0
$\begingroup$

I have half-hourly electricity data of several homes for a duration of one month. This data is represented in xts time-series format. Now, I need to make half-hourly forecasts using the same data for coming day. The forecasting interval is one day (i.e., very short term forecast). I assume that electricity usage follows daywise seasonality as the number of users/occupants remain fixed. This assumption is obeyed in some homes while some other follow random electricity usage.

Currently, I use historical one month data to make half-hourly forecasts of coming day using auto.arima found in forecast pacakage. Using this approach I do get forecasts for next day (48 forecasted values). 48 forecasted values correspond to 48 half-hours of the day. But, I do not know

  1. How should I specify the seasonality fact, i.e., how should I mention that data is assumed seasonal day-wise. In other words, how should I mention within historical data of one month, there are 30 periods and each period consist of 48 observations.
  2. Is xts representation suitable for this task or I need to represent this in ts format?

Here I have attached half-hourly data of 26 days. I have removed timestamps in order to fit the data according to stackExchange limits. This data does not contain any missing readings. It contains 1248 (26 x 48) observations

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"))
$\endgroup$
2
$\begingroup$

On the one hand, you can certainly use ts objects. Specify the season length through the frequency parameter:

auto.arima(ts(data[,1],frequency=48))

However, electricity consumption usually has multiple seasonalities. You have the intra-day seasonality, but you will usually also have weekly seasonality, since weekends have different power consumption than weekdays - people are at home instead of at work, industrial production is reduced etc. Plus, there may be yearly seasonality, with air conditioners and heaters consuming a lot of electricity in summer/winter.

Use msts objects to encode time series with multiple seasonalities:

msts(data[,1],seasonal.periods=c(48,7*48))

You can then fit models with multiple seasonalities using tbats:

tbats(msts(data[,1],seasonal.periods=c(48,7*48)))

Both are again in the forecast package. You may want to look at earlier questions on "multiple seasonalities".

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.