I have half-hourly electricity data of several homes for a duration of one month. Also, I have ambient temperature at same sampling rate. Now, I need to make half-hourly forecasts using historical electricity data and forecasted temperature for coming day.
Currently, I am facing a problem with seasonality, i.e., in some homes I observe (via visual inspection) day-wise seasonality and in some other homes no pattern is found. Stephan suggested to check for weekly seasonality as well, but visually I do not find any. So, I thought to try models with different forced seasonalities to find the prediction accuracy. I can think of two options:
- Model_1 with daily seasonality (frequency = 48 observations)
- Model_2 with weekly and daily seasonality (48, 7*48)
Keeping the above approach in mind, I am facing the following issue:
- For Model_1, I can use
auto.arima()withxregoption to specify an extratemperaturepredictor. However, this only works for a single seasonality. - For Model_2, I tried to use the
tbats()forecasting function, which models multiple seasonalities, but does not allow extra predictor variables.
Is there a forecasting function which allows both multiple predictors and multiple seasonalities?
Here is the electricity data of one month.
data <- structure(c(1642.8, 1467.1, 165.57, 1630.99, 1618.65, 1629.29,
1598.93, 1839.9, 1604.52, 1606.73, 1473.82, 1669.17, 1698.9,
2111.21, 2056.41, 3671.29, 2808.01, 1336.15, 794.11, 1212.15,
377.36, 888.54, 174.58, 218.54, 420.76, 389.58, 397.77, 395.31,
359.11, 364.8, 376.13, 389.37, 929.5, 1702.38, 519.65, 2452.28,
1354.45, 1842.96, 725.41, 661.11, 528.44, 733.4, 429.51, 310.47,
279.72, 407.83, 1791.1, 1754.53, 1536.73, 1608.37, 1432.23, 1401.72,
1582.14, 1558.75, 1536.24, 1745.59, 1375.61, 1556.71, 1671.12,
1206.77, 1391.84, 876.23, 1617.3, 1638.99, 1833.61, 1591.42,
1455, 183.87, 177.55, 184.36, 332.99, 352.95, 425.1, 945.67,
342.3, 348.45, 227.18, 382.15, 268.91, 335.88, 326.94, 233.23,
169.71, 179.51, 195.3, 207.23, 1681.9, 1493.32, 941.52, 980.36,
924.31, 379.02, 1229.89, 1590.21, 1250.92, 1149.24, 1124.04,
993.78, 883.98, 860.69, 934.17, 969.31, 1049.55, 1104.94, 904.3,
1220.23, 1183.9, 891.26, 825.33, 787.77, 1060.93, 1029.1, 982.25,
193.13, 182.65, 181.75, 167.68, 165.89, 291.02, 300.2, 418.4,
297.66, 231.89, 305.66, 701.18, 338.5, 337.24, 332.11, 332.66,
187.8, 179.03, 130.22, 177.73, 172.24, 173.45, 334.23, 810.53,
359.41, 330.23, 333.29, 568.85, 2462.46, 1660.32, 1156.13, 1136.2,
1189.07, 832.73, 181.91, 185.93, 1076.77, 672.78, 1376.71, 1020.17,
382.18, 1160.74, 791.36, 1569.4, 817.78, 850.71, 747.21, 826.12,
1306.46, 506.23, 140.05, 132.6, 304.19, 308.14, 406.13, 290.73,
188.9, 165.59, 174.56, 145.97, 151.83, 142.29, 443.58, 799.9,
279.36, 223.88, 221.03, 291.26, 374.97, 431.36, 598.98, 625.82,
1052.02, 2036.83, 1230.03, 1429.81, 1099.34, 1646.03, 1668.56,
1631.79, 1604.04, 2849.49, 2998.63, 2476.96, 1601.04, 1216.42,
2004.2, 1868.51, 1961.91, 1813.35, 1500.22, 1276.94, 1369.29,
632.43, 238.15, 488.76, 467.6, 330.27, 144.67, 153.36, 924.12,
1348.18, 799.01, 524.3, 420.5, 264.34, 283.86, 198.95, 206.52,
217.33, 356.16, 207.83, 197.6, 194.03, 193.01, 249.85, 271.22,
244.25, 442.5, 660.49, 245.66, 356.13, 443.32, 336.15, 849.74,
1709.21, 1542.09, 1315.69, 2628.6, 2261.8, 1576.42, 1776.48,
1239.64, 1401.12, 1106.17, 1378.55, 1315.57, 1141, 1642.63, 2484.13,
1968.94, 3059.42, 1317.32, 905.05, 484.42, 486.86, 96.79, 183.45,
173.94, 342, 255.96, 320.54, 106.19, 147.88, 150.77, 176.17,
344.75, 371.73, 309.46, 237.86, 187.32, 202.61, 292.5, 248.28,
259.3, 283.67, 365.09, 230.47, 326.15, 350.92, 335.42, 419.39,
345.31, 1093.22, 1392.87, 1298.11, 919.16, 1654.53, 1045.99,
558.42, 437.29, 857.9, 758.34, 1220.04, 1390.62, 956.74, 909.93,
584.67, 409.87, 387.3, 387.93, 1276.28, 871.06, 413.8, 313.2,
199.5, 330.21, 210.9, 358.28, 352.13, 233.62, 259.18, 123.57,
255.58, 411.78, 427.65, 318.95, 298.5, 283.23, 279.85, 200.45,
205.97, 254.24, 307.98, 1090.53, 289.71, 215.14, 286.63, 328.55,
288.96, 1281.19, 1354.8, 1302.05, 1254.46, 261.95, 270.09, 243.28,
696.61, 314.27, 241.73, 245.68, 157.74, 222.55, 294.36, 185.46,
203.49, 182.14, 246.69, 178.26, 397.5, 330.2, 212.02, 248.72,
265.48, 249.37, 130.59, 248.97, 279.94, 319.07, 358.5, 278.98,
251.92, 304.66, 455.05, 365.95, 340.93, 287.51, 264.82, 260.18,
34.35, 35.11, 184.09, 247.18, 160.9, 139.27, 284.96, 296.31,
252.3, 342.65, 353.03, 380.52, 346.19, 350.06, 218.52, 133.94,
173.7, 128.26, 167.8, 112.77, 147.8, 129, 170.54, 89.88, 243.08,
97.61, 190.31, 193.94, 268.17, 233.5, 205.27, 92.29, 167.43,
168.34, 151.99, 193.84, 379.1, 318.69, 327.28, 487.39, 414.01,
336.06, 278.02, 168.05, 155.6, 236.4, 264.94, 296.05, 326.46,
357.43, 356.31, 340.29, 319.81, 312.79, 341.53, 317.36, 309.62,
440.6, 285.5, 282.06, 288.99, 334.48, 196.54, 144.24, 218.55,
173.64, 242.29, 251.78, 186.81, 184.36, 141.62, 208.91, 157.53,
154.03, 139.44, 137.66, 256.75, 1202.05, 177.36, 177.93, 72.83,
252.9, 231.35, 1090.39, 442.91, 363.12, 248.96, 478.75, 249.64,
297.29, 227.28, 365.82, 879.7, 488.93, 184.79, 138.13, 151.77,
123.18, 175.76, 251.84, 208.06, 126.68, 246.3, 307.34, 319.79,
324.3, 379.6, 309.53, 253.17, 221.91, 228.42, 150.24, 148.59,
118.79, 86.89, 140.51, 200.43, 212.15, 276.14, 441.81, 125.77,
152.42, 329.28, 269.21, 177.35, 1106.29, 128.92, 96.35, 63.53,
520.62, 940.25, 1014.34, 314.99, 390.2, 330.1, 377.04, 341.35,
342.79, 241.79, 249.9, 391.92, 292.68, 105.02, 179.99, 118.53,
154.17, 90.53, 206.7, 345.33, 244.75, 291.68, 820.57, 1777.84,
1805.83, 1753.73, 1416.7, 279.2, 262.82, 1345.88, 467.98, 1136.66,
170.02, 159.96, 1478.8, 1414.12, 1347.93, 1505.59, 1341.69, 445.53,
277.59, 1609.61, 1476.45, 244.08, 192.57, 213.55, 439.02, 112.86,
128.54, 376.09, 251.15, 116.27, 254.82, 302.56, 304.6, 198.5,
240.05, 219.35, 70.3, 190.96, 211.95, 328.53, 714.62, 3176.56,
2604.09, 191.65, 145.25, 93.93, 83.6, 81.13, 146.12, 331.75,
250.24, 1144.53, 1616.47, 1008.7, 316.65, 311.46, 1152.99, 1504.86,
1543.21, 1081.54, 1428.07, 1358.23, 1349.75, 190.23, 2398.92,
2196.11, 1466.94, 2249.77, 2150.2, 2542.25, 618.03, 453.22, 880.99,
1497.86, 440.96, 161.85, 324.88, 434.11, 316.33, 444.66, 359.14,
277.41, 1237.28, 761.41, 183.53, 309.44, 213.48, 121.64, 346.7,
149.86, 2060.39, 1102.13, 347.97, 600.24, 912.6, 590.77, 1805.76,
1673.93, 1573.91, 505.74, 446.76, 1033.41, 1668.68, 1293.9, 383.81,
1419.99, 1349.4, 711.55, 218.63, 182, 401.93, 1876, 1486.34,
1543.11, 2313.8, 478.57, 615.19, 542.68, 971.98, 531.11, 766.21,
489.76, 344.47, 319.86, 321.26, 311.41, 288.67, 310.67, 305.15,
419.33, 422.84, 950.08, 2188.88, 3454.92, 1989.54, 590.33, 327.05,
354.78, 578.41, 1583.29, 2016.66, 1481.03, 293.21, 1864.84, 399.65,
366.76, 357.7, 2074.97, 1626.86, 1133, 1624.61, 1506.93, 628.4,
1405.68, 217.8, 1223.11, 1356.97, 1171.72, 1182.86, 1642.11,
2289.02, 814.39, 595.76, 542.78, 1596.41, 884.97, 235.25, 1540.68,
781.95, 115.71, 1204.98, 718.66, 452.09, 305.58, 444.67, 356.76,
182.54, 674.47, 153.8, 862.25, 1322.88, 323.33, 1659.64, 496.72,
304.74, 246.6, 327.12, 239.31, 246.72, 225.72, 234.7, 324.07,
304.27, 171.86, 97.64, 242.69, 295, 324.53, 513.81, 1100.65,
1151.77, 231.56, 189.88, 786.3, 1164.87, 676.09, 882.82, 1496.3,
1027.91, 872.92, 809.1, 840.31, 1302.18, 2055.87, 677.74, 934.66,
263.91, 186.68, 248.5, 214.62, 371.54, 298, 294.52, 304.86, 1295.77,
942.5, 305, 265.78, 255.89, 255.63, 151.54, 108.16, 116.81, 100.19,
224.75, 84.11, 1143.89, 262.15, 784.21, 1728.29, 1506.79, 434.94,
374.29, 265.43, 560.74, 1651.49, 1063.07, 1054.69, 1298.4, 1261.59,
1132.75, 692.82, 660.57, 198.25, 97.81, 1258.67, 833.64, 796.35,
868.76, 999.86, 2240.02, 885.72, 1317.52, 1267.18, 167.93, 133.22,
364.44, 267.17, 406.13, 412.52, 1036.04, 779.34, 655.43, 1901.2,
270.18, 266.31, 284.21, 288.66, 135.38, 176.11, 154.86, 160.21,
146.28, 163.72, 139.75, 278.12, 253.51, 319.62, 396.39, 1662.69,
1577.09, 1059.71, 241.64, 407.54, 290.49, 846.17, 1325.31, 1418.23,
1432.5, 1412.6, 1015.87, 1619.88, 1426.58, 1333.32, 1963.35,
1638.11, 1081.89, 285.56, 1084.58, 2038.77, 1022.39, 1145.92,
513.87, 107.7, 176.19, 143.77, 374.3, 373.99, 221.76, 148.3,
331.01, 2323.12, 1502.09, 347.17, 296.7, 306.06, 313.03, 221.69,
295.35, 301.95, 250.92, 231.54, 140.6, 717.63, 863.5, 402.15,
1337.78, 1575.44, 1738.49, 1675.57, 1617.66, 1365.58, 242.8,
286.29, 712.34, 1559.59, 1600.34, 3447.88, 3432.89, 3337.23,
1472.21, 1323.76, 1265.31, 1221.65, 1312.63, 2016.09, 2972.13,
1451.67, 735.67, 130.13, 379.87, 162.21, 226.48, 417.18, 357.51,
346.37, 200.89, 190.15, 276.05, 942.74, 1471.99, 1047.53, 1240.06,
742.62, 169.34, 144.28, 220.58, 165.23, 344.8, 227.47, 254.64,
742.37, 1809.01, 436.11, 1692.87, 1697.74, 1474.91, 1635.68,
1664.2, 1489.85, 1316.4, 1364.07, 1510.02, 1497.89, 1709.17,
2846.71, 2736.08, 1015.43, 1017.08, 1195.21, 751.18, 523.89,
199.69, 2148.71, 1151.39, 1182.84, 788.91, 259.31, 146.29, 141.09,
299.38, 349.53, 404.08, 449.9, 391.77, 251.89, 222.25, 281.04,
565.4, 371.24, 219.75, 324.45, 227, 157.67, 212.48, 201.69, 140.84,
220.67, 187.64, 399.79, 157.92, 275.49, 326.99, 1340.51, 1578.68,
1599.41, 1667.74, 1129.07, 1312.55, 1393.09, 1368.69, 1130.85,
968.71, 1130.2, 1223.1, 1124.5, 1077.09, 1052.42, 1255.31, 918.21,
1263.93, 706.21, 3080.29, 1620.18, 1122.48, 750.06, 262.89, 110.02,
236.83, 413, 227.53, 355, 277.51, 258.03, 368.44, 656.68, 1808.17,
1493.41, 1272.21, 330.67, 1674.18, 719.45, 1089.68, 784.01, 275.73,
312.69, 345.11, 761.8, 1020.11, 259.16, 345.98, 270.23, 580.15,
1303.68, 1659.7, 1732.94, 204.9, 373.58, 373.36, 1381.52, 1437.74,
1262.78, 1264.6, 1184.54, 1175.12, 857.09, 1428.34, 841.92, 232.47,
223.22, 473.24, 382.7, 189.84, 1737.48, 1689.34, 378.48, 872.56,
180.12, 363.03, 301.38, 412.57, 401.17, 387.35, 417.63, 300.61,
376.82, 284.31, 232.31, 269.96, 188.41, 203.79, 134.88, 193.66,
57.86, 89.71, 167.66, 60.84, 197.03, 703.66, 1638.7, 1467.03,
347.22, 1397.23, 1511.92, 1362.25, 1397.18, 1106.19, 826.5, 1033.04,
1039.46, 584.98, 706.35, 548.07, 373.39, 681.6, 1231.28, 288.94,
649.36, 79.28, 209.23, 290.75, 304.12, 132.57, 91.2, 355.37,
197.45, 343.17, 339.2, 284.65, 229, 234.73, 322.36, 323.43, 295.1,
197.03, 308.17, 223.88, 235.08, 225.16, 172.83, 236.26, 135.17,
394.89, 479.2, 315.34, 280.9, 282.36, 204.78, 367.24, 1712.29,
1521, 1686.09, 960.19, 1019.12, 1062.77, 851.88, 1369.98, 689.2,
580.5, 751.74, 547.67, 556.64, 493.85, 404.15, 428.07, 716.2,
1442.05, 1045.81, 1497.07, 567.59, 155.07, 537.72, 446.03, 282.57,
642.88, 409.37, 338.91, 173.89, 358.63, 195.42, 209.95, 186.44,
152.34, 105.51, 132.26, 82.14, 122.88, 149.38, 211.42, 350.17,
429.72, 336.4, 982.21, 1436.25, 1726.87, 1830.42, 1282.05, 1293.4,
1121.01, 946.2, 707.1, 154.53, 767.56, 607.78, 448, 288.23, 270.32,
223.93, 166.22, 262.45, 223.74, 159.31, 210.44, 257.94, 183.99,
151.38, 206.11, 193.43, 388.95, 577.98, 304.64, 285.13, 256.59,
420.26, 289.34, 356.02, 358.08, 325.22, 275.95, 164.46, 213.23,
142.99, 221.66, 270.61, 206.56, 213.68, 254.33, 250.15, 267.99,
403.95, 671.2, 1574.11, 396.34, 477.88, 631.08, 618.25, 1366.88,
298.19, 287.05, 290.38, 332.44, 235.9, 229.79, 831.6, 1320.86,
477.31, 944.84, 547.33, 411.21, 705.43, 873.49, 572.81, 585.36,
1229.69, 701.01, 653.49, 74.81, 162.47, 179.54, 330.27, 544.51,
332.41, 296.66, 130.66, 1055.61, 556.79, 265.43, 383.44, 398.22,
362.66, 223.99, 130.35, 193.67, 217.68, 273.3, 247.84, 161.66,
320.08, 322.52, 274.61, 811.44, 353.85, 323.41, 383.61, 389.5
), .Dim = c(1248L, 1L), .Dimnames = list(NULL, "power"))
Temperature predictor values are:
temp<-structure(c(31, 31, 31, 31, 30, 29, 28, 27.5, 27, 26, 26, 26,
26, 26, 26, 28, 29, 29, 30, 31, 32, 33, 33, 34, 34, 35, 36, 36,
36.5, 37, 38, 38, 39, 39, 39, 38, 37, 36, 36, 35, 34, 33, 33,
33, 32.5, 32, 32, 31, 30, 26, 24, 24, 24, 24, 24, 24, 25, 25,
25, 25, 26, 26, 26, 27, 28.3, 29.7, 31, 32, 33, 33, 34, 34, 34,
35, 35, 35, 36, 37, 38, 39, 39, 39, 39, 38.5, 38, 37, 36, 35,
34, 34, 33, 32.5, 32, 30, 30, 30, 28, 28, 27, 25, 25, 24, 24,
24, 24, 24, 25, 25, 25, 25, 25, 27, 28, 30, 31, 33, 34, 37, 37,
38, 38, 39, 39.3, 39.7, 40, 40, 40, 40, 41, 40, 40, 38, 38, 36,
35, 34, 33, 31, 31, 30, 31, 30, 30, 29, 28, 28, 28, 27, 27, 28,
27, 24, 24, 24, 23, 23, 23, 24, 24, 26, 27, 28, 29.7, 31.3, 33,
34, 35.3, 36.7, 38, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39,
39, 38, 37, 36, 34, 33, 32, 32, 30, 28.5, 27, 27, 27, 27, 27,
26, 26, 26, 25.3, 24.7, 24, 24, 24, 24, 23, 23, 24.5, 26, 28,
29.7, 31.3, 33, 34.5, 36, 37, 38, 39, 40, 40, 40.3, 40.7, 41,
41, 41, 41, 41, 41, 41, 39.5, 38, 37, 37, 35, 34, 34, 33, 33,
33, 32, 31, 31, 30, 30, 30, 29, 29, 28.5, 28, 28, 28, 29, 29,
28.5, 28, 29, 29, 30, 31, 31, 32.5, 34, 35, 37, 39.5, 42, 42,
42, 42, 42, 43, 44, 45, 45, 44, 43, 42, 42, 41, 39, 36.5, 34,
34, 33, 33, 33, 33, 33, 33, 32, 32, 32, 32, 31.5, 31, 30, 30,
30, 29, 29, 28, 27, 28, 29, 30, 31, 32.5, 34, 34, 35, 37, 40,
41, 41, 42, 42, 42.5, 43, 43, 43, 42, 42, 43, 42, 42, 41, 40,
39, 37.5, 36, 35, 35, 34, 34, 33, 32, 32, 32, 32, 31, 31, 31,
31, 31, 28, 28, 28, 28, 28, 28.5, 29, 30, 30.5, 31, 32, 33.5,
35, 36, 37, 38, 39, 38, 39, 40, 41, 42, 42, 43, 42, 42, 42, 41,
41, 40, 39, 38, 37, 36, 35, 34, 34, 33, 32, 32, 31, 30.5, 30,
30, 30, 30, 29, 29, 29, 28, 27, 27, 27, 27, 28.5, 30, 31.5, 33,
34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 42, 42, 42, 42, 42, 42,
42, 42, 42, 42, 40, 40, 39, 37, 37, 36.5, 36, 35, 34, 34, 33,
33, 32, 32, 32, 32, 32, 32, 31, 31, 30, 30, 30, 30, 31, 31, 31,
32, 33.5, 35, 35.5, 36, 37, 37, 38, 39, 40, 41, 41, 42, 42, 42,
43, 43, 42, 41, 41, 40, 38, 36, 35, 34, 34, 35, 36, 36, 35, 35,
33, 33, 32, 31, 31, 30, 30, 29, 29, 29, 29, 29, 31, 31.5, 32,
31, 30, 31, 32, 33, 34, 34, 35, 36, 36, 37, 37, 38, 38, 38, 39,
39, 39, 39, 39, 39, 39, 38, 37, 37, 37, 37, 35, 33, 31, 31, 31,
30, 30, 30, 30, 30, 30, 30, 30, 29, 29, 28, 28, 27, 27, 26, 29,
29, 30, 31, 32, 32, 33, 33, 33, 34, 34, 35, 35, 37, 37, 37, 37,
37, 38, 38, 38, 38, 37, 37, 36, 35, 34.5, 34, 34, 33, 33, 32,
32, 32, 32, 32, 31, 31, 31, 31, 31, 31, 31, 30, 30, 29.5, 29,
29, 30, 30, 31, 32, 32, 33, 33.5, 34, 34, 34, 30.7, 27.3, 24,
24, 24, 24.7, 25.3, 26, 27, 28, 29, 29, 29, 28, 28, 27, 27, 26,
25, 25, 25, 24.5, 24, 24, 24, 24, 24, 24, 24, 24, 23, 23, 23,
23, 23, 23, 24, 24, 24, 25, 25, 26, 28, 29, 30, 31, 31, 32, 33,
34, 35, 35, 36, 37, 37, 37, 37, 37, 37, 37, 35, 34, 33, 33, 33,
32, 31.7, 31.3, 31, 31, 31, 31, 30, 30, 30, 30, 28, 28, 27, 27,
26, 26, 25, 25, 25, 25, 25, 26, 27, 28, 29.7, 31.3, 33, 34, 34,
35, 36, 37, 36, 36, 35, 35, 34, 32, 32, 33, 31.3, 29.7, 28, 28,
29, 29, 29, 29, 28, 27.5, 27, 26.5, 26, 26, 26, 26, 26, 26, 25,
25, 25, 25, 25, 24, 24, 23, 23, 23, 24.5, 26, 27, 28, 29, 30,
31, 32, 32, 32, 33, 34, 35, 36, 36, 36, 36, 36, 36, 36, 37, 37,
37, 36, 36, 34, 34, 33, 32, 32, 31, 31, 30, 28, 28, 28, 28, 27,
27, 27, 27, 27, 27, 27, 27, 26.5, 26, 26, 26, 26, 27, 28.8, 30.5,
32.2, 34, 34, 34, 35, 36, 37, 38, 38, 38, 39, 40, 39, 39, 39,
40, 40, 40, 39, 39, 38, 37, 35, 35, 34, 34, 34, 33, 32, 32, 32,
32, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 32, 33, 34,
35, 37, 37, 37.3, 37.7, 38, 39, 40, 43, 43, 43, 44, 44, 43, 43,
43, 43, 43, 43, 42, 41, 40, 39, 38, 37, 36, 35, 35, 34, 34, 34,
34, 34, 33, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 34,
35, 36, 37, 38, 38, 40, 40.5, 41, 42, 42, 42, 42, 41, 40, 40,
39, 39, 37, 32, 27, 26, 26, 27, 28, 27, 27, 27, 26, 25, 25, 25,
25, 25, 25, 25, 25, 25, 25, 25, 24, 23, 23, 22.5, 22, 22, 23,
24, 25, 26.3, 27.7, 29, 30, 32, 33, 34, 36, 37, 37, 39, 40, 40.5,
41, 42, 42, 42, 43, 43, 42, 41.5, 41, 39, 38, 35, 35, 35, 34,
33, 33, 33, 33, 32, 32, 31, 31, 30, 30, 30, 29, 29, 28, 28, 28,
28.5, 29, 29, 29, 30, 32, 32, 34, 35, 37, 38, 39, 40, 41, 42,
42, 43, 44, 44, 44, 45, 45, 45, 44, 43, 43, 42, 40, 38.5, 37,
35, 35, 34, 34, 33, 34, 33, 33, 33, 33, 32, 32, 31, 32, 31, 30,
29, 29, 29, 29, 30, 30, 31, 32.7, 34.3, 36, 37, 38, 39, 40, 41,
41, 42, 42, 43, 44, 44, 44, 44, 44, 43.5, 43, 43, 42, 42, 40,
38, 38, 37, 36, 36, 36, 36, 35, 35, 34, 34, 34, 34, 32, 32, 31.5,
31, 31, 30, 30, 30, 30, 31, 33, 34, 35, 37, 38, 39, 40, 40, 42,
42, 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 43, 42, 40, 40,
40, 39, 38, 38, 38, 37, 37, 36, 36, 35.5, 35, 34.5, 34, 33, 33,
32, 32, 31, 30, 30, 30, 31, 32, 33.5, 35, 36.5, 38, 38, 39, 40,
41, 41, 41, 42, 42, 42, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43,
42, 40.5, 39, 38, 38, 37, 37, 37, 36, 36, 36, 36, 36, 36, 36,
35, 35, 34, 34, 34, 32, 32, 31, 31, 33, 34, 35, 35, 36, 38, 39,
40, 41, 42, 42.5, 43, 43, 44, 44, 45, 45, 45, 45, 45, 45, 45,
44, 43.5, 43, 43, 42, 41, 40, 40, 39, 39, 38, 38, 37, 36, 36,
35, 34, 34, 34, 32, 32, 32, 32, 32, 32, 32, 34, 35, 35, 37, 38,
38, 39, 39, 40, 41, 42, 43, 44, 44, 44, 45, 45, 46, 46, 46, 45,
45, 45, 44, 42, 40, 38, 37, 37, 37, 37, 37, 36, 35), .Dim = c(1248L,
1L), .Dimnames = list(NULL, "temperature"))
Forecasted temperature values are:
forecast_temp <- structure(c(35, 34, 34, 33, 33, 30, 29.7, 29.3, 29, 28, 28, 27,
27.3, 27.7, 28, 29, 30.5, 32, 33.5, 35, 36, 36, 37, 39, 39.5,
40, 40, 41, 42, 42, 43, 43, 43, 44, 44, 44, 43, 42, 40, 39, 39,
38, 37, 37, 36, 35, 35, 34), .Dim = c(48L, 1L), .Dimnames = list(
NULL, "temperature"))
UPDATE-1
From @Stephan's suggestion, I followed the approach mentioned by Prof. Rob at link1, link2 as
library(forecast)
tsob <- ts(train_power,frequency = 48) #training electriciy data at daily frequency
tsob_weekly <- fourier(ts(train_power,frequency = 7*48),K=3) #training data at weekly frequency
tempob <- ts(train_temperature,frequency = 48) #Temperature, another predictor variable
fit <- auto.arima(tsob,xreg=cbind(tsob_weekly,tempob),seasonal=FALSE)
tempob_forecast <- ts(test_temperature,frequency = 48) #forecasted temperauture values
forecast_val <- forecast(fit,xreg=tempob_forecast,h=48*5) #forecast for coming 5 days
As evident from the code, I have used Fourier transformation suggested at above links to show weekly seasonal affect. Up to auto.arima(), it works properly but at forecast function an error is thrown as:
Error in forecast.Arima(fit, xreg = tempob_forecast, h = 48 * 5) :
Number of regressors does not match fitted model
The error is clear, i.e., I do not provide the forecasted regressor values of tsob_weekly, which I don't have. How should I handle this issue? Prof. Rob has used the same value of regressor for both the auto.arima and forecast functions.
Best Answer
This is a nice question.
First, note that the
arima(),Arima()andauto.arima()functions in R fit regressions with ARIMA errors, not ARIMAX models, and yes, there is a difference.This immediately suggests one possible way forward: regress your historical data on your regressors, using
lm()or similar (possibly accounting for heteroskedasticity). Afterwards, fit atbatsmodel to the residuals from that initial regression. For forecasting, forecast both models separately and add the predictions.Alternatively, you could "roll your own model". Use
lm()or similar to regress your observations on temperature etc., and also add periodic dummies to capture the seasonality. For instance, periodic B-splines or "bumps" are often nice for time seasonality, and you could use six Boolean dummies for the days of the week, since adjacent days will be less similar than adjacent hours.