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I am working on a weekly revenue forecasting problem and have developed time series models using Holt winter, ARIMA, SARIMA techniques.

ARIMA/SARIMA models are able to follow the variation in training data. But it generates nearly flat prediction for the test period. These models have been developed using auto.arima() in R and best model with lowest AICc are ARIMA(2,1,3) and SARIMA ((3,1,1), (1,0,0)[52]) respectively. 

fit.test <- model_arima %>% forecast(h=length(ts_test))

I am unable to understand what can be the reason for flat predictions from ARIMA/SARIMA models and how can I fix it? Any explanation whether it is normal or am I doing something wrong? I have performed stationarity check and investigated ACF, PACF plots to verify the pdq and PDQ values. They look reasonable.

Attaching the actual and prediction from 3 models (restricted to last 3 years for legibility).Actual and Prediction]1

Please note that : 1) Holt-winter model is giving less accurate but more sensible result (follows the pattern). ARIMA/SARIMA model is able to follow the the pattern during training period but failing during test period. 2) The target variable time series has considerable trend and seasonality component.

seasonal_contribution <- round(100*mean(abs(ts_train_decomposed$seasonal/ts_train), na.rm = TRUE),1)

Output: 13.2%

random_contribution <- round(100*mean(abs(ts_train_decomposed $random/ts_train), na.rm = TRUE),1)

Output: 7.7%

trend_contribution <- round(100*mean(abs(ts_train_decomposed $trend/ts_train), na.rm = TRUE),1)

Output: 104% (more than 100 is due to absolute function)

Any thoughts/help?

Here is the data:

Start = FY2010, Week 01 End = FY2018, Week 13

1959189, 1573675, 1258684, 1038388, 1346920, 1156653, 1172789, 782047, 870728, 1133976, 1011534, 1304332, 1269927, 1047852, 1361486, 1005164, 1246667, 1267948, 1041692, 1142241, 1259407, 933189, 782047, 1514561, 1759276, 1334329, 922097, 1047790, 1279392, 1239161, 1111337, 1045116, 1201222, 929220, 805944, 819779, 1522034, 1104780, 1239074, 1622941, 880228, 863659, 828446, 1330982, 895415, 1118139, 903667, 1158941, 1068804, 2307597, 1137761, 1196090, 873531, 1104650, 1716808, 796287, 1123559, 1316773, 1029280, 1068907, 782047, 1432149, 1204378, 1023484, 1512827, 1231125, 1468412, 1510226, 1436849, 1319531, 1317915, 1198752, 1388767, 1352301, 1324010, 1269487, 1863747, 2058150, 1413770, 1321356, 1463094, 1715242, 1526448, 1143213, 1561302, 1442019, 1788990, 1499733, 1042288, 1668024, 1952906, 1653359, 1591791, 1494158, 1353269, 1865162, 1546087, 1239404, 1582361, 1368341, 1754117, 1396834, 1220825, 1435585, 1847726, 1720784, 1604816, 1130380, 1565318, 1445552, 1631004, 2009591, 1297239, 1184528, 1554808, 1416285, 2239310, 2218959, 1189417, 1807349, 1891570, 1676539, 1220811, 1605616, 1664673, 2556152, 1610225, 1722956, 1757235, 1450615, 1378257, 2333802, 2556152, 2233017, 1398128, 1480723, 1923171, 1875508, 1261523, 1586025, 1604109, 1941551, 1501347, 2288835, 1251904, 1802435, 2093982, 1740865, 1237555, 1897851, 1543548, 1173039, 1259979, 1601316, 1446519, 1076966, 954971, 1129883, 1263593, 782047, 897828, 1290891, 1413336, 997762, 983204, 782047, 1065418, 1159127, 791068, 1043431, 782047, 830819, 922374, 1021230, 847911, 782047, 1057342, 782047, 1157389, 1272318, 1289570, 1395980, 1223472, 978282, 1321670, 959815, 1475352, 1106440, 800046, 821108, 818370, 782047, 782047, 1242577, 1081033, 782047, 1448997, 1191356, 1429888, 1310220, 952511, 955341, 1051744, 1089665, 1131111, 1006489, 1192535, 1227825, 1036490, 1496919, 1049842, 1083797, 1107783, 1024543, 1855261, 1462685, 782047, 940500, 1613491, 1808394, 2212106, 1827206, 1923534, 1588854, 1676109, 2234710, 1355893, 1642197, 2226086, 1674348, 1614326, 2107147, 1568432, 1552264, 1278844, 1378970, 1961640, 1660352, 1144726, 2143711, 2051977, 1931923, 1974407, 1597270, 2153559, 1635501, 2286962, 1945646, 2228916, 1725973, 1639916, 1991420, 1079652, 1926280, 1615502, 2556152, 2556152, 1645739, 1746870, 2441064, 2031501, 2001977, 2006674, 2556152, 1521703, 2205566, 2170396, 2556152, 1302373, 1485302, 2416051, 2196048, 2138209, 1586797, 1875878, 2556152, 1645020, 2455561, 2172600, 2556152, 2124959, 1118315, 2556152, 1407323, 2555802, 1514549, 1870840, 1833463, 2153760, 1864644, 2310299, 1774127, 1635691, 1952792, 2113635, 2470245, 1825313, 1637294, 2189646, 1757277, 1803715, 1643972, 1789035, 1767729, 2073812, 1339570, 1539184, 1455790, 1959051, 2100652, 2106001, 2037153, 1696659, 1811707, 1809964, 1717314, 2144991, 2070006, 1899734, 1353059, 1528576, 1825641, 1806848, 1486352, 2412612, 2088937, 1529353, 2556152, 2076129, 2471180, 1453428, 1656793, 1652996, 1531299, 2556152, 1936218, 2093920, 2556152, 2226654, 1650638, 2286591, 2058582, 1365863, 1894659, 1417108, 2231441, 2556152, 1429978, 1938148, 2024870, 2424811, 1728066, 2074629, 1475372, 2556152, 2171855, 1380194, 2556152, 2556152, 2486197, 1755661, 2255167, 2065043, 1717144, 2084956, 1806475, 2431370, 1686421, 2556152, 1689584, 1889099, 2521364, 1567775, 1420724, 1296041, 2401485, 2556152, 2125505, 2154862, 2382272, 1467155, 1729242, 2390314, 1771184, 2443733, 2399748, 2261835, 2184166, 2463478, 1694602, 2275110, 2206839, 2556152, 1799998, 1776979, 2186701, 1818336, 2113879, 2204912, 1859430, 1793548, 2556152, 1900793, 1739210, 2556152, 1387605, 2090728, 1575912, 1553005, 2556152, 1895172, 2351205, 1980909, 1754811, 1594241, 2100697, 1638142, 2233797, 2552686, 2523388, 1725781, 1549130, 1697765, 1758447, 1192503, 1624003, 2556152, 1479136, 2353199

Mark
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1 Answers1

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HW uses trend and seasonal dummies (in a presumptive way ) thus their deterministic forecasts can be different while ARIMA uses memory (previous values) which in your case converge. Post your data in a csv file and I will try to help further. The solution is to correctly/optimally integrate deterministic structure and memory . See How to determine order of sarima? for my comments on identifying and combining deterministic structure and memory.

IrishStat
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