How to decompose following gps time series ?? Please help me

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Chris Martin
Chris Martin on 5 Mar 2013
The time series contain position of a gps site from 2007-2011. Here the first column is the time and second column is the position and third one is the standard error.
2007.00137 1.56954 0.00367
2007.00411 1.57119 0.00357
2007.00685 1.57185 0.00357
2007.00959 1.56980 0.00354
2007.01233 1.57311 0.00358
2007.01507 1.57543 0.00352
2007.01781 1.57261 0.00389
2007.02055 1.57557 0.00432
2007.02329 1.57508 0.00374
2007.02603 1.57176 0.00379
2007.02877 1.57425 0.00370
2007.03150 1.57342 0.00367
2007.03424 1.57477 0.00367
2007.03698 1.57507 0.00348
2007.03972 1.57431 0.00368
2007.04246 1.57365 0.00356
2007.04520 1.57356 0.00429
2007.04794 1.57394 0.00373
2007.05068 1.56943 0.00377
2007.05342 1.57371 0.00395
2007.05616 1.57291 0.00379
2007.05890 1.57486 0.00370
2007.06164 1.57595 0.00351
2007.06438 1.57601 0.00333
2007.06712 1.57461 0.00343
2007.06986 1.57349 0.00345
2007.07260 1.57378 0.00385
2007.07534 1.57531 0.00376
2007.07808 1.57553 0.00380
2007.08082 1.57588 0.00354
2007.08356 1.57471 0.00349
2007.08630 1.57656 0.00356
2007.08904 1.57867 0.00335
2007.09178 1.57809 0.00337
2007.09452 1.58016 0.00376
2007.09726 1.57677 0.00349
2007.10000 1.57834 0.00339
2007.10274 1.57807 0.00334
2007.10548 1.57783 0.00342
2007.10822 1.58044 0.00342
2007.11096 1.57999 0.00338
2007.11644 1.58517 0.00342
2007.11918 1.58198 0.00332
2007.12192 1.58058 0.00330
2007.12466 1.58050 0.00344
2007.12740 1.58114 0.00323
2007.13014 1.58252 0.00344
2007.13287 1.58243 0.00337
2007.13561 1.58281 0.00328
2007.13835 1.58017 0.00333
2007.14109 1.58194 0.00325
2007.14383 1.58304 0.00324
2007.14657 1.58323 0.00330
2007.14931 1.58240 0.00329
2007.15205 1.58007 0.00337
2007.15479 1.58450 0.00363
2007.15753 1.58209 0.00342
2007.16027 1.58307 0.00326
2007.16301 1.58021 0.00344
2007.16575 1.57952 0.00343
2007.16849 1.58394 0.00346
2007.17123 1.58361 0.00334
2007.17397 1.58183 0.00341
2007.17671 1.58343 0.00355
2007.17945 1.58263 0.00338
2007.18219 1.58189 0.00336
2007.18493 1.58322 0.00337
2007.18767 1.58113 0.00349
2007.19041 1.58400 0.00340
2007.19315 1.58279 0.00332
2007.19589 1.58315 0.00340
2007.20137 1.58288 0.00340
2007.20411 1.58428 0.00346
2007.20685 1.58110 0.00340
2007.20959 1.58349 0.00378
2007.21233 1.58411 0.00353
2007.21507 1.58312 0.00356
2007.21781 1.58388 0.00339
2007.22055 1.58321 0.00347
2007.22329 1.58510 0.00331
2007.22603 1.58362 0.00340
2007.22877 1.58334 0.00347
2007.23150 1.58527 0.00351
2007.23424 1.58493 0.00335
2007.23698 1.58397 0.00357
2007.23972 1.58276 0.00353
2007.24246 1.58275 0.00339
2007.24520 1.58519 0.00357
2007.24794 1.58216 0.00364
2007.25068 1.58406 0.00342
2007.25342 1.58464 0.00355
2007.25616 1.58829 0.00362
2007.25890 1.58328 0.00341
2007.26164 1.58600 0.00344
2007.26438 1.58468 0.00354
2007.26712 1.58463 0.00349
2007.26986 1.58587 0.00355
2007.27260 1.58601 0.00366
2007.27534 1.58374 0.00377
2007.27808 1.58775 0.00425
2007.28082 1.58570 0.00432
2007.28356 1.58758 0.00415
2007.28630 1.58663 0.00363
2007.28904 1.58658 0.00363
2007.29178 1.58803 0.00401
2007.29452 1.58743 0.00417
2007.29726 1.59811 0.00545
2007.30000 1.59489 0.00455
2007.30274 1.59898 0.00488
2007.30548 1.59727 0.00483
2007.30822 1.59115 0.00359
2007.31096 1.58812 0.00385
2007.31370 1.58738 0.00363
2007.31644 1.58902 0.00352
2007.31918 1.58878 0.00367
2007.32192 1.58849 0.00375
2007.32466 1.58652 0.00361
2007.32740 1.58845 0.00401
2007.33014 1.58779 0.00402
2007.33287 1.58765 0.00433
2007.33561 1.58918 0.00426
2007.33835 1.58582 0.00351
2007.34109 1.58803 0.00379
2007.34383 1.58853 0.00401
2007.34657 1.58881 0.00358
2007.34931 1.58729 0.00347
2007.35205 1.58868 0.00339
2007.35479 1.58904 0.00347
2007.35753 1.58876 0.00344
2007.36027 1.58783 0.00333
2007.36301 1.58732 0.00341
2007.36575 1.58983 0.00366
2007.36849 1.58935 0.00361
2007.37123 1.58959 0.00334
2007.37397 1.58994 0.00363
2007.37671 1.58925 0.00373
2007.37945 1.58886 0.00392
2007.38219 1.59304 0.00390
2007.38493 1.59038 0.00346
2007.38767 1.59130 0.00356
2007.39041 1.59295 0.00417
2007.39315 1.59323 0.00663
2007.39589 1.59401 0.00383
2007.39863 1.59246 0.00367
2007.40137 1.58997 0.00412
2007.40411 1.59189 0.00371
2007.40685 1.59275 0.00354
2007.40959 1.59013 0.00365
2007.41233 1.58903 0.00383
2007.41507 1.58927 0.00390
2007.41781 1.59369 0.00380
2007.42055 1.59210 0.00398
2007.42329 1.59364 0.00441
2007.42603 1.59105 0.00390
2007.42877 1.58943 0.00406
2007.43150 1.59061 0.00386
2007.43424 1.59123 0.00345
2007.43698 1.59293 0.00345
2007.43972 1.59075 0.00340
2007.44246 1.59167 0.00372
2007.44520 1.59399 0.00411
2007.44794 1.59251 0.00379
2007.45068 1.59278 0.00364
2007.45342 1.59536 0.00360
2007.45616 1.59191 0.00341
2007.45890 1.59346 0.00348
2007.46164 1.59145 0.00344
2007.46438 1.59347 0.00346
2007.46712 1.59182 0.00342
2007.46986 1.59151 0.00364
2007.47260 1.59280 0.00340
2007.47534 1.59258 0.00358
2007.47808 1.59525 0.00354
2007.48082 1.59364 0.00340
2007.48356 1.59824 0.00366
2007.48630 1.59303 0.00356
2007.48904 1.59833 0.00365
2007.49178 1.59615 0.00379
2007.49452 1.59639 0.00371
2007.49726 1.59489 0.00360
2007.50000 1.59473 0.00365
2007.50274 1.59629 0.00366
2007.50548 1.59446 0.00350
2007.50822 1.59816 0.00378
2007.51096 1.59618 0.00363
2007.51370 1.59688 0.00361
2007.51644 1.59788 0.00362
2007.51918 1.59485 0.00358
2007.52192 1.59528 0.00359
2007.52466 1.59667 0.00351
2007.52740 1.59618 0.00370
2007.53014 1.59611 0.00377
2007.53287 1.59711 0.00364
2007.53561 1.59686 0.00354
2007.53835 1.59507 0.00351
2007.54109 1.59617 0.00382
2007.54383 1.59661 0.00354
2007.54657 1.60108 0.00417
2007.54931 1.59467 0.00377
2007.55205 1.59855 0.00366
2007.55479 1.59723 0.00360
2007.55753 1.59821 0.00360
2007.56027 1.60016 0.00378
2007.56301 1.60052 0.00366
2007.56575 1.59465 0.00428
2007.56849 1.59962 0.00371
2007.57123 1.60099 0.00365
2007.57397 1.59855 0.00364
2007.57671 1.60001 0.00361
2007.57945 1.59913 0.00372
2007.58219 1.59623 0.00371
2007.58493 1.59975 0.00357
2007.58767 1.59974 0.00356
2007.59041 1.59990 0.00388
2007.59315 1.60074 0.00379
2007.59589 1.60285 0.00376
2007.59863 1.60303 0.00370
2007.60137 1.60045 0.00393
2007.60411 1.60128 0.00364
2007.60685 1.60081 0.00374
2007.60959 1.59954 0.00369
2007.61233 1.60369 0.00373
2007.61507 1.59816 0.00376
2007.61781 1.59998 0.00361
2007.62055 1.60186 0.00354
2007.62329 1.60193 0.00360
2007.62603 1.60148 0.00339
2007.62877 1.60392 0.00373
2007.63150 1.60806 0.00400
2007.63424 1.60722 0.00388
2007.63698 1.60381 0.00362
2007.63972 1.60487 0.00356
2007.64246 1.60162 0.00377
2007.64520 1.60445 0.00365
2007.64794 1.60376 0.00375
2007.65068 1.60256 0.00351
2007.65342 1.60354 0.00346
2007.65616 1.60254 0.00341
2007.65890 1.60350 0.00363
2007.66164 1.60344 0.00346
2007.66438 1.60195 0.00339
2007.66712 1.60318 0.00333
2007.66986 1.60373 0.00338
2007.67260 1.60335 0.00330
2007.67534 1.60462 0.00357
2007.67808 1.60298 0.00347
2007.68082 1.60553 0.00344
2007.68356 1.60626 0.00337
2007.68630 1.60230 0.00382
2007.68904 1.60275 0.00401
2007.69178 1.60604 0.00372
2007.69452 1.60355 0.00409
2007.69726 1.60613 0.00451
2007.70000 1.60517 0.00416
2007.70274 1.60389 0.00401
2007.70548 1.60265 0.00380
2007.70822 1.60608 0.00399
2007.71096 1.60367 0.00395
2007.71370 1.60339 0.00425
2007.72192 1.60874 0.00387
2007.72740 1.60610 0.00389
2007.73014 1.60665 0.00349
2007.73287 1.60502 0.00348
2007.73561 1.60480 0.00340
2007.73835 1.60702 0.00357
2007.74109 1.60748 0.00350
2007.74383 1.60625 0.00382
2007.74657 1.60606 0.00353
2007.74931 1.60450 0.00374
2007.75205 1.60780 0.00375
2007.75479 1.60385 0.00339
2007.75753 1.60631 0.00361
2007.76027 1.60524 0.00336
2007.76301 1.60562 0.00348
2007.76575 1.60577 0.00363
2007.76849 1.60590 0.00371
2007.77123 1.60484 0.00334
2007.77397 1.60533 0.00417
2007.77671 1.60855 0.00380
2007.77945 1.60537 0.00384
2007.78219 1.60667 0.00335
2007.78493 1.60488 0.00342
2007.78767 1.60557 0.00333
2007.79041 1.60803 0.00357
2007.79315 1.60953 0.00413
2007.79589 1.60780 0.00459
2007.79863 1.60817 0.00379
2007.80685 1.60808 0.00437
2007.80959 1.60806 0.00420
2007.81233 1.61256 0.00478
2007.81507 1.60760 0.00382
2007.81781 1.60678 0.00385
2007.82055 1.60939 0.00378
2007.82329 1.60686 0.00361
2007.82603 1.60997 0.00410
2007.82877 1.60885 0.00361
2007.83150 1.60795 0.00381
2007.83424 1.60850 0.00381
2007.83698 1.60851 0.00377
2007.83972 1.60936 0.00376
2007.84246 1.60898 0.00341
2007.84520 1.60831 0.00365
2007.84794 1.60653 0.00417
2007.85068 1.60618 0.00367
2007.85342 1.61567 0.00473
2007.85616 1.61283 0.00449
2007.85890 1.61026 0.00351
2007.86164 1.61067 0.00354
2007.86438 1.60912 0.00344
2007.86712 1.60767 0.00357
2007.86986 1.60889 0.00330
2007.87260 1.61001 0.00337
2007.87534 1.60901 0.00344
2007.87808 1.60869 0.00355
2007.88082 1.61099 0.00355
2007.88356 1.60973 0.00353
2007.88630 1.60890 0.00336
2007.88904 1.61131 0.00340
2007.89178 1.60911 0.00339
2007.89452 1.61097 0.00336
2007.89726 1.60800 0.00335
2007.90000 1.61080 0.00340
2007.90274 1.61159 0.00343
2007.90548 1.61050 0.00359
2007.90822 1.61164 0.00339
2007.91096 1.61018 0.00340
2007.91370 1.61122 0.00349
2007.91644 1.61151 0.00334
2007.91918 1.61004 0.00345
2007.92192 1.61044 0.00333
2007.92466 1.60973 0.00357
2007.92740 1.61039 0.00371
2007.93014 1.61323 0.00358
2007.93287 1.61033 0.00340
2007.93561 1.61169 0.00342
2007.93835 1.61039 0.00344
2007.94109 1.60934 0.00348
2007.94383 1.61211 0.00357
2007.94657 1.61198 0.00342
2007.94931 1.61118 0.00366
2007.95205 1.61154 0.00383
2007.95479 1.61057 0.00376
2007.95753 1.61481 0.00353
2007.96027 1.61429 0.00364
2007.96301 1.61377 0.00366
2007.96575 1.61414 0.00373
2007.96849 1.62056 0.00420
2007.97123 1.62199 0.00435
2007.97397 1.62567 0.00425
2007.97671 1.62579 0.00405
2007.97945 1.62427 0.00413
2007.98219 1.62607 0.00404
2007.98493 1.62663 0.00393
2007.98767 1.61194 0.00343
2007.99041 1.61374 0.00342
2007.99315 1.61521 0.00339
2007.99589 1.61517 0.00346
2007.99863 1.61565 0.00346
2008.00136 1.61565 0.00339
2008.00410 1.61551 0.00339
2008.00683 1.61815 0.00346
2008.00956 1.61741 0.00377
2008.01229 1.61519 0.00363
2008.01503 1.61738 0.00370
2008.01776 1.61548 0.00355
2008.02322 1.61909 0.00431
2008.02595 1.62338 0.00450
2008.02869 1.62386 0.00432
2008.03142 1.62582 0.00428
2008.03415 1.62383 0.00442
2008.03962 1.62246 0.00435
2008.04508 1.61848 0.00420
2008.05054 1.62487 0.00453
2008.05328 1.62261 0.00457
2008.05601 1.62100 0.00473
2008.05874 1.62344 0.00456
2008.06147 1.62631 0.00428
2008.06421 1.62949 0.00439
2008.06694 1.62786 0.00415
2008.06967 1.62955 0.00422
2008.07240 1.62838 0.00417
2008.07513 1.62530 0.00429
2008.08060 1.62769 0.00423
2008.08333 1.62998 0.00411
2008.08606 1.62870 0.00418
2008.08880 1.62762 0.00454
2008.09153 1.63317 0.00459
2008.09426 1.62738 0.00425
2008.09699 1.62848 0.00455
2008.09972 1.63007 0.00437
2008.10246 1.62912 0.00410
2008.10519 1.63193 0.00404
2008.10792 1.62956 0.00417
2008.11065 1.63158 0.00504
2008.11339 1.62890 0.00460
2008.11612 1.63520 0.00447
2008.11885 1.63399 0.00432
2008.12158 1.62944 0.00431
2008.12705 1.62723 0.00404
2008.12978 1.62890 0.00397
2008.13251 1.63093 0.00406
2008.13524 1.62974 0.00424
2008.13798 1.63228 0.00431
2008.14071 1.62872 0.00445
2008.14344 1.62642 0.00414
2008.14617 1.63164 0.00415
2008.14891 1.63325 0.00405
2008.15164 1.62933 0.00410
2008.15437 1.63246 0.00397
2008.15710 1.63251 0.00405
2008.15983 1.63365 0.00401
2008.16257 1.63258 0.00399
2008.16530 1.63413 0.00462
2008.16803 1.63221 0.00423
2008.17076 1.63454 0.00412
2008.17350 1.63279 0.00423
2008.17623 1.63291 0.00404
2008.17896 1.63272 0.00413
2008.18169 1.63647 0.00418
2008.18442 1.63710 0.00452
2008.18716 1.63407 0.00463
2008.18989 1.63648 0.00461
2008.19262 1.63500 0.00449
2008.19535 1.63610 0.00444
2008.19809 1.63459 0.00463
2008.20082 1.63294 0.00525
2008.20355 1.63631 0.00460
2008.20628 1.63504 0.00437
2008.20901 1.63550 0.00442
2008.21175 1.63557 0.00429
2008.21448 1.63423 0.00447
2008.21721 1.63419 0.00430
2008.21994 1.63609 0.00428
2008.22268 1.63341 0.00432
2008.22541 1.63221 0.00436
2008.22814 1.63247 0.00422
2008.23087 1.63478 0.00462
2008.23360 1.63928 0.00574
2008.23634 1.63598 0.00469
2008.23907 1.63232 0.00515
2008.24180 1.63372 0.00453
2008.24453 1.63478 0.00521
2008.24727 1.63255 0.00446
2008.25000 1.63231 0.00449
2008.25273 1.63388 0.00531
2008.25546 1.63440 0.00412
2008.25819 1.63709 0.00501
2008.26093 1.63446 0.00457
2008.26366 1.63367 0.00427
2008.26912 1.63309 0.00433
2008.27186 1.63343 0.00423
2008.27459 1.63515 0.00429
2008.27732 1.63434 0.00428
2008.28005 1.63578 0.00434
2008.28278 1.63562 0.00418
2008.28552 1.63463 0.00416
2008.28825 1.63355 0.00438
2008.29098 1.63558 0.00447
2008.29371 1.63793 0.00476
2008.29645 1.63495 0.00467
2008.29918 1.63652 0.00423
2008.30191 1.63707 0.00445
2008.30464 1.63496 0.00426
2008.30738 1.63796 0.00456
2008.31284 1.63357 0.00458
2008.31557 1.63681 0.00437
2008.31830 1.63976 0.00458
2008.32104 1.63790 0.00470
2008.32377 1.63760 0.00474
2008.32650 1.63744 0.00472
2008.32923 1.63500 0.00506
2008.33197 1.63645 0.00446
2008.33470 1.63625 0.00476
2008.33743 1.63873 0.00448
2008.34016 1.64138 0.00449
2008.34289 1.63773 0.00434
2008.34563 1.63742 0.00444
2008.34836 1.63519 0.00443
2008.35109 1.64145 0.00516
2008.35382 1.64029 0.00440
2008.35656 1.64058 0.00433
2008.35929 1.63919 0.00468
2008.36202 1.64052 0.00470
2008.36475 1.64078 0.00443
2008.36748 1.63707 0.00450
2008.37022 1.63993 0.00423
2008.37295 1.64087 0.00422
2008.37568 1.64178 0.00470
2008.37841 1.63981 0.00477
2008.38115 1.63826 0.00583
2008.38388 1.63542 0.00473
2008.38661 1.63430 0.00485
2008.38934 1.64399 0.00470
2008.39207 1.64243 0.00473
2008.39481 1.64076 0.00465
2008.39754 1.64189 0.00483
2008.40027 1.63857 0.00476
2008.40300 1.63533 0.00511
2008.40574 1.63793 0.00475
2008.40847 1.63900 0.00498
2008.41120 1.63812 0.00465
2008.41393 1.64223 0.00483
2008.41666 1.63985 0.00465
2008.41940 1.64172 0.00439
2008.42213 1.63859 0.00452
2008.42486 1.64097 0.00444
2008.42759 1.63924 0.00435
2008.43033 1.64172 0.00452
2008.56694 1.63742 0.00443
2008.56967 1.63620 0.00364
2008.57240 1.63600 0.00435
2008.57513 1.63910 0.00339
2008.57787 1.63791 0.00367
2008.58060 1.63912 0.00347
2008.58333 1.63794 0.00374
2008.58606 1.64038 0.00335
2008.58880 1.64914 0.00422
2008.59153 1.65370 0.00407
2008.59426 1.65434 0.00428
2008.59699 1.65021 0.00430
2008.60246 1.64127 0.00327
2008.60519 1.64051 0.00328
2008.60792 1.64203 0.00338
2008.61065 1.64149 0.00329
2008.61339 1.64061 0.00335
2008.61612 1.64019 0.00333
2008.61885 1.64089 0.00348
2008.62158 1.64130 0.00325
2008.62432 1.64113 0.00348
2008.62705 1.64036 0.00344
2008.62978 1.64185 0.00361
2008.63251 1.64262 0.00338
2008.63524 1.64093 0.00327
2008.63798 1.64231 0.00347
2008.64071 1.64205 0.00333
2008.64344 1.64172 0.00336
2008.65164 1.63872 0.00400
2008.65437 1.64358 0.00437
2008.65983 1.64573 0.00373
2008.66257 1.64519 0.00390
2008.66530 1.64346 0.00380
2008.66803 1.64622 0.00372
2008.67076 1.64209 0.00402
2008.67350 1.64618 0.00413
2008.67623 1.64491 0.00394
2008.67896 1.64489 0.00361
2008.68169 1.64472 0.00353
2008.68442 1.64402 0.00344
2008.68716 1.64467 0.00342
2008.68989 1.64528 0.00329
2008.69262 1.64362 0.00335
2008.69535 1.64602 0.00351
2008.69809 1.64355 0.00369
2008.70082 1.64528 0.00361
2008.70355 1.64460 0.00353
2008.70628 1.64684 0.00344
2008.70901 1.64669 0.00337
2008.71448 1.64508 0.00330
2008.71721 1.64511 0.00333
2008.71994 1.64580 0.00339
2008.72268 1.64500 0.00345
2008.72541 1.64511 0.00352
2008.72814 1.64425 0.00334
2008.73087 1.64421 0.00367
2008.73360 1.64639 0.00341
2008.73634 1.64610 0.00345
2008.73907 1.64742 0.00358
2008.74180 1.64584 0.00334
2008.74453 1.64724 0.00370
2008.74727 1.64646 0.00371
2008.75000 1.64517 0.00377
2008.75273 1.64548 0.00408
2008.75546 1.64476 0.00379
2008.75819 1.65039 0.00420
2008.76093 1.64631 0.00360
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2010.64794 1.72782 0.00353
2010.65068 1.74118 0.00445
2010.65342 1.72708 0.00370
2010.65616 1.73172 0.00388
2010.65890 1.72871 0.00381
2010.66164 1.73008 0.00352
2010.66438 1.73200 0.00359
2010.66712 1.73151 0.00382
2010.66986 1.72047 0.01873
2010.67534 1.72204 0.00614
2010.67808 1.72824 0.00505
2010.68082 1.73147 0.00373
2010.68356 1.73118 0.00368
2010.68630 1.72933 0.00375
2010.68904 1.72992 0.00377
2010.69178 1.73291 0.00377
2010.69452 1.73243 0.00363
2010.69726 1.73326 0.00373
2010.70000 1.73278 0.00369
2010.70274 1.73181 0.00358
2010.70548 1.73267 0.00350
2010.70822 1.73042 0.00351
2010.71096 1.72704 0.00349
2010.71370 1.72934 0.00367
2010.71644 1.73154 0.00699
2010.86164 1.74065 0.00397
2010.91644 1.73975 0.00635
2010.91918 1.73537 0.00569
2010.92192 1.73400 0.00680
2010.92740 1.74150 0.00433
2010.93014 1.74322 0.00380
2010.93287 1.74467 0.00840
2011.04520 1.74708 0.00404
2011.04794 1.74887 0.00350
2011.05068 1.74853 0.00351
2011.05342 1.74741 0.00337
2011.05616 1.74870 0.00339
2011.05890 1.74839 0.00351
2011.06164 1.74773 0.00347
2011.06438 1.74882 0.00351
2011.06712 1.74804 0.00347
2011.06986 1.74744 0.00344
2011.07260 1.74940 0.00348
2011.07534 1.74837 0.00347
2011.07808 1.74580 0.00351
2011.08082 1.74761 0.00356
2011.08356 1.74842 0.00339
2011.08630 1.74793 0.00346
2011.08904 1.74910 0.00344
2011.09178 1.75070 0.00365
2011.09452 1.75253 0.00342
2011.09726 1.75101 0.00337
2011.10000 1.75154 0.00340
2011.10274 1.75266 0.00343
2011.10548 1.75132 0.00348
2011.10822 1.74988 0.00338
2011.11096 1.74986 0.00347
2011.11370 1.75162 0.00344
2011.11644 1.74821 0.00364
2011.11918 1.75158 0.00352
2011.12192 1.75161 0.00343
2011.12466 1.75065 0.00352
2011.12740 1.75110 0.00345
2011.13014 1.75373 0.00364
2011.13287 1.75217 0.00392
2011.13561 1.75346 0.00398
2011.13835 1.75300 0.00459
2011.14109 1.74977 0.00446
2011.14383 1.75348 0.00362
2011.14657 1.75571 0.00408
2011.14931 1.75055 0.00370
2011.15205 1.75883 0.00437
2011.15479 1.75525 0.00385
2011.15753 1.75479 0.00349
2011.16027 1.75419 0.00351
2011.16301 1.75330 0.00350
2011.16575 1.75362 0.00350
2011.16849 1.75188 0.00344
2011.17123 1.75264 0.00349
2011.17397 1.75337 0.00352
2011.17671 1.75338 0.00345
2011.17945 1.75262 0.00355
2011.18219 1.75482 0.00370
2011.18493 1.75338 0.00360
2011.18767 1.75303 0.00369
2011.19041 1.75394 0.00354
2011.19315 1.75329 0.00361
2011.19589 1.75238 0.00402
2011.19863 1.75413 0.00352
2011.20137 1.75653 0.00360
2011.20411 1.75276 0.00368
2011.20685 1.75428 0.00390
2011.20959 1.75472 0.00344
2011.21233 1.75527 0.00354
2011.21507 1.75366 0.00357
2011.21781 1.76515 0.00461
2011.22055 1.76729 0.00466
2011.22329 1.75454 0.00376
2011.22603 1.75338 0.00382
2011.22877 1.75218 0.00394
2011.23150 1.75386 0.00421
2011.23424 1.75215 0.00386
2011.23698 1.75546 0.00378
2011.23972 1.75559 0.00388
2011.24246 1.75657 0.00500
2011.24520 1.75760 0.00449
2011.24794 1.75811 0.00433
2011.25068 1.76495 0.00474
2011.25342 1.75809 0.00491
2011.25616 1.75467 0.00444
2011.25890 1.75768 0.00544
2011.26164 1.75537 0.00415
2011.26438 1.75467 0.00413
2011.26712 1.76028 0.00479
2011.26986 1.75276 0.00453
2011.27260 1.76059 0.00494
2011.27534 1.75725 0.00383
2011.27808 1.75778 0.00373
2011.28082 1.75772 0.00382
2011.28356 1.75727 0.00409
2011.28630 1.75607 0.00415
2011.28904 1.75941 0.00385
2011.29178 1.75794 0.00380
2011.29452 1.75549 0.00387
2011.29726 1.75690 0.00412
2011.30000 1.75683 0.00392
2011.30274 1.75729 0.00382
2011.30548 1.75755 0.00374
2011.30822 1.75931 0.00421
2011.31096 1.75860 0.00425
2011.31370 1.75915 0.00386
2011.31644 1.75755 0.00390
2011.31918 1.76112 0.00379
2011.32192 1.76032 0.00450
2011.32466 1.75967 0.00415
2011.32740 1.76169 0.00448
2011.33014 1.75911 0.00437
2011.33287 1.76131 0.00478
2011.33561 1.75982 0.00450
2011.33835 1.76121 0.00378
2011.34109 1.75930 0.00360
2011.34383 1.75852 0.00356
2011.34657 1.75820 0.00352
2011.34931 1.76004 0.00377
2011.35205 1.75870 0.00391
2011.35479 1.75951 0.00403
2011.35753 1.76261 0.00445
2011.36027 1.76084 0.00451
2011.36301 1.76120 0.00396
2011.36575 1.75895 0.00386
2011.36849 1.76305 0.00392
2011.37123 1.76348 0.00400
2011.37397 1.76060 0.00442
2011.37671 1.76188 0.00382
2011.37945 1.75962 0.00384
2011.38219 1.76039 0.00341
2011.38493 1.75813 0.00375
2011.38767 1.75750 0.00357
2011.39041 1.75987 0.00459
2011.39315 1.76712 0.00473
2011.39589 1.76565 0.00418
2011.39863 1.76464 0.00370
2011.40137 1.76267 0.00391
2011.40411 1.76179 0.00361
2011.40685 1.76155 0.00358
2011.40959 1.76728 0.00433
2011.41233 1.76160 0.00360
2011.41507 1.76299 0.00360
2011.41781 1.76121 0.00343
2011.42055 1.76137 0.00354
2011.42329 1.76240 0.00370
2011.42603 1.76153 0.00357
2011.42877 1.76246 0.00377
2011.43150 1.76365 0.00401
2011.43424 1.76335 0.00397
2011.43698 1.76323 0.00380
2011.43972 1.76575 0.00391
2011.44246 1.76600 0.00392
2011.44520 1.76813 0.00378
2011.44794 1.76402 0.00361
2011.45068 1.76339 0.00356
2011.45342 1.76281 0.00356
2011.45616 1.76512 0.00413
2011.45890 1.76933 0.00405
2011.46164 1.76582 0.00362
2011.46438 1.76520 0.00363
2011.46712 1.76699 0.00374
2011.46986 1.76685 0.00362
2011.47260 1.76553 0.00362
2011.47534 1.76561 0.00356
2011.47808 1.76537 0.00386
2011.48082 1.76676 0.00418
2011.48356 1.76716 0.00384
2011.48630 1.76643 0.00349
2011.48904 1.76680 0.00344
2011.49178 1.76633 0.00347
2011.49452 1.76592 0.00374
2011.49726 1.76488 0.00356
2011.50000 1.76593 0.00349
2011.50274 1.76755 0.00350
2011.50548 1.76654 0.00365
2011.51096 1.76889 0.00363
2011.51370 1.76636 0.00354
2011.51644 1.76817 0.00353
2011.51918 1.76871 0.00354
2011.52192 1.77061 0.00358
2011.52466 1.76714 0.00341
2011.52740 1.76979 0.00358
2011.53014 1.76779 0.00333
2011.53287 1.76845 0.00370
2011.53561 1.76582 0.00364
2011.53835 1.76902 0.00345
2011.54109 1.76685 0.00338
2011.54383 1.76840 0.00335
2011.54657 1.76772 0.00349
2011.54931 1.76986 0.00348
2011.55205 1.76720 0.00362
2011.55479 1.76857 0.00363
2011.55753 1.76821 0.00381
2011.56027 1.77123 0.00423
2011.56301 1.76970 0.00389
2011.56575 1.76969 0.00357
2011.56849 1.76855 0.00347
2011.57123 1.76900 0.00342
2011.57397 1.76771 0.00336
2011.57671 1.77013 0.00337
2011.57945 1.76801 0.00352
2011.58219 1.76894 0.00386
2011.58493 1.76828 0.00349
2011.58767 1.76998 0.00366
2011.59041 1.77108 0.00355
2011.59315 1.76837 0.00375
2011.59589 1.76897 0.00370
2011.59863 1.76913 0.00355
2011.60137 1.76995 0.00383
2011.60411 1.77146 0.00367
2011.60685 1.76808 0.00344
2011.60959 1.76921 0.00378
2011.61233 1.77869 0.00475
2011.61507 1.77824 0.00460
2011.61781 1.78117 0.00454
2011.62055 1.78386 0.00496
2011.62329 1.78243 0.00505
2011.62603 1.78263 0.00463
2011.62877 1.78425 0.00465
2011.63150 1.78312 0.00443
2011.63424 1.78174 0.00453
2011.63698 1.78404 0.00453
2011.63972 1.78115 0.00439
2011.64246 1.78327 0.00454
2011.64520 1.78334 0.00441
2011.64794 1.78026 0.00443
2011.65068 1.78320 0.00460
2011.65342 1.77990 0.00495
2011.65616 1.78269 0.00468
2011.65890 1.78135 0.00440
2011.66164 1.78303 0.00445
2011.66438 1.78068 0.00466
2011.66712 1.78189 0.00486
2011.66986 1.78131 0.00441
2011.67260 1.77993 0.00473
2011.67534 1.78086 0.00484
2011.67808 1.77790 0.00516
2011.68082 1.78053 0.00469
2011.68356 1.78292 0.00447
2011.68630 1.78241 0.00455
2011.68904 1.78243 0.00469
2011.69178 1.77835 0.00493
2011.69452 1.77864 0.00528
2011.69726 1.77540 0.00491
2011.70000 1.77114 0.00356
2011.70274 1.77243 0.00370
2011.70548 1.77380 0.00362
2011.70822 1.77059 0.00380
2011.71096 1.77235 0.00383
2011.71370 1.77175 0.00366
2011.71644 1.77115 0.00407
2011.71918 1.77210 0.00364
2011.72192 1.77076 0.00410
2011.72466 1.77237 0.00377
2011.72740 1.77126 0.00400
2011.73014 1.77398 0.00398
2011.73287 1.77043 0.00363
2011.73561 1.77077 0.00371
2011.73835 1.77204 0.00364
2011.74109 1.76911 0.00402
2011.74383 1.77180 0.00365
2011.74657 1.77357 0.00424
2011.74931 1.77258 0.00395
2011.75205 1.77524 0.00377
2011.75479 1.77310 0.00491
2011.75753 1.77386 0.00425
2011.76027 1.77271 0.00396
2011.76301 1.77577 0.00434
2011.76575 1.77707 0.00452
2011.76849 1.77539 0.00433
2011.77123 1.77965 0.00429
2011.77397 1.77535 0.00460
2011.77671 1.77352 0.00420
2011.77945 1.77616 0.00375
2011.78219 1.77431 0.00440
2011.78493 1.77534 0.00423
2011.78767 1.78020 0.00467
2011.79041 1.77808 0.00414
2011.79315 1.77749 0.00438
2011.79589 1.77506 0.00436
2011.79863 1.77986 0.00390
2011.80137 1.77520 0.00414
2011.80411 1.77851 0.00367
2011.80685 1.77783 0.00391
2011.80959 1.77596 0.00385
2011.81233 1.77746 0.00375
2011.81507 1.77786 0.00387
2011.81781 1.77723 0.00382
2011.82055 1.77969 0.00402
2011.82329 1.78139 0.00405
2011.82603 1.78120 0.00417
2011.82877 1.78089 0.00405
2011.83150 1.78132 0.00376
2011.83424 1.77869 0.00394
2011.83698 1.77767 0.00441
2011.83972 1.77595 0.00409
2011.84246 1.78581 0.00545
2011.84794 1.78080 0.00406
2011.85068 1.77580 0.00415
2011.85342 1.77905 0.00364
2011.85616 1.77836 0.00380
2011.85890 1.77435 0.00431
2011.86164 1.77712 0.00420
2011.86438 1.77997 0.00528
2011.86712 1.77859 0.00413
2011.86986 1.77705 0.00426
2011.87260 1.77884 0.00413
2011.87534 1.77773 0.00446
2011.87808 1.77649 0.00518
2011.88082 1.78088 0.00466
2011.88356 1.77651 0.00393
2011.88630 1.77853 0.00394
2011.88904 1.77769 0.00399
2011.89178 1.77957 0.00407
2011.89452 1.78058 0.00422
2011.89726 1.77978 0.00437
2011.90000 1.78191 0.00429
2011.90274 1.77803 0.00399
2011.90548 1.77951 0.00394
2011.90822 1.78020 0.00371
2011.91096 1.77825 0.00474
2011.91370 1.77937 0.00386
2011.91644 1.78087 0.00394
2011.91918 1.78063 0.00389
2011.92192 1.78143 0.00375
2011.92466 1.77993 0.00414
2011.92740 1.77945 0.00393
2011.93014 1.78140 0.00453
2011.93287 1.78168 0.00393
2011.93561 1.77830 0.00406
2011.93835 1.78425 0.00418
2011.94109 1.77772 0.00425
2011.94383 1.78236 0.00367
2011.94657 1.78082 0.00381
2011.94931 1.78318 0.00385
2011.95205 1.78338 0.00399
2011.95479 1.78738 0.00424
2011.95753 1.78163 0.00393
2011.96027 1.78538 0.00373
2011.96301 1.78439 0.00372
2011.96575 1.78421 0.00389
2011.96849 1.78582 0.00483
2011.97123 1.78604 0.00370
2011.97397 1.78696 0.00378
2011.97671 1.78828 0.00410
2011.97945 1.78763 0.00397
2011.98219 1.78483 0.00365
2011.98493 1.78617 0.00368
2011.98767 1.78597 0.00373
2011.99041 1.78502 0.00370
2011.99315 1.78300 0.00415
2011.99589 1.78571 0.00382
2011.99863 1.78502 0.00396
  2 Comments
Chris Martin
Chris Martin on 6 Mar 2013
I want to extract the trend and the seasonal component from the time seris ie from the second column of my time series which represents continuous plate motion along with some seasonal fluctuation

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Accepted Answer

Wayne King
Wayne King on 6 Mar 2013
Edited: Wayne King on 6 Mar 2013
OK, I suspected but then didn't check, that was dumb of me..
So with that in mind:
resid = y-yfit;
% find the DFT of the residuals
residDFT = fft(resid);
Fs = 1;
freq = 0:Fs/length(resid):Fs/2;
residDFT = residDFT(1:floor(length(resid)/2)+1);
plot(freq(1:100),abs(residDFT(1:100)))
You'll see the biggest peak at a frequency of 0.002 cycles/day, which is a period of 500 days. Looks to me like the next most prominent peak is at 0.0059 cycles/day which is a period of almost 170 days (169.89).
I think if you fit those two frequencies using the Fourier coefficients along with the linear model fitted above, you'll have a very good fit to the data.
  2 Comments
Chris Martin
Chris Martin on 7 Mar 2013
I think this is the power spectrum?? Is not it sir..... And what is the unit in y-axis..

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More Answers (1)

Wayne King
Wayne King on 6 Mar 2013
Edited: Wayne King on 6 Mar 2013
Hi Chris, you can certainly fit the trend here by just using a simple linear model.
I'll use the variable gps_data to represent the 1529x3 data matrix.
% the design matrix
X = ones(size(gps_data,1),2);
X(:,2) = gps_data(:,1);
% the response variable
y = gps_data(:,2);
% if you have the Statistics Toolbox
[B,BINT,R,RINT,STATS] = regress(y,X);
% the fitted model
yfit = B(1)+B(2)*gps_data(:,1);
plot(gps_data(:,1),gps_data(:,2));
hold on
plot(gps_data(:,1),yfit,'r','linewidth',2)
If you do not have the Statistics Toolbox, then use
beta = X\y;
Next form the residuals to find the seasonal component
resid = y-yfit;
% find the DFT of the residuals
residDFT = fft(resid);
dt = 0.0027;
Fs = 1/dt;
freq = 0:Fs/length(resid):Fs/2;
residDFT = residDFT(1:floor(length(resid)/2)+1);
plot(freq(1:100),abs(residDFT(1:100)))
Can you tell me what this sampling interval of 0.0027 means here (that is not constant by the way, there are a few instances when that sampling interval changes...)
I need to understand the sampling interval to assign the correct frequency to the seasonal component.
  2 Comments
Chris Martin
Chris Martin on 6 Mar 2013
interval 0.00274 is equivalent to 1/365 i.e the unit of the second column is in per year.
365 days = 1 year 1 day=1/365 year
Chris Martin
Chris Martin on 7 Mar 2013
Thank you sir.... Now I want to obtain the amplitude of the noise present in the time series using MLE technique. How to approach ??? please help me

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