R
如何找到時間序列之間的相似性？
在以下示例中，我有一個數據框，其中包含在海洋中 5 個深度記錄的水溫測量的時間序列，其中 in 的每個值
Temp對應於 in 的日期DateTime和 in 的深度Depth。set.seed(1) Temp <- rnorm(43800,sd=20) AirT <- rnorm(8760,sd=20) Depth <- c(1:5) DateTime = seq(from=as.POSIXct("2010-01-01 00:00"), to=as.POSIXct("2010-12-31 23:00"), length=8760) Time <- as.POSIXct(DateTime, format = "%Y-%m-%d %H:%M") DatT <- data.frame(Temp) ## bind together FinalDat <- cbind(DatT, Date = rep(Time,5)) FinalDat <- cbind(FinalDat, AirT = rep(AirT, 5), Depth = rep(Depth, each = 8760), Doy = as.numeric(format(Time,format = "%j")), DecTime = rep(seq(1,366, length = 8760),5))從中我想找到
AirT這些不同深度的氣溫（ ）和水溫之間的相似性。我可以計算不同深度的氣溫和水溫之間的相關性，這表明相關性隨著深度而降低，但是，我正在尋找一種更複雜的方法（而不是為每個時間序列接收一個值）。任何人都可以提出一個適當的方法來實現這一目標嗎？這是我的 data.frame (FinalDat) 的精簡版本：
Temp Date AirT Depth 1 3.4069 2011-01-01 6.52710 0.5 2 3.2165 2011-01-08 6.77050 0.5 3 3.5630 2011-01-15 6.61410 0.5 4 3.8027 2011-01-22 -2.94440 0.5 5 3.7328 2011-01-29 -2.92900 0.5 6 4.1008 2011-02-05 12.74800 0.5 7 5.1825 2011-02-12 8.91900 0.5 8 5.0460 2011-02-19 4.43910 0.5 9 5.6156 2011-02-26 8.58090 0.5 10 5.5237 2011-03-05 1.56630 0.5 11 5.5110 2011-03-12 7.94470 0.5 12 6.5645 2011-03-19 -0.25485 0.5 13 7.8872 2011-03-26 4.11280 0.5 14 8.9096 2011-04-02 12.88700 0.5 15 10.8740 2011-04-09 6.34800 0.5 16 10.9600 2011-04-16 9.44190 0.5 17 14.6930 2011-04-23 12.37300 0.5 18 15.1330 2011-04-30 11.40200 0.5 19 14.2740 2011-05-07 14.48400 0.5 20 14.5670 2011-05-14 5.68590 0.5 21 14.0330 2011-05-21 8.36570 0.5 22 13.3870 2011-05-28 11.03900 0.5 23 16.5560 2011-06-04 13.10300 0.5 24 16.4140 2011-06-11 7.56720 0.5 25 16.2590 2011-06-18 12.02400 0.5 26 16.5120 2011-06-25 11.43100 0.5 27 17.9290 2011-07-02 8.75940 0.5 28 18.7150 2011-07-09 13.06100 0.5 29 19.4970 2011-07-16 14.96000 0.5 30 17.7090 2011-07-23 10.06100 0.5 31 19.5090 2011-07-30 11.76200 0.5 32 20.4780 2011-08-06 12.56800 0.5 33 17.8850 2011-08-13 16.93200 0.5 34 17.7440 2011-08-20 14.82700 0.5 35 18.1400 2011-08-27 12.14800 0.5 36 17.0460 2011-09-03 17.19700 0.5 37 16.5960 2011-09-10 18.45800 0.5 38 15.6430 2011-09-17 13.07600 0.5 39 14.9960 2011-09-24 13.19300 0.5 40 16.9880 2011-10-01 20.17800 0.5 41 14.5380 2011-10-08 10.92600 0.5 42 14.3770 2011-10-15 9.64180 0.5 43 12.6210 2011-10-22 11.71200 0.5 44 11.7810 2011-10-29 7.32770 0.5 45 11.8270 2011-11-05 11.15600 0.5 46 10.9790 2011-11-12 11.30000 0.5 47 10.3410 2011-11-19 10.77100 0.5 48 9.6291 2011-11-26 6.81090 0.5 49 8.5466 2011-12-03 9.11540 0.5 50 7.1007 2011-12-10 3.52720 0.5 51 6.3081 2011-12-17 0.32245 0.5 52 6.1304 2011-12-24 5.40000 0.5 53 6.1974 2011-12-31 11.93100 0.5 54 3.2471 2011-01-07 0.44508 4.0 55 3.4851 2011-01-14 8.43040 4.0 56 3.8537 2011-01-21 -2.26530 4.0 57 3.8496 2011-01-28 1.33950 4.0 58 3.8461 2011-02-04 10.18700 4.0 59 4.7892 2011-02-11 6.91330 4.0 60 5.1160 2011-02-18 5.30300 4.0 61 5.4236 2011-02-25 10.40700 4.0 62 5.3190 2011-03-04 3.63990 4.0 63 5.5318 2011-03-11 5.49690 4.0 64 6.0956 2011-03-18 2.12060 4.0 65 6.7955 2011-03-25 5.66700 4.0 66 8.5056 2011-04-01 12.13400 4.0 67 9.8450 2011-04-08 6.11440 4.0 68 10.7220 2011-04-15 9.85800 4.0 69 11.3970 2011-04-22 11.39300 4.0 70 12.6660 2011-04-29 9.54510 4.0 71 13.6370 2011-05-06 12.99600 4.0 72 14.7530 2011-05-13 8.83800 4.0 73 13.8210 2011-05-20 8.81900 4.0 74 13.5120 2011-05-27 10.80500 4.0 75 14.2630 2011-06-03 11.08700 4.0 76 15.6330 2011-06-10 7.20970 4.0 77 15.5290 2011-06-17 10.11400 4.0 78 16.6340 2011-06-24 11.29400 4.0 79 17.4820 2011-07-01 11.43900 4.0 80 17.8620 2011-07-08 13.29700 4.0 81 18.8970 2011-07-15 11.61900 4.0 82 17.4720 2011-07-22 12.73800 4.0 83 17.8640 2011-07-29 14.95600 4.0 84 17.6610 2011-08-05 16.48600 4.0 85 17.4880 2011-08-12 16.06000 4.0 86 17.5980 2011-08-19 11.38900 4.0 87 17.8150 2011-08-26 10.69200 4.0 88 16.7470 2011-09-02 14.71100 4.0 89 16.0230 2011-09-09 14.09600 4.0 90 15.5350 2011-09-16 13.03500 4.0 91 15.0200 2011-09-23 11.81800 4.0 92 15.1200 2011-09-30 14.49800 4.0 93 15.0590 2011-10-07 10.76800 4.0 94 14.5790 2011-10-14 13.91800 4.0 95 12.7810 2011-10-21 8.84760 4.0 96 11.9060 2011-10-28 8.37600 4.0 97 11.7150 2011-11-04 12.57400 4.0 98 11.1170 2011-11-11 11.26200 4.0 99 10.3560 2011-11-18 11.11100 4.0 100 9.8484 2011-11-25 12.91700 4.0 101 8.7573 2011-12-02 2.43560 4.0 102 7.2890 2011-12-09 5.87070 4.0 103 6.4547 2011-12-16 2.31850 4.0 104 6.0336 2011-12-23 11.12900 4.0 105 6.2363 2011-12-30 4.78220 4.0 106 3.4241 2011-01-06 2.92880 6.0 107 3.4075 2011-01-13 9.59030 6.0 108 3.9650 2011-01-20 -1.45990 6.0 109 3.9061 2011-01-27 3.49050 6.0 110 3.8072 2011-02-03 6.15450 6.0 111 4.7597 2011-02-10 8.87270 6.0 112 4.9920 2011-02-17 4.61980 6.0 113 5.1485 2011-02-24 7.66730 6.0 114 5.4556 2011-03-03 -0.73976 6.0 115 5.4305 2011-03-10 9.08700 6.0 116 5.9204 2011-03-17 6.57230 6.0 117 6.4393 2011-03-24 4.21580 6.0 118 6.7361 2011-03-31 9.55530 6.0 119 8.9556 2011-04-07 10.24900 6.0 120 10.7240 2011-04-14 8.15550 6.0 121 10.4810 2011-04-21 9.75940 6.0 122 10.6310 2011-04-28 6.43770 6.0 123 13.2840 2011-05-05 10.70900 6.0 124 14.1380 2011-05-12 9.11810 6.0 125 13.7850 2011-05-19 8.26810 6.0 126 13.6800 2011-05-26 11.65000 6.0 127 13.8950 2011-06-02 13.10500 6.0 128 13.8530 2011-06-09 11.09500 6.0 129 14.6830 2011-06-16 12.63000 6.0 130 15.3570 2011-06-23 12.66100 6.0 131 15.5860 2011-06-30 9.57130 6.0 132 16.2190 2011-07-07 13.84300 6.0 133 16.1140 2011-07-14 10.93200 6.0 134 17.1240 2011-07-21 13.44100 6.0 135 17.2110 2011-07-28 13.41700 6.0 136 16.9800 2011-08-04 14.81500 6.0 137 17.4610 2011-08-11 16.33900 6.0 138 17.5690 2011-08-18 10.04300 6.0 139 17.3600 2011-08-25 11.87600 6.0 140 16.6180 2011-09-01 11.71000 6.0 141 16.1330 2011-09-08 11.84600 6.0 142 15.6770 2011-09-15 12.17800 6.0 143 15.1640 2011-09-22 11.90200 6.0 144 14.8160 2011-09-29 17.07200 6.0 145 15.0100 2011-10-06 13.21700 6.0 146 14.4410 2011-10-13 12.01300 6.0 147 13.0510 2011-10-20 3.75340 6.0 148 12.0580 2011-10-27 8.76700 6.0 149 11.6430 2011-11-03 13.96900 6.0 150 11.1400 2011-11-10 13.03200 6.0 151 10.5090 2011-11-17 8.26000 6.0 152 9.8690 2011-11-24 12.02100 6.0 153 8.9167 2011-12-01 9.64050 6.0 154 7.3953 2011-12-08 4.99180 6.0 155 6.5533 2011-12-15 3.73240 6.0 156 5.9886 2011-12-22 12.69300 6.0 157 6.3341 2011-12-29 7.12550 6.0 158 3.4249 2011-01-05 5.66070 8.0 159 3.4232 2011-01-12 4.42930 8.0 160 3.9632 2011-01-19 0.04384 8.0 161 3.9203 2011-01-26 5.33010 8.0 162 3.7569 2011-02-02 4.74030 8.0 163 4.6606 2011-02-09 6.48010 8.0 164 4.9632 2011-02-16 5.92770 8.0 165 4.9742 2011-02-23 7.15490 8.0 166 5.3302 2011-03-02 1.52250 8.0 167 5.3380 2011-03-09 6.46400 8.0 168 5.7341 2011-03-16 6.49500 8.0 169 6.1663 2011-03-23 4.01320 8.0 170 6.1420 2011-03-30 10.23300 8.0 171 7.1226 2011-04-06 12.10300 8.0 172 8.4905 2011-04-13 5.66120 8.0 173 8.7548 2011-04-20 7.94430 8.0 174 8.7160 2011-04-27 9.66080 8.0 175 10.1360 2011-05-04 5.13940 8.0 176 9.6597 2011-05-11 12.00800 8.0 177 12.8610 2011-05-18 13.42900 8.0 178 13.1300 2011-05-25 7.96200 8.0 179 13.6080 2011-06-01 8.94920 8.0 180 13.4880 2011-06-08 10.58700 8.0 181 13.6130 2011-06-15 14.82200 8.0 182 13.4320 2011-06-22 13.28300 8.0 183 13.3850 2011-06-29 10.09900 8.0 184 13.1230 2011-07-06 14.30500 8.0 185 13.2270 2011-07-13 13.44700 8.0 186 13.3370 2011-07-20 13.27900 8.0 187 13.4860 2011-07-27 16.17600 8.0 188 14.1970 2011-08-03 15.40500 8.0 189 14.0740 2011-08-10 11.20800 8.0 190 14.2160 2011-08-17 10.92000 8.0 191 14.7250 2011-08-24 13.57000 8.0 192 16.2060 2011-08-31 12.35700 8.0 193 15.6070 2011-09-07 13.77500 8.0 194 15.7620 2011-09-14 13.05900 8.0 195 15.1750 2011-09-21 11.50800 8.0 196 14.7600 2011-09-28 15.44600 8.0 197 14.7480 2011-10-05 15.41900 8.0 198 14.3420 2011-10-12 12.46600 8.0 199 13.3520 2011-10-19 8.04520 8.0 200 12.1960 2011-10-26 9.85760 8.0 201 11.6640 2011-11-02 9.94480 8.0 202 11.1650 2011-11-09 9.83490 8.0 203 10.6510 2011-11-16 7.18460 8.0 204 10.0600 2011-11-23 3.36370 8.0 205 9.1110 2011-11-30 6.19500 8.0 206 7.7550 2011-12-07 5.57610 8.0 207 6.7252 2011-12-14 5.46150 8.0 208 5.9302 2011-12-21 6.02540 8.0 209 6.4421 2011-12-28 8.87860 8.0 210 3.5953 2011-01-04 -0.87434 10.0 211 3.3527 2011-01-11 7.57030 10.0 212 3.9915 2011-01-18 4.65410 10.0 213 3.8234 2011-01-25 7.24100 10.0 214 3.8257 2011-02-01 2.03130 10.0 215 4.6403 2011-02-08 4.28250 10.0 216 5.0439 2011-02-15 2.09610 10.0 217 4.9152 2011-02-22 4.52120 10.0 218 5.3290 2011-03-01 4.09410 10.0 219 5.4156 2011-03-08 -0.97393 10.0 220 5.7129 2011-03-15 5.77950 10.0 221 6.0155 2011-03-22 4.84410 10.0 222 5.9742 2011-03-29 4.10630 10.0 223 6.1641 2011-04-05 10.80000 10.0 224 6.4420 2011-04-12 7.07030 10.0 225 6.6906 2011-04-19 9.72580 10.0 226 6.8168 2011-04-26 11.22400 10.0 227 6.5933 2011-05-03 7.08340 10.0 228 7.7907 2011-05-10 10.99000 10.0 229 6.8976 2011-05-17 12.02200 10.0 230 7.1110 2011-05-24 9.37830 10.0 231 10.1990 2011-05-31 7.85870 10.0 232 9.9413 2011-06-07 9.30420 10.0 233 10.2710 2011-06-14 10.07000 10.0 234 9.6727 2011-06-21 15.00500 10.0 235 10.0280 2011-06-28 13.74500 10.0 236 10.3870 2011-07-05 17.47700 10.0 237 9.9664 2011-07-12 15.32100 10.0 238 9.8633 2011-07-19 13.27000 10.0 239 10.1500 2011-07-26 11.90700 10.0 240 9.6085 2011-08-02 17.43300 10.0 241 10.2650 2011-08-09 13.26100 10.0 242 10.2090 2011-08-16 13.34400 10.0 243 9.9657 2011-08-23 16.62600 10.0 244 10.1730 2011-08-30 13.30700 10.0 245 10.4790 2011-09-06 14.72500 10.0 246 10.5400 2011-09-13 14.77800 10.0 247 11.9570 2011-09-20 15.70200 10.0 248 12.4710 2011-09-27 11.22700 10.0 249 12.1980 2011-10-04 13.29700 10.0 250 13.8790 2011-10-11 16.68600 10.0 251 13.7680 2011-10-18 7.88400 10.0 252 12.1430 2011-10-25 13.14200 10.0 253 11.5050 2011-11-01 13.24000 10.0 254 11.1610 2011-11-08 10.43400 10.0 255 10.7390 2011-11-15 9.17300 10.0 256 10.0850 2011-11-22 9.06990 10.0 257 9.1183 2011-11-29 12.74600 10.0 258 7.9380 2011-12-06 4.43310 10.0 259 6.8017 2011-12-13 9.05250 10.0 260 5.9501 2011-12-20 7.67070 10.0 261 6.3240 2011-12-27 10.47900 10.0 262 3.6034 2011-01-03 0.44518 12.0 263 3.2966 2011-01-10 1.92110 12.0 264 3.8193 2011-01-17 5.50270 12.0 265 3.8413 2011-01-24 2.38370 12.0 266 3.8157 2011-01-31 -0.20332 12.0 267 4.3896 2011-02-07 10.31200 12.0 268 4.9550 2011-02-14 6.72160 12.0 269 4.9230 2011-02-21 4.14600 12.0 270 5.3725 2011-02-28 4.17540 12.0 271 5.4386 2011-03-07 -0.17011 12.0 272 5.6663 2011-03-14 -0.20653 12.0 273 5.6173 2011-03-21 9.40060 12.0 274 5.7879 2011-03-28 3.42890 12.0 275 5.8027 2011-04-04 5.26820 12.0 276 5.7847 2011-04-11 8.31470 12.0 277 5.9425 2011-04-18 8.85620 12.0 278 6.2409 2011-04-25 6.88140 12.0 279 5.9921 2011-05-02 9.72310 12.0 280 6.0906 2011-05-09 12.04900 12.0 281 6.0394 2011-05-16 12.44600 12.0 282 6.0922 2011-05-23 9.88280 12.0 283 6.4765 2011-05-30 12.69800 12.0 284 6.6011 2011-06-06 11.33400 12.0 285 6.6846 2011-06-13 15.29900 12.0 286 6.9803 2011-06-20 9.87070 12.0 287 6.6561 2011-06-27 19.08300 12.0 288 7.2964 2011-07-04 12.62800 12.0 289 6.5017 2011-07-11 11.53500 12.0 290 7.4560 2011-07-18 13.64600 12.0 291 7.4972 2011-07-25 9.44130 12.0 292 7.1581 2011-08-01 18.45400 12.0 293 7.4089 2011-08-08 11.82800 12.0 294 7.5630 2011-08-15 12.00700 12.0 295 7.5153 2011-08-22 12.84500 12.0 296 7.4694 2011-08-29 11.80500 12.0 297 7.5982 2011-09-05 11.41900 12.0 298 7.5733 2011-09-12 13.39300 12.0 299 7.7114 2011-09-19 13.35600 12.0 300 7.9359 2011-09-26 15.57900 12.0 301 7.7604 2011-10-03 15.83000 12.0 302 8.2146 2011-10-10 16.05000 12.0 303 8.8018 2011-10-17 11.35400 12.0 304 12.0390 2011-10-24 14.38700 12.0 305 11.3230 2011-10-31 14.43600 12.0 306 11.4140 2011-11-07 2.19910 12.0 307 10.9020 2011-11-14 9.79220 12.0 308 10.1070 2011-11-21 9.87410 12.0 309 9.2805 2011-11-28 4.62830 12.0 310 8.2556 2011-12-05 2.57670 12.0 311 6.9548 2011-12-12 4.16250 12.0 312 6.0980 2011-12-19 1.10680 12.0 313 6.1540 2011-12-26 12.25600 12.0 314 3.6293 2011-01-02 2.14550 14.0 315 3.3969 2011-01-09 4.79400 14.0 316 3.8152 2011-01-16 11.32500 14.0 317 3.9532 2011-01-23 0.58015 14.0 318 3.8262 2011-01-30 -0.96998 14.0 319 4.1869 2011-02-06 10.84800 14.0 320 4.7450 2011-02-13 6.02670 14.0 321 4.9848 2011-02-20 1.09370 14.0 322 5.2429 2011-02-27 5.34090 14.0 323 5.3107 2011-03-06 4.29060 14.0 324 5.5456 2011-03-13 6.86140 14.0 325 5.6181 2011-03-20 6.71190 14.0 326 5.6648 2011-03-27 7.01350 14.0 327 5.6326 2011-04-03 7.26700 14.0 328 5.7413 2011-04-10 9.25000 14.0 329 5.7310 2011-04-17 7.36030 14.0 330 5.6897 2011-04-24 9.62540 14.0 331 5.8051 2011-05-01 9.68150 14.0 332 5.6844 2011-05-08 14.67800 14.0 333 5.7530 2011-05-15 9.46050 14.0 334 5.7696 2011-05-22 10.65700 14.0 335 5.8255 2011-05-29 12.23400 14.0 336 5.8422 2011-06-05 12.08500 14.0 337 5.9016 2011-06-12 5.82010 14.0 338 5.8791 2011-06-19 12.82400 14.0 339 5.9407 2011-06-26 15.17000 14.0 340 5.9502 2011-07-03 11.82400 14.0 341 5.8969 2011-07-10 10.83500 14.0 342 5.9582 2011-07-17 12.44000 14.0 343 6.1421 2011-07-24 12.59700 14.0 344 6.0970 2011-07-31 15.59200 14.0 345 6.1043 2011-08-07 12.65400 14.0 346 6.1677 2011-08-14 13.57600 14.0 347 6.3980 2011-08-21 15.59100 14.0 348 6.4571 2011-08-28 12.29000 14.0 349 6.0783 2011-09-04 15.58600 14.0 350 6.5784 2011-09-11 14.65100 14.0 351 6.5329 2011-09-18 8.72590 14.0 352 6.5395 2011-09-25 14.24400 14.0 353 6.8765 2011-10-02 14.41700 14.0 354 6.5151 2011-10-09 15.62400 14.0 355 6.5328 2011-10-16 10.04000 14.0 356 6.7127 2011-10-23 11.33300 14.0 357 7.0375 2011-10-30 11.93500 14.0 358 7.1903 2011-11-06 6.52240 14.0 359 8.4702 2011-11-13 7.77260 14.0 360 9.5075 2011-11-20 5.02910 14.0 361 9.3919 2011-11-27 13.07300 14.0 362 8.3426 2011-12-04 7.68420 14.0 363 6.9961 2011-12-11 5.19810 14.0 364 6.2100 2011-12-18 0.97878 14.0 365 6.0532 2011-12-25 10.49000 14.0 366 3.5866 2011-01-01 6.52710 16.0 367 3.6081 2011-01-08 6.77050 16.0 368 3.5889 2011-01-15 6.61410 16.0 369 3.9475 2011-01-22 -2.94440 16.0 370 3.8560 2011-01-29 -2.92900 16.0 371 4.0730 2011-02-05 12.74800 16.0 372 4.6510 2011-02-12 8.91900 16.0 373 5.0101 2011-02-19 4.43910 16.0 374 4.8702 2011-02-26 8.58090 16.0 375 5.2720 2011-03-05 1.56630 16.0 376 5.5106 2011-03-12 7.94470 16.0 377 5.6273 2011-03-19 -0.25485 16.0 378 5.6357 2011-03-26 4.11280 16.0 379 5.6058 2011-04-02 12.88700 16.0 380 5.6570 2011-04-09 6.34800 16.0 381 5.6360 2011-04-16 9.44190 16.0 382 5.6088 2011-04-23 12.37300 16.0 383 5.6481 2011-04-30 11.40200 16.0 384 5.6099 2011-05-07 14.48400 16.0 385 5.6895 2011-05-14 5.68590 16.0 386 5.6614 2011-05-21 8.36570 16.0 387 5.6061 2011-05-28 11.03900 16.0 388 5.6570 2011-06-04 13.10300 16.0 389 5.6595 2011-06-11 7.56720 16.0 390 5.6647 2011-06-18 12.02400 16.0 391 5.6749 2011-06-25 11.43100 16.0 392 5.6809 2011-07-02 8.75940 16.0 393 5.6509 2011-07-09 13.06100 16.0 394 5.6534 2011-07-16 14.96000 16.0 395 5.6758 2011-07-23 10.06100 16.0 396 5.8929 2011-07-30 11.76200 16.0 397 5.8423 2011-08-06 12.56800 16.0 398 5.8163 2011-08-13 16.93200 16.0 399 5.8350 2011-08-20 14.82700 16.0 400 5.8429 2011-08-27 12.14800 16.0 401 5.8970 2011-09-03 17.19700 16.0 402 5.8458 2011-09-10 18.45800 16.0 403 5.9711 2011-09-17 13.07600 16.0 404 5.9550 2011-09-24 13.19300 16.0 405 6.1380 2011-10-01 20.17800 16.0 406 6.0951 2011-10-08 10.92600 16.0 407 5.9874 2011-10-15 9.64180 16.0 408 6.1145 2011-10-22 11.71200 16.0 409 6.1598 2011-10-29 7.32770 16.0 410 6.1276 2011-11-05 11.15600 16.0 411 6.2428 2011-11-12 11.30000 16.0 412 6.2374 2011-11-19 10.77100 16.0 413 7.8198 2011-11-26 6.81090 16.0 414 8.4979 2011-12-03 9.11540 16.0 415 7.0908 2011-12-10 3.52720 16.0 416 6.3069 2011-12-17 0.32245 16.0 417 6.1082 2011-12-24 5.40000 16.0 418 6.1375 2011-12-31 11.93100 16.0 419 3.5696 2011-01-07 0.44508 18.0 420 3.0958 2011-01-14 8.43040 18.0 421 3.8281 2011-01-21 -2.26530 18.0 422 3.7336 2011-01-28 1.33950 18.0 423 3.6466 2011-02-04 10.18700 18.0 424 4.4241 2011-02-11 6.91330 18.0 425 4.7528 2011-02-18 5.30300 18.0 426 4.6170 2011-02-25 10.40700 18.0 427 5.1216 2011-03-04 3.63990 18.0 428 5.3997 2011-03-11 5.49690 18.0 429 5.4961 2011-03-18 2.12060 18.0 430 5.4625 2011-03-25 5.66700 18.0 431 5.4426 2011-04-01 12.13400 18.0 432 5.4857 2011-04-08 6.11440 18.0 433 5.5036 2011-04-15 9.85800 18.0 434 5.5052 2011-04-22 11.39300 18.0 435 5.5101 2011-04-29 9.54510 18.0 436 5.4935 2011-05-06 12.99600 18.0 437 5.5244 2011-05-13 8.83800 18.0 438 5.5015 2011-05-20 8.81900 18.0 439 5.5059 2011-05-27 10.80500 18.0 440 5.5142 2011-06-03 11.08700 18.0 441 5.5896 2011-06-10 7.20970 18.0 442 5.5319 2011-06-17 10.11400 18.0 443 5.5354 2011-06-24 11.29400 18.0 444 5.5589 2011-07-01 11.43900 18.0 445 5.5371 2011-07-08 13.29700 18.0 446 5.5686 2011-07-15 11.61900 18.0 447 5.5670 2011-07-22 12.73800 18.0 448 5.6439 2011-07-29 14.95600 18.0 449 5.6940 2011-08-05 16.48600 18.0 450 5.6338 2011-08-12 16.06000 18.0 451 5.6322 2011-08-19 11.38900 18.0 452 5.6545 2011-08-26 10.69200 18.0 453 5.7226 2011-09-02 14.71100 18.0 454 5.7256 2011-09-09 14.09600 18.0 455 5.7185 2011-09-16 13.03500 18.0 456 5.7454 2011-09-23 11.81800 18.0 457 5.8026 2011-09-30 14.49800 18.0 458 5.8097 2011-10-07 10.76800 18.0 459 5.7557 2011-10-14 13.91800 18.0 460 5.8051 2011-10-21 8.84760 18.0 461 5.8297 2011-10-28 8.37600 18.0 462 5.7679 2011-11-04 12.57400 18.0 463 5.8322 2011-11-11 11.26200 18.0 464 5.8059 2011-11-18 11.11100 18.0 465 5.8491 2011-11-25 12.91700 18.0 466 7.4509 2011-12-02 2.43560 18.0 467 7.1933 2011-12-09 5.87070 18.0 468 6.3294 2011-12-16 2.31850 18.0 469 5.8866 2011-12-23 11.12900 18.0 470 6.1258 2011-12-30 4.78220 18.0 471 3.6297 2011-01-06 2.92880 20.0 472 3.3468 2011-01-13 9.59030 20.0 473 3.8969 2011-01-20 -1.45990 20.0 474 3.8649 2011-01-27 3.49050 20.0 475 3.7189 2011-02-03 6.15450 20.0 476 4.5689 2011-02-10 8.87270 20.0 477 4.8594 2011-02-17 4.61980 20.0 478 4.8374 2011-02-24 7.66730 20.0 479 5.2294 2011-03-03 -0.73976 20.0 480 5.3550 2011-03-10 9.08700 20.0 481 5.5199 2011-03-17 6.57230 20.0 482 5.5185 2011-03-24 4.21580 20.0 483 5.5391 2011-03-31 9.55530 20.0 484 5.5010 2011-04-07 10.24900 20.0 485 5.5107 2011-04-14 8.15550 20.0 486 5.5052 2011-04-21 9.75940 20.0 487 5.5200 2011-04-28 6.43770 20.0 488 5.5096 2011-05-05 10.70900 20.0 489 5.5201 2011-05-12 9.11810 20.0 490 5.5574 2011-05-19 8.26810 20.0 491 5.5375 2011-05-26 11.65000 20.0 492 5.5331 2011-06-02 13.10500 20.0 493 5.5330 2011-06-09 11.09500 20.0 494 5.5517 2011-06-16 12.63000 20.0 495 5.5645 2011-06-23 12.66100 20.0 496 5.5771 2011-06-30 9.57130 20.0 497 5.5920 2011-07-07 13.84300 20.0 498 5.5822 2011-07-14 10.93200 20.0 499 5.6023 2011-07-21 13.44100 20.0 500 5.6408 2011-07-28 13.41700 20.0 501 5.6308 2011-08-04 14.81500 20.0 502 5.6300 2011-08-11 16.33900 20.0 503 5.6460 2011-08-18 10.04300 20.0 504 5.6596 2011-08-25 11.87600 20.0 505 5.6706 2011-09-01 11.71000 20.0 506 5.6735 2011-09-08 11.84600 20.0 507 5.6815 2011-09-15 12.17800 20.0 508 5.6948 2011-09-22 11.90200 20.0 509 5.6955 2011-09-29 17.07200 20.0 510 5.7011 2011-10-06 13.21700 20.0 511 5.7241 2011-10-13 12.01300 20.0 512 5.7566 2011-10-20 3.75340 20.0 513 5.7440 2011-10-27 8.76700 20.0 514 5.7583 2011-11-03 13.96900 20.0 515 5.7599 2011-11-10 13.03200 20.0 516 5.7876 2011-11-17 8.26000 20.0 517 5.7958 2011-11-24 12.02100 20.0 518 5.8690 2011-12-01 9.64050 20.0 519 7.2601 2011-12-08 4.99180 20.0 520 6.4506 2011-12-15 3.73240 20.0 521 5.9143 2011-12-22 12.69300 20.0 522 6.2010 2011-12-29 7.12550 20.0 523 3.7158 2011-01-05 5.66070 22.0 524 3.3825 2011-01-12 4.42930 22.0 525 3.9394 2011-01-19 0.04384 22.0 526 3.8967 2011-01-26 5.33010 22.0 527 3.8006 2011-02-02 4.74030 22.0 528 4.6272 2011-02-09 6.48010 22.0 529 4.8906 2011-02-16 5.92770 22.0 530 4.8437 2011-02-23 7.15490 22.0 531 5.2401 2011-03-02 1.52250 22.0 532 5.2371 2011-03-09 6.46400 22.0 533 5.4725 2011-03-16 6.49500 22.0 534 5.5676 2011-03-23 4.01320 22.0 535 5.5634 2011-03-30 10.23300 22.0 536 5.5158 2011-04-06 12.10300 22.0 537 5.5711 2011-04-13 5.66120 22.0 538 5.5681 2011-04-20 7.94430 22.0 539 5.5749 2011-04-27 9.66080 22.0 540 5.5829 2011-05-04 5.13940 22.0 541 5.5900 2011-05-11 12.00800 22.0 542 5.5885 2011-05-18 13.42900 22.0 543 5.6147 2011-05-25 7.96200 22.0 544 5.6210 2011-06-01 8.94920 22.0 545 5.6379 2011-06-08 10.58700 22.0 546 5.6279 2011-06-15 14.82200 22.0 547 5.6317 2011-06-22 13.28300 22.0 548 5.6570 2011-06-29 10.09900 22.0 549 5.6468 2011-07-06 14.30500 22.0 550 5.6739 2011-07-13 13.44700 22.0 551 5.6677 2011-07-20 13.27900 22.0 552 5.6808 2011-07-27 16.17600 22.0 553 5.6797 2011-08-03 15.40500 22.0 554 5.7022 2011-08-10 11.20800 22.0 555 5.7044 2011-08-17 10.92000 22.0 556 5.7113 2011-08-24 13.57000 22.0 557 5.7130 2011-08-31 12.35700 22.0 558 5.7259 2011-09-07 13.77500 22.0 559 5.7374 2011-09-14 13.05900 22.0 560 5.7435 2011-09-21 11.50800 22.0 561 5.7419 2011-09-28 15.44600 22.0 562 5.7606 2011-10-05 15.41900 22.0 563 5.7488 2011-10-12 12.46600 22.0 564 5.7847 2011-10-19 8.04520 22.0 565 5.7825 2011-10-26 9.85760 22.0 566 5.7979 2011-11-02 9.94480 22.0 567 5.7828 2011-11-09 9.83490 22.0 568 5.8190 2011-11-16 7.18460 22.0 569 5.8245 2011-11-23 3.36370 22.0 570 5.8462 2011-11-30 6.19500 22.0 571 6.8035 2011-12-07 5.57610 22.0 572 6.6398 2011-12-14 5.46150 22.0 573 5.8833 2011-12-21 6.02540 22.0 574 6.0826 2011-12-28 8.87860 22.0 575 3.7401 2011-01-04 -0.87434 24.0 576 3.2508 2011-01-11 7.57030 24.0 577 3.8161 2011-01-18 4.65410 24.0 578 3.8529 2011-01-25 7.24100 24.0 579 3.7638 2011-02-01 2.03130 24.0 580 4.5356 2011-02-08 4.28250 24.0 581 4.6182 2011-02-15 2.09610 24.0 582 4.7871 2011-02-22 4.52120 24.0 583 5.1305 2011-03-01 4.09410 24.0 584 5.2040 2011-03-08 -0.97393 24.0 585 5.4503 2011-03-15 5.77950 24.0 586 5.4623 2011-03-22 4.84410 24.0 587 5.4744 2011-03-29 4.10630 24.0 588 5.4610 2011-04-05 10.80000 24.0 589 5.4958 2011-04-12 7.07030 24.0 590 5.4913 2011-04-19 9.72580 24.0 591 5.4967 2011-04-26 11.22400 24.0 592 5.5384 2011-05-03 7.08340 24.0 593 5.5223 2011-05-10 10.99000 24.0 594 5.5361 2011-05-17 12.02200 24.0 595 5.5549 2011-05-24 9.37830 24.0 596 5.5721 2011-05-31 7.85870 24.0 597 5.5697 2011-06-07 9.30420 24.0 598 5.5709 2011-06-14 10.07000 24.0 599 5.5695 2011-06-21 15.00500 24.0 600 5.5792 2011-06-28 13.74500 24.0 601 5.5783 2011-07-05 17.47700 24.0 602 5.5969 2011-07-12 15.32100 24.0 603 5.6055 2011-07-19 13.27000 24.0 604 5.6135 2011-07-26 11.90700 24.0 605 5.6078 2011-08-02 17.43300 24.0 606 5.6343 2011-08-09 13.26100 24.0 607 5.6386 2011-08-16 13.34400 24.0 608 5.6365 2011-08-23 16.62600 24.0 609 5.6493 2011-08-30 13.30700 24.0 610 5.6607 2011-09-06 14.72500 24.0 611 5.6561 2011-09-13 14.77800 24.0 612 5.6629 2011-09-20 15.70200 24.0 613 5.6921 2011-09-27 11.22700 24.0 614 5.6948 2011-10-04 13.29700 24.0 615 5.6826 2011-10-11 16.68600 24.0 616 5.7206 2011-10-18 7.88400 24.0 617 5.7105 2011-10-25 13.14200 24.0 618 5.6953 2011-11-01 13.24000 24.0 619 5.7325 2011-11-08 10.43400 24.0 620 5.7176 2011-11-15 9.17300 24.0 621 5.7275 2011-11-22 9.06990 24.0 622 5.7293 2011-11-29 12.74600 24.0 623 5.7733 2011-12-06 4.43310 24.0 624 6.7186 2011-12-13 9.05250 24.0 625 5.8346 2011-12-20 7.67070 24.0 626 5.9464 2011-12-27 10.47900 24.0
您擁有的是 K (5) 組，其中您有一個依賴（水溫）和一個獨立系列（空氣溫度）。這個問題被稱為匯集橫截面時間序列分析。為每個 K 組構建一個單獨的傳遞函數 (ARMAX) 模型。確定一個合適的通用模型（抗異常值）。使用所有數據全局估計該模型，然後執行 F 檢驗以檢驗一組公共參數的假設。在找到具有統計學意義的 F 值後，檢查係數以確定哪些（K 組）是相似的。我目前的研究是為此開發一個自動測試，我們讓它在當前的 AUTOBOX Beta 版本中運行（http://www.autobox.com）。我很樂意為您演示這一點，請發布您的數據。在了解 AUTOBOX 如何進行此測試後，您可能可以自己對其進行編程，或者至少有一個“目的地”。希望這可以幫助。
使用凱特的數據的其他評論：
我採用前 4 個組（深度為 0.5、4、6 和 8）並使用前 52 個值來構建此示例分析。以下是 4 個圖表，描繪了 4 個深度的 Y（水溫）和 X（空氣溫度）隨時間的變化；深度1；
; 深度 2；
; 深度 3；
和深度 4；
. 對 Y 與 X 的內部關係的分析產生了一個典型的模型
. 為了更一般的表達，我選擇在噪音中添加另一個 AR 術語。所有四個示例都受到異常的顯著影響，因此有人可能會爭論/建議應該繼續使用異常值調整序列或乾預清理序列，即“清理序列”。出於演示目的，這裡沒有這樣做。我們現在開始估計 4 個數據集和復合數據集的“典型模型”。這產生了
。F 測試只是常數參數的 Chow 測試http://en.wikipedia.org/wiki/Chow_test，它產生了顯著的 F。Chow 測試只是將 4 個案例中的每一個案例的錯誤 sos 相加（每個案例有 52 個值）並將其與復合的誤差 sos（208 個值）進行比較。希望這可以幫助。