机器算法验证 - ARIMA 预测直线？ - 吾爱随笔录

ARIMA 预测直线？

机器算法验证预测有马预言

2022-03-18 09:56:01

我有 856 个观测值的每日平均温度数据，没有丢失数据。

我auto.arima()从forecast包中使用并获得了 ARIMA(1,1,2) 模型：

fit <- auto.arima(y, stepwise=FALSE, approximation=FALSE)

我的目标是预测一年甚至更长的每日温度。每次运行预测时获得不同的试验/值非常重要，以便在给定时间获得分布函数。有人建议引导，但我不知道如何使用它......

另一个问题是我在预测时得到一条直线而不是锯齿形：

plot(forecast(fit, h=730))

我该如何解决这个问题以获得每个预测的不同值和一条漂亮的之字形线？

这是数据（的输出dput(y)）：

structure(c(2.72107, 2.07831, 2.28904, 5.19602, 3.91104, 4.72452, 
  6.93097, 3.47825, 3.32989, 5.07382, 4.63729, 4.1209, 4.97381, 5.36145, 
  5.20141, 6.50965, 6.11698, 5.17949, 5.59227, 5.98244, 8.89354, 11.6026, 
  10.9734, 8.35629, 6.45573, 4.29485, 4.02906, 5.86246, 7.05204, 9.25902, 
  12.1916, 10.1092, 8.29306, 8.3226, 4.91195, 3.23493, 7.56046, 9.65728, 
  10.5852, 9.71882, 9.89834, 9.70065, 10.881, 7.94012, 7.96884, 6.76446, 
  5.87689, 7.42511, 7.23663, 6.88842, 7.46532, 8.28891, 9.98618, 12.8484, 
  15.0866, 16.1529, 12.998, 11.2972, 10.4044, 18.1593, 13.0845, 10.1179, 
  9.73825, 11.699, 13.7335, 15.8953, 12.2394, 14.6368, 17.3849, 17.7564, 
  16.4018, 13.3457, 10.1037, 11.9855, 13.6543, 12.8223, 12.7669, 14.8924, 
  20.8229, 20.9681, 19.4538, 15.8028, 16.2083, 18.5207, 13.8544, 16.5748, 
  19.8769, 13.0502, 14.1493, 17.4757, 13.4282, 13.626, 17.5759, 18.4219, 
  16.1828, 15.7175, 15.9433, 18.4769, 19.4068, 19.804, 15.0896, 13.0475, 
  16.2968, 18.4375, 15.5119, 18.3765, 16.6796, 20.6907, 21.1161, 20.6478, 
  23.9783, 26.679, 23.1433, 18.3136, 17.6282, 19.4527, 22.0328, 23.9067, 
  24.0465, 20.467, 18.9685, 15.6098, 18.9734, 18.469, 16.3081, 15.9136, 
  17.9241, 17.684, 13.4759, 15.3975, 20.9233, 21.5037, 21.2381, 21.6311, 
  24.0587, 25.0831, 24.6393, 26.3389, 29.1436, 31.3079, 30.4857, 24.8496, 
  27.8717, 21.693, 17.8961, 18.3907, 19.2113, 20.6967, 19.7234, 19.7314, 
  21.7928, 25.1407, 27.7266, 26.6256, 21.084, 23.1858, 26.1919, 27.907, 
  23.4193, 23.788, 24.127, 21.0114, 20.5417, 19.7877, 19.4958, 18.7987, 
  17.5373, 21.6209, 25.4621, 27.2367, 28.1586, 25.1398, 28.5401, 29.7519, 
  28.2289, 25.1979, 27.5075, 29.6323, 25.5448, 26.0691, 28.2604, 27.7191, 
  25.9823, 25.0804, 21.6709, 22.1457, 22.2224, 22.649, 22.6009, 21.5145, 
  23.8828, 21.0305, 22.9268, 22.7175, 19.8786, 21.2565, 24.217, 28.7001, 
  25.0747, 19.1498, 17.2221, 17.9607, 16.7414, 15.9127, 16.0407, 16.3318,       
  15.1847, 16.2885, 15.5795, 19.1367, 20.6138, 19.1671, 17.0597, 18.4442, 
  20.6328, 17.2387, 16.6262, 15.0164, 14.4777, 16.652, 15.549, 15.6622, 
  15.648, 15.0444, 14.024, 14.0647, 13.996, 13.5328, 12.3894, 12.6372, 
  14.004, 16.6147, 15.0356, 15.0433, 13.9245, 9.521, 10.2423, 7.6857, 
  6.44648, 5.79129, 5.81486, 6.62451, 7.66923, 9.49628, 9.68583, 10.2271, 
  9.55193, 10.9726, 11.18, 10.3731, 12.7261, 10.0939, 11.4238, 9.04498, 
  9.13095, 8.67738, 7.3758, 8.5583, 11.5121, 10.1994, 8.11629, 5.45508, 
  4.51418, 10.0511, 12.0646, 16.0265, 14.8723, 14.8256, 15.5313, 15.1156, 
  13.5751, 12.4647, 9.20753, 11.6803, 12.1874, 13.0886, 13.1678, 12.4585, 
  9.10043, 6.46029, 3.37006, 2.2908, 2.4312, 4.25444, 5.95889, 3.60558, 
  2.20294, 6.68003, 7.5045, 7.23778, 9.72496, 9.24511, 7.7357, 7.56718, 
  9.35735, 12.0612, 9.39335, 7.61897, 4.42504, 5.30344, 6.76715, 7.29574, 
  2.37094, 6.26673, 7.22273, 10.7688, 11.9598, 10.346, 10.0571, 10.8452, 
  12.109, 11.9974, 7.67068, 10.291, 13.359, 11.5015, 9.96903, 5.44976, 
  1.85815, 0.78936, 3.00597, -1.55573, -7.82983, -7.30225, -6.80859, 
  -6.29809, -3.50606, 3.05057, 1.67047, 1.36792, 3.37618, 4.16687, 
  3.92503, 2.82102, 1.28058, 1.42854, 0.5677, -2.14501, -5.05476, 
  -0.41695, -2.43226, -5.41841, -0.39281, 4.84296, 7.71332, 9.56437, 
  11.0887, 8.18858, 5.8414, 8.03361, 5.6096, 9.51988, 10.3942, 7.05369, 
  4.80606, 4.91824, 8.7106, 7.06899, 8.87901, 9.22051, 6.83539, 5.44371, 
  4.01937, 2.90695, 4.21192, 4.44994, 1.86072, 1.42361, 4.05833, 5.06767, 
  3.9083, 9.2123, 8.6767, 6.64929, 4.55591, 3.16506, 3.36553, 2.66953, 
  4.61189, 2.86679, 3.46284, 6.13807, 5.41028, 4.73737, 7.6795, 4.84524, 
  4.9108, 4.53722, 4.56058, 7.29702, 5.64094, 4.30165, 3.33385, 5.68806, 
  6.04968, 6.52409, 7.5586, 6.0639, 8.24474, 7.06717, 7.5784, 8.51599, 
  6.8743, 6.72083, 7.88874, 11.6331, 10.6445, 10.9836, 9.44053, 9.56508, 
  10.1753, 10.9394, 11.3226, 14.6938, 17.2642, 17.8183, 13.8324, 12.43, 
  11.0775, 11.123, 10.2947, 11.8338, 13.0022, 14.6161, 11.1305, 10.791, 
  12.6827, 11.5605, 10.6563, 12.7656, 11.8701, 12.3721, 11.9769, 10.0403, 
  7.73329, 8.85496, 8.73682, 8.07419, 8.17325, 11.511, 15.145, 15.6102, 
  16.5022, 16.1709, 13.3761, 17.264, 19.687, 20.4323, 21.0252, 21.3723, 
  21.2475, 21.2702, 21.0671, 19.5805, 13.7568, 11.7916, 12.5975, 11.8184, 
  16.3091, 20.1004, 20.0868, 22.3407, 24.2997, 22.7583, 18.9745, 15.9035, 
  16.024, 19.1914, 21.2084, 23.9281, 23.6516, 23.0966, 23.0041, 22.9038, 
  24.5299, 25.7326, 25.4938, 22.6473, 23.7885, 23.8734, 21.9514, 19.2988, 
  20.6958, 18.5028, 16.8761, 20.9387, 18.937, 19.435, 18.4327, 19.8158, 
  20.1101, 21.5998, 21.9932, 24.751, 29.3753, 31.5999, 29.4495, 22.9165, 
  23.2686, 23.2402, 22.9602, 22.2173, 25.9632, 21.593, 20.2721, 21.5224, 
  22.341, 18.6498, 20.1219, 21.8584, 21.6239, 28.0738, 26.4142, 24.7725, 
  21.4159, 17.5402, 17.3853, 21.0012, 22.416, 21.1456, 24.0809, 26.4007, 
  25.5508, 26.0414, 24.3579, 26.1739, 27.2164, 26.8201, 22.8504, 24.2559, 
  24.2006, 24.1552, 23.2342, 21.051, 18.4151, 20.9081, 21.6861, 20.6203, 
  20.4817, 22.5381, 24.1143, 19.6215, 16.6826, 16.2553, 18.6091, 24.0527, 
  21.3717, 19.4247, 18.5746, 18.7393, 18.4001, 22.8524, 22.7096, 20.6259, 
  21.2019, 21.87, 24.6202, 24.5928, 26.9341, 26.6528, 26.7856, 22.2157, 
  19.9978, 21.8183, 21.9206, 22.9321, 23.6834, 21.3737, 20.1084, 19.7119, 
  21.2076, 23.822, 23.8937, 23.4248, 25.1253, 25.6262, 25.5971, 24.2764, 
  22.0123, 22.1025, 19.9025, 17.8464, 17.7661, 16.6241, 17.323, 15.7588, 
  18.1355, 17.9416, 16.9906, 17.0112, 16.7238, 17.8862, 21.1513, 18.0348, 
  14.3367, 15.6564, 13.8713, 13.7946, 11.2834, 11.7613, 11.885, 11.5518, 
  10.1908, 10.3692, 9.66055, 8.75373, 8.11604, 9.20452, 10.0488, 10.4606, 
  9.51533, 11.2533, 11.3637, 9.82202, 9.48856, 9.40134, 9.27895, 9.38484, 
  9.79952, 8.88519, 9.56215, 12.2427, 10.7091, 9.51377, 8.09934, 10.8873, 
  7.91766, 5.03482, 6.79236, 8.02243, 7.74082, 5.97028, 4.93483, 2.84844, 
  2.32958, 2.47728, 0.47363, -0.76344, 0.09932, 4.81134, 8.81348, 
  10.3823, 10.8289, 7.0082, 6.53356, 9.58075, 10.5326, 8.3427, 6.55907, 
  3.43094, 2.91497, 2.75453, 1.51518, 0.21427, 2.24033, 5.84257, 4.55094, 
  1.28517, 0.44241, -1.07106, 1.5077, 3.62158, 8.52128, 8.64829, 10.4853, 
  8.7851, 3.99424, 2.03719, 5.40644, 4.14184, 1.94103, 0.49676, 4.73742, 
  5.46961, 2.09845, 0.8062, 1.13084, 4.14573, 5.41751, 7.99036, 9.54456, 
  7.88317, 7.38799, 4.7107, 1.23217, 1.34194, 3.12594, 2.34215, 3.92943, 
  4.28814, -1.53473, -4.34937, -4.16307, -1.25413, -0.09237, -1.31465, 
  -0.73119, 4.82179, 2.77908, 1.39675, 1.68791, -0.38393, -0.9407, 
  -2.50807, -1.0896, 1.48579, 3.35333, 1.50063, -1.34165, 0.59049, 
  2.07425, 1.62417, -0.45723, -2.24363, 1.2715, 1.70886, 1.32975, 1.4235, 
  0.9802, 1.76901, 2.76971, 3.04066, 0.54875, 0.09775, -1.96935, 
  -2.13567, -1.34802, -0.7473, -0.67197, -1.6728, -1.46587, 3.21076, 
  6.30966, 6.53933, 5.62505, 5.5555, 8.67007, 8.87044, 8.66096, 8.24027, 
  5.36522, 4.60007, 9.09482, 10.9243, 10.1554, 6.20283, 7.00011, 7.76748, 
  10.4434, 11.0272, 7.61685, 4.76488, 8.14287, 9.63522, 8.39318, 4.85702, 
  4.04467, 5.76991, 8.27829, 11.6219, 9.99523, 9.03931, 8.4335, 6.2979, 
  12.9158, 11.189, 8.99983, 8.23214, 10.008, 9.91901, 9.73224, 12.2664, 
  14.6688, 12.9589, 15.8025, 17.6097, 18.3155, 16.456, 11.5136, 11.4097, 
  12.1716, 11.1276, 10.7415, 12.9543, 16.4937, 14.3856, 9.6745, 11.7042, 
  11.2507, 10.6121, 10.2075, 7.9494, 8.26806, 7.21374, 5.15729, 5.86262, 
  11.5133, 9.20826, 8.23779, 10.0843, 10.5073, 8.72061, 10.8578, 10.7059, 
  10.4765, 10.5897, 12.0793, 11.509, 13.7639, 10.9014, 13.0556, 15.2923, 
  16.9558, 10.1238, 8.65529, 11.9741, 15.5228, 18.4538, 18.4287, 18.2232, 
  19.961, 17.3346, 23.6051, 24.8603, 25.0482, 18.7485, 20.2472, 20.9434, 
  20.6219, 15.9234, 17.3461, 21.7219, 23.1824, 25.6746, 27.706, 25.5171, 
  21.6963, 19.7247, 22.6762, 19.4907, 19.0308, 20.3303, 21.4342, 18.2569, 
  18.8592, 23.5841, 22.4464, 25.9043, 22.603, 19.2794, 21.1827, 24.1214, 
  19.5582, 19.7619, 23.9857, 28.3474), .Dim = c(856L, 1L), .Dimnames = 
  list(NULL, "AT [Celcius]"), .Tsp = c(1, 856, 1), class = "ts")

1个回答

通常，平坦的预测实际上比非平凡的 ARIMA 更好，仅提及这一点。

但是，您的数据肯定不是这种情况。

一个问题是您没有告诉 R 您的数据是频率为 365 的时间序列。在这种情况下，R 不能“自行”确定存在季节性。毕竟，一长串数据可能具有各种季节性，例如，周期长度为 7（具有每周季节性的每日数据）、365.25（具有年度季节性的每日数据）、30（具有每月季节性的每日数据）、60、 3600、24（我让你猜）、11（每年的太阳黑子数据）等等。你不能只是“让算法决定”。frequency如果您的时间序列可能是季节性的，请始终指定参数。

即使您指定了frequency，ARIMA 在检测数据中很少长周期的季节性方面存在重大问题 - 即使季节性对于人类来说是“明显的”。

library(forecast)

set.seed(1)
temps <- 20+10*sin(2*pi*(1:856)/365)+arima.sim(list(0.8),856,sd=2)

plot(forecast(auto.arima(temps),h=365))
plot(forecast(auto.arima(ts(temps,frequency=365)),h=365))

最后两个命令实际上产生了完全相同的图，因为auto.arima()根本没有检测到季节性。

解决方案是通过指定强制auto.arima()使用季节性模型D=1：

plot(forecast(auto.arima(ts(temps,frequency=365),D=1),h=365))

另请参阅这个较早的问题。

所以。这有望解决您的一个问题。你的另一个问题是，老实说，我不清楚。每次运行建模时，您如何期望得到不同的预测（假设您每次都在相同的数据上重新运行）？ARIMA 不涉及任何随机化。它是确定性的。

但是，您确实已经获得了预测分布和预测区间。查看预测的扇形图。

也许这个较早的问题是有帮助的：如何将实际历史数据的不确定性纳入预测预测区间？

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