R

如何找到時間序列之間的相似性?

  • July 17, 2012

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;在此處輸入圖像描述; 深度 2;在此處輸入圖像描述; 深度 3;在此處輸入圖像描述和深度 4;在此處輸入圖像描述. 對 Y 與 X 的內部關係的分析產生了一個典型的模型在此處輸入圖像描述. 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”。這產生了在此處輸入圖像描述。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。

引用自:https://stats.stackexchange.com/questions/32447

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