24 25 1160 1488 765 847 708 646 551 2001 3257 ``` <img src="index_files/figure-html/unnamed-chunk-6-1.png" width="100%" /> --- ## Composition of labels and mean MASE <img src="index_files/figure-html/unnamed-chunk-7-1.png" width="100%" /> <img src="index_files/figure-html/unnamed-chunk-8-1.png" width="100%" /> --- ## Distribution of MASE values <img src="index_files/figure-html/unnamed-chunk-9-1.png" width="100%" /> --- .pull-left[ forecaster-1 ``` forecaster rank values 1 1 1 1601 2 1 2 1807 3 1 3 1356 4 1 4 1208 5 1 5 1064 6 1 6 961 7 1 7 931 8 1 8 881 9 1 9 791 10 1 10 642 11 1 11 673 12 1 12 619 13 1 13 651 14 1 14 637 15 1 15 668 16 1 16 729 17 1 17 801 18 1 18 795 19 1 19 868 20 1 20 844 21 1 21 870 22 1 22 857 23 1 23 1066 24 1 24 1171 25 1 25 509 ``` ] .pull-right[ forecaster-25 ``` forecaster rank values 601 25 1 3257 602 25 2 1307 603 25 3 1038 604 25 4 849 605 25 5 718 606 25 6 558 607 25 7 437 608 25 8 384 609 25 9 361 610 25 10 390 611 25 11 305 612 25 12 361 613 25 13 330 614 25 14 343 615 25 15 400 616 25 16 387 617 25 17 484 618 25 18 508 619 25 19 628 620 25 20 825 621 25 21 982 622 25 22 1283 623 25 23 1314 624 25 24 1908 625 25 25 3643 ``` ] --- ## Distribution of ranks by forecasters <img src="index_files/figure-html/unnamed-chunk-12-1.png" width="100%" /> --- ## Distribution of ranks by forecasters <img src="index_files/figure-html/unnamed-chunk-13-1.png" width="100%" /> ---  --- ## Time series features ``` [1] "trend" "spike" "linearity" "curvature" [5] "e_acf1" "e_acf10" "entropy" "x_acf1" [9] "x_acf10" "diff1_acf1" "diff1_acf10" "diff2_acf1" [13] "diff2_acf10" "x_pacf5" "diff1x_pacf5" "diff2x_pacf5" [17] "max_level_shift" "time_level_shift" "max_var_shift" "time_var_shift" [21] "max_kl_shift" "time_kl_shift" "crossing_points" "flat_spots" [25] "hurst" "unitroot_kpss" "unitroot_pp" "alpha" [29] "beta" "arch_acf" "garch_acf" "arch_r2" [33] "garch_r2" "nonlinearity" "ARCH.LM" "firstzero_ac" [37] "firstmin_ac" "zero_proportion" ``` -- ## t-distributed stochastic neighbor embedding (t-SNE) The goal is to take a set of points in a high-dimensional space and find a representation of those points in a lower-dimensional space, while preserving the local structure of the high dimensional data (that is to group neighboring data points together). --- ## Forecasting Model Territories <img src="index_files/figure-html/unnamed-chunk-15-1.png" width="100%" /> --- <img src="index_files/figure-html/unnamed-chunk-16-1.png" width="100%" /> --- <img src="index_files/figure-html/unnamed-chunk-17-1.png" width="100%" /> --- #### Distribution of features <img src="index_files/figure-html/unnamed-chunk-18-1.png" width="100%" /> --- #### Heatmap visualization of MASE rows: time series, columns: forecasters, cell: MASE <img src="heat.png" width="90%" /> --- class: center, middle # Thank You! <span><i class="fab fa-twitter fa-3x faa-float animated " style=" color:lightblue;"></i></span> <span><i class="fab fa-github fa-3x faa-float animated " style=" color:black;"></i></span> # @thiyangt ### web: https://thiyanga.netlify.app/talk/isf21-talk/ email: ttalagala@sjp.ac.lk