How to use Maximum Likelihood estimation technique to asses time correlated noise in the time series. I want to use MLE to characterize the amplitude of stochastic processes, please help me
Asked by Chris Martin on 17 Jan 2013
Latest activity Commented on by Chris Martin on 19 Jan 2013
How to use Maximum Likelihood estimation technique to asses time correlated noise in the time series. I want to use MLE to characterize the amplitude of stochastic processes please help me
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Answer by Shashank on 17 Jan 2013
MLE is used to fit a distribution, and in your situation I suppose a noise model. A least squares might work as well for normally distributed noise or errors but the fit statistics may be way off and you may have to use a HAC estimator to get an unbiased estimation of the fit statistics. To start with use the Durbin-Watson test (dwtest) to check for serial correlation in the residuals. Now to your question, is there a specific error model you are interested in? What is the distribution of you errors? is it normal or another distribution? MATLAB has mle to fit distributions based on data, as long as you can specify what distribution you want.
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Shashank on 17 Jan 2013
Sure, but you will have to define your distribution, do you already have a distribution assumption for the noise? if you do you then its as simple as plugging it into MLE function along with your data. I am not still unsure how to help you, any more information you could provide? about the data, noise model, maybe equations? anything more?
Chris Martin on 17 Jan 2013
MY data is GPS time series, the equation which governs the time series is y(t)=yl(t)+ys(t)+yn(t), where yl is the linear trend origination from long tectnoic movement, ys is the seasonal signal and yn is the noise. I am giving the time series below:
2005.10274 4.09545 0.00220 2005.10548 4.09536 0.00208 2005.10822 4.09617 0.00205 2005.11096 4.09598 0.00210 2005.11370 4.09613 0.00209 2005.11644 4.09542 0.00246 2005.11918 4.09971 0.00272 2005.12192 4.09823 0.00217 2005.12466 4.09820 0.00219 2005.12740 4.09889 0.00229 2005.13014 4.09800 0.00275 2005.13287 4.09814 0.00238 2005.13561 4.10149 0.00278 2005.13835 4.10014 0.00310 2005.14109 4.09741 0.00245 2005.14383 4.09702 0.00228 2005.14657 4.09793 0.00231 2005.14931 4.09854 0.00229 2005.15205 4.09778 0.00219 2005.15479 4.09807 0.00236 2005.15753 4.09898 0.00219 2005.16027 4.09919 0.00214 2005.16301 4.10132 0.00242 2005.16575 4.09928 0.00220 2005.16849 4.10011 0.00247 2005.17123 4.09893 0.00223 2005.17397 4.09844 0.00251 2005.17671 4.10027 0.00248 2005.17945 4.09816 0.00276 2005.18219 4.09862 0.00248 2005.18493 4.09730 0.00348 2005.20137 4.10211 0.00346 2005.20411 4.10057 0.00301 2005.20685 4.10015 0.00261 2005.20959 4.09938 0.00219 2005.21233 4.10160 0.00257 2005.21507 4.10149 0.00298 2005.21781 4.09779 0.00279 2005.22055 4.10304 0.00396 2005.22329 4.10156 0.00358 2005.22603 4.10307 0.00312 2005.22877 4.10139 0.00283 2005.23150 4.10112 0.00249 2005.23424 4.10368 0.00240 2005.23698 4.10373 0.00423 2005.23972 4.09897 0.00321 2005.24246 4.10522 0.00304 2005.24520 4.09993 0.00329 2005.24794 4.10410 0.00308 2005.25068 4.10149 0.00267 2005.25342 4.10057 0.00329 2005.25890 4.10206 0.00234 2005.26164 4.10517 0.00316 2005.26438 4.10357 0.00390 2005.26712 4.10267 0.00345 2005.26986 4.10598 0.00410 2005.27260 4.11013 0.00496 2005.27534 4.10229 0.00407 2005.27808 4.10341 0.00303 2005.28082 4.10247 0.00275 2005.28356 4.10513 0.00286 2005.28630 4.10494 0.00337 2005.28904 4.10370 0.00327 2005.29178 4.10104 0.00437 2005.29452 4.10274 0.00375 2005.29726 4.10152 0.00304 2005.30000 4.10538 0.00374 2005.30274 4.10502 0.00269 2005.30548 4.10301 0.00314 2005.30822 4.10429 0.00289 2005.31096 4.10465 0.00338 2005.31370 4.10479 0.00367 2005.31644 4.10138 0.00456 2005.31918 4.10326 0.00360 2005.32192 4.09906 0.00308 2005.32466 4.10260 0.00362 2005.32740 4.09836 0.00261 2005.33014 4.10237 0.00296 2005.33287 4.10147 0.00285 2005.33561 4.10085 0.00363 2005.33835 4.09766 0.00334 2005.34109 4.10119 0.00292 2005.34383 4.09967 0.00294 2005.34657 4.10336 0.00291 2005.34931 4.09844 0.00271 2005.35205 4.10176 0.00308 2005.35479 4.10043 0.00420 2005.35753 4.09916 0.00328 2005.36027 4.10588 0.00378 2005.36301 4.10510 0.00389 2005.36575 4.10071 0.00372 2005.36849 4.10378 0.00309 2005.37123 4.10389 0.00340 2005.37397 4.10348 0.00280 2005.37671 4.10369 0.00340 2005.37945 4.10277 0.00323 2005.38219 4.10494 0.00295 2005.38493 4.10544 0.00288 2005.38767 4.10343 0.00253 2005.39041 4.10602 0.00268 2005.39315 4.10594 0.00306 2005.39589 4.10699 0.00353 2005.39863 4.10586 0.00317 2005.40137 4.10352 0.00349 2005.40411 4.10355 0.00407 2005.40685 4.10518 0.00353 2005.40959 4.10672 0.00260 2005.41233 4.10463 0.00331 2005.41507 4.10456 0.00372 2005.41781 4.10280 0.00362 2005.42055 4.10774 0.00345 2005.42329 4.10100 0.01067 2005.42603 4.10529 0.00279 2005.42877 4.10760 0.00280 2005.43150 4.10816 0.00277 2005.43424 4.10526 0.00278 2005.43698 4.10609 0.00298 2005.43972 4.10313 0.00304 2005.44246 4.10300 0.00317 2005.44520 4.10427 0.00396 2005.44794 4.10368 0.00275 2005.45068 4.10500 0.00351 2005.45342 4.10498 0.00462 2005.45616 4.10387 0.00316 2005.45890 4.10560 0.00270 2005.46164 4.10445 0.00298 2005.46438 4.10554 0.00304 2005.46712 4.10405 0.00312 2005.46986 4.10783 0.00258 2005.47260 4.10753 0.00268 2005.47534 4.10439 0.00271 2005.47808 4.10429 0.00280 2005.48082 4.10518 0.00264 2005.48356 4.10730 0.00291 2005.48630 4.10270 0.00278 2005.48904 4.10448 0.00307 2005.49178 4.10684 0.00407 2005.49452 4.10504 0.00311 2005.49726 4.10364 0.00318 2005.50000 4.10577 0.00259 2005.50274 4.10526 0.00301 2005.50548 4.10902 0.00298 2005.50822 4.10692 0.00259 2005.51096 4.10984 0.00285 2005.51370 4.10874 0.00292 2005.51644 4.10414 0.00303 2005.51918 4.10585 0.00265 2005.52192 4.10745 0.00254 2005.52466 4.10559 0.00248 2005.52740 4.10853 0.00249 2005.53014 4.10845 0.00256 2005.53287 4.10613 0.00250 2005.53561 4.10607 0.00244 2005.53835 4.10627 0.00233 2005.54109 4.10897 0.00241 2005.54383 4.10794 0.00249 2005.54657 4.10611 0.00263 2005.54931 4.11164 0.00271 2005.55205 4.10668 0.00280 2005.55479 4.10612 0.00279 2005.55753 4.10588 0.00269 2005.56027 4.10681 0.00250 2005.56301 4.10635 0.00311 2005.56575 4.10742 0.00282 2005.56849 4.10595 0.00261 2005.57123 4.10671 0.00258 2005.57397 4.10731 0.00277 2005.57671 4.11049 0.00315 2005.57945 4.10874 0.00278 2005.58219 4.10649 0.00242 2005.58493 4.11129 0.00265 2005.58767 4.10699 0.00303 2005.59041 4.10875 0.00259 2005.59315 4.10785 0.00265 2005.59589 4.10714 0.00258 2005.59863 4.10772 0.00251 2005.60137 4.10669 0.00275 2005.60411 4.10799 0.00258 2005.60685 4.10712 0.00267 2005.60959 4.10774 0.00258 2005.61233 4.10836 0.00249 2005.61507 4.10960 0.00319 2005.61781 4.11177 0.00274 2005.62055 4.11125 0.00317 2005.62329 4.10753 0.00240 2005.62603 4.10862 0.00251 2005.62877 4.10859 0.00270 2005.63150 4.10684 0.00292 2005.63424 4.10799 0.00292 2005.63698 4.10874 0.00278 2005.63972 4.10934 0.00267 2005.64246 4.11033 0.00308 2005.64520 4.11309 0.00291 2005.64794 4.10747 0.00264 2005.65068 4.10581 0.00325 2005.65342 4.10647 0.00335 2005.65616 4.10607 0.00321 2005.65890 4.10862 0.00363 2005.66164 4.11129 0.00308 2005.66438 4.10802 0.00250 2005.66712 4.10939 0.00266 2005.66986 4.11200 0.00313 2005.67260 4.10943 0.00273 2005.67534 4.10756 0.00270 2005.67808 4.10795 0.00230 2005.68082 4.10901 0.00236 2005.68356 4.10729 0.00254 2005.68630 4.10764 0.00279 2005.68904 4.10823 0.00268 2005.69178 4.10932 0.00256 2005.69452 4.11077 0.00271 2005.69726 4.10934 0.00253 2005.70000 4.11048 0.00282 2005.70274 4.10977 0.00253 2005.70548 4.11002 0.00266 2005.70822 4.10922 0.00272 2005.71096 4.10991 0.00229 2005.71370 4.10965 0.00241 2005.71644 4.11050 0.00244 2005.71918 4.10968 0.00252 2005.72192 4.10970 0.00246 2005.72466 4.11007 0.00238 2005.72740 4.10698 0.00282 2005.73014 4.11300 0.00275 2005.73287 4.10849 0.00263 2005.73561 4.10883 0.00264 2005.73835 4.10837 0.00274 2005.74109 4.11009 0.00262 2005.74383 4.10850 0.00285 2005.74657 4.11092 0.00356 2005.74931 4.11059 0.00250 2005.75205 4.10912 0.00243 2005.75479 4.11143 0.00240 2005.75753 4.10913 0.00285 2005.76027 4.11125 0.00273 2005.76301 4.11064 0.00279 2005.76575 4.11052 0.00309 2005.76849 4.11014 0.00278 2005.77123 4.11014 0.00289 2005.77397 4.11042 0.00297 2005.77671 4.11181 0.00273 2005.77945 4.11266 0.00310 2005.78219 4.11269 0.00318 2005.78493 4.11150 0.00253 2005.78767 4.11280 0.00261 2005.79041 4.11317 0.00285 2005.79315 4.11311 0.00278 2005.79589 4.11313 0.00237 2005.79863 4.11367 0.00252 2005.80137 4.11380 0.00232 2005.80411 4.11348 0.00222 2005.80685 4.11354 0.00282 2005.80959 4.11255 0.00277 2005.81233 4.11187 0.00217 2005.81507 4.11241 0.00241 2005.81781 4.11254 0.00231 2005.82055 4.11100 0.00271 2005.82329 4.11277 0.00227 2005.82603 4.11159 0.00230 2005.82877 4.11025 0.00247 2005.83150 4.11204 0.00299 2005.83424 4.11282 0.00244 2005.83698 4.11209 0.00230 2005.83972 4.11176 0.00220 2005.84246 4.11267 0.00275 2005.84520 4.11383 0.00244 2005.84794 4.11183 0.00235 2005.85068 4.10868 0.00245 2005.85342 4.11237 0.00237 2005.85616 4.11061 0.00243 2005.85890 4.10971 0.00246 2005.86164 4.11215 0.00230 2005.86438 4.11522 0.00230 2005.86712 4.11395 0.00230 2005.86986 4.11453 0.00216 2005.87260 4.11535 0.00213 2005.87534 4.11574 0.00213 2005.87808 4.11464 0.00239 2005.88082 4.11461 0.00226 2005.88356 4.11389 0.00232 2005.88630 4.11555 0.00224 2005.88904 4.11473 0.00243 2005.89178 4.11377 0.00237 2005.89452 4.11513 0.00230 2005.89726 4.11527 0.00232 2005.90000 4.11732 0.00217 2005.90274 4.12105 0.00220 2005.90548 4.11698 0.00218 2005.90822 4.11680 0.00228 2005.91096 4.11627 0.00216 2005.91370 4.11607 0.00215 2005.91644 4.11557 0.00218 2005.91918 4.11870 0.00216 2005.92192 4.11756 0.00214 2005.92466 4.11605 0.00224 2005.92740 4.11677 0.00221 2005.93014 4.11689 0.00208 2005.93287 4.11757 0.00215 2005.93561 4.11859 0.00214 2005.93835 4.12318 0.00226 2005.94109 4.12160 0.00236 2005.94383 4.11909 0.00217 2005.94657 4.11879 0.00216 2005.94931 4.11870 0.00225 2005.95205 4.11725 0.00220 2005.95479 4.11810 0.00221 2005.95753 4.11909 0.00224 2005.96027 4.11729 0.00219 2005.96301 4.11676 0.00221 2005.96575 4.11794 0.00216 2005.96849 4.11895 0.00222 2005.97123 4.11680 0.00233 2005.97397 4.11676 0.00244 2005.97671 4.11752 0.00228 2005.97945 4.11780 0.00217 2005.98219 4.11819 0.00219 2005.98493 4.11821 0.00225 2005.98767 4.11947 0.00222 2005.99041 4.11651 0.00233 2005.99315 4.11599 0.00221 2005.99589 4.11607 0.00216 2005.99863 4.11688 0.00209 2006.00137 4.11699 0.00205 2006.00411 4.11653 0.00214 2006.00685 4.11574 0.00213 2006.00959 4.11806 0.00215 2006.01233 4.11936 0.00224 2006.01507 4.11837 0.00222 2006.01781 4.11605 0.00227 2006.02055 4.12354 0.00236 2006.02329 4.12688 0.00232 2006.02603 4.12758 0.00229 2006.02877 4.13006 0.00332 2006.04520 4.11826 0.00280 2006.04794 4.11942 0.00218 2006.05068 4.12038 0.00211 2006.05342 4.12102 0.00213 2006.05616 4.12192 0.00212 2006.05890 4.12102 0.00224 2006.06164 4.12100 0.00215 2006.06438 4.12215 0.00216 2006.06712 4.12062 0.00216 2006.06986 4.12232 0.00251 2006.07260 4.12194 0.00217 2006.07534 4.12181 0.00220 2006.07808 4.12231 0.00237 2006.08082 4.12086 0.00211 2006.08356 4.12222 0.00204 2006.08630 4.12317 0.00207 2006.08904 4.12346 0.00211 2006.09178 4.12399 0.00211 2006.09726 4.12215 0.00226 2006.10000 4.12159 0.00287 2006.10274 4.12363 0.00225 2006.10548 4.12349 0.00223 2006.10822 4.12245 0.00305 2006.11096 4.12118 0.00225 2006.11370 4.12125 0.00215 2006.11644 4.12234 0.00220 2006.11918 4.12371 0.00220 2006.12192 4.12169 0.00225 2006.12466 4.12504 0.00307 2006.12740 4.12362 0.00256 2006.13014 4.12402 0.00274 2006.13287 4.12324 0.00217 2006.13561 4.12507 0.00210 2006.13835 4.12631 0.00223 2006.14109 4.12516 0.00250 2006.14383 4.12600 0.00241 2006.14657 4.12513 0.00217 2006.14931 4.12497 0.00241 2006.15205 4.12554 0.00233 2006.15479 4.12582 0.00237 2006.15753 4.12452 0.00247 2006.16027 4.12452 0.00350 2006.20959 4.12704 0.00263 2006.21233 4.12483 0.00244 2006.21507 4.12586 0.00227 2006.21781 4.12592 0.00235 2006.22055 4.12710 0.00301 2006.22329 4.12663 0.00258 2006.22603 4.12648 0.00233 2006.22877 4.12630 0.00232 2006.23150 4.12760 0.00246 2006.23424 4.12929 0.00248 2006.23698 4.12801 0.00269 2006.23972 4.12809 0.00250 2006.24246 4.12731 0.00245 2006.24520 4.12751 0.00232 2006.24794 4.12627 0.00280 2006.25068 4.12611 0.00350 2006.25342 4.12751 0.00299 2006.25616 4.12614 0.00379 2006.25890 4.12681 0.00366 2006.26164 4.12806 0.00362 2006.26438 4.12965 0.00288 2006.26712 4.12416 0.00572 2006.27534 4.12984 0.00345 2006.27808 4.12758 0.00351 2006.28082 4.12857 0.00351 2006.28356 4.13161 0.00293 2006.28630 4.12988 0.00306 2006.28904 4.12827 0.00292 2006.29178 4.12715 0.00289 2006.29452 4.12612 0.00253 2006.29726 4.12835 0.00254 2006.30000 4.12754 0.00289 2006.30274 4.12921 0.00271 2006.30548 4.12862 0.00246 2006.30822 4.12970 0.00241 2006.31096 4.12907 0.00268 2006.31370 4.13277 0.00329 2006.31918 4.13131 0.00244 2006.32192 4.13014 0.00266 2006.32466 4.12885 0.00249 2006.32740 4.12962 0.00239 2006.33014 4.12786 0.00281 2006.33287 4.12904 0.00275 2006.33561 4.12808 0.00298 2006.33835 4.13034 0.00354 2006.34109 4.13001 0.00327 2006.34383 4.13042 0.00266 2006.34657 4.13153 0.00247 2006.34931 4.13211 0.00256 2006.35205 4.13206 0.00276 2006.35479 4.13546 0.00335 2006.35753 4.13148 0.00280 2006.36027 4.13213 0.00398 2006.36301 4.13363 0.00265 2006.36575 4.13327 0.00253 2006.36849 4.12991 0.00300 2006.37123 4.13215 0.00297 2006.37397 4.12956 0.00325 2006.37671 4.13370 0.00302 2006.37945 4.13351 0.00338 2006.38219 4.12916 0.00299 2006.38493 4.13108 0.00323 2006.38767 4.13301 0.00247 2006.39041 4.13271 0.00273 2006.39315 4.13351 0.00254 2006.39589 4.13176 0.00291 2006.39863 4.13452 0.00248 2006.40137 4.13227 0.00252 2006.40411 4.13140 0.00252 2006.40685 4.13312 0.00312 2006.40959 4.13293 0.00302 2006.41233 4.12820 0.00322 2006.41507 4.13055 0.00249 2006.41781 4.13272 0.00265 2006.42055 4.13049 0.00253 2006.42329 4.12985 0.00272 2006.42603 4.13370 0.00281 2006.42877 4.13339 0.00282 2006.43150 4.13288 0.00314 2006.43424 4.13254 0.00382 2006.43698 4.13406 0.00265 2006.43972 4.13330 0.00254 2006.44246 4.13160 0.00321 2006.44520 4.13296 0.00454 2006.44794 4.13181 0.00370 2006.45068 4.13114 0.00344 2006.45342 4.13500 0.00320 2006.45616 4.13533 0.00320 2006.45890 4.13381 0.00265 2006.46164 4.13402 0.00265 2006.46438 4.13318 0.00285 2006.46712 4.13448 0.00280 2006.46986 4.13393 0.00254 2006.47260 4.13186 0.00352 2006.47534 4.13223 0.00270 2006.47808 4.13455 0.00259 2006.48082 4.13376 0.00253 2006.48356 4.13226 0.00248 2006.48630 4.13219 0.00269 2006.48904 4.13328 0.00253 2006.49178 4.13538 0.00264 2006.49452 4.13460 0.00281 2006.49726 4.13463 0.00258 2006.50000 4.13441 0.00293 2006.50274 4.13687 0.00301 2006.50548 4.13690 0.00283 2006.50822 4.13814 0.00302 2006.51096 4.13804 0.00295 2006.51370 4.13772 0.00287 2006.51644 4.13704 0.00269 2006.51918 4.13790 0.00305 2006.52192 4.13561 0.00294 2006.52466 4.13676 0.00263 2006.52740 4.13332 0.00283 2006.53014 4.13356 0.00252 2006.53287 4.13540 0.00261 2006.53561 4.13366 0.00269 2006.53835 4.13378 0.00275 2006.54109 4.13491 0.00290 2006.54383 4.13491 0.00249 2006.54657 4.13499 0.00252 2006.54931 4.13403 0.00269 2006.55205 4.13541 0.00274 2006.55479 4.13713 0.00246 2006.55753 4.13510 0.00333 2006.56027 4.13682 0.00314 2006.56301 4.13722 0.00250 2006.56575 4.13324 0.00253 2006.56849 4.13436 0.00264 2006.57123 4.13333 0.00282 2006.57397 4.13337 0.00329 2006.57671 4.13589 0.00241 2006.57945 4.13557 0.00274 2006.58219 4.13564 0.00243 2006.58493 4.13569 0.00264 2006.58767 4.13490 0.00266 2006.59041 4.13596 0.00269 2006.59315 4.13224 0.00243 2006.59589 4.13307 0.00245 2006.59863 4.13624 0.00239 2006.60137 4.13434 0.00252 2006.60411 4.13610 0.00249 2006.60685 4.13499 0.00248 2006.60959 4.13730 0.00362 2006.61507 4.13788 0.00256 2006.61781 4.13724 0.00268 2006.62055 4.13418 0.00271 2006.62329 4.13804 0.00291 2006.62603 4.13724 0.00262 2006.62877 4.13094 0.00278 2006.63150 4.13442 0.00256 2006.63424 4.13338 0.00273 2006.63698 4.13955 0.00256 2006.63972 4.13542 0.00246 2006.64246 4.13694 0.00274 2006.64520 4.13646 0.00302 2006.64794 4.13601 0.00276 2006.65068 4.13661 0.00254 2006.65342 4.13719 0.00261 2006.65616 4.13624 0.00236 2006.65890 4.13861 0.00248 2006.66164 4.13744 0.00240 2006.66438 4.13642 0.00243 2006.66712 4.13761 0.00248 2006.66986 4.13936 0.00300 2006.67260 4.14029 0.00275 2006.67534 4.13921 0.00249 2006.67808 4.13745 0.00266 2006.68082 4.13658 0.00319 2006.68356 4.13740 0.00258 2006.68630 4.13933 0.00256 2006.68904 4.13899 0.00256 2006.69178 4.13989 0.00280 2006.69452 4.13675 0.00244 2006.69726 4.13673 0.00242 2006.70000 4.13934 0.00289 2006.70274 4.13939 0.00292 2006.70548 4.13645 0.00285 2006.71918 4.13837 0.00331 2006.72192 4.14068 0.00238 2006.72466 4.13847 0.00230 2006.72740 4.13939 0.00239 2006.73014 4.13898 0.00252 2006.73287 4.13991 0.00249 2006.73561 4.13973 0.00267 2006.73835 4.13837 0.00289 2006.74109 4.13659 0.00287 2006.74383 4.14025 0.00443 2006.76027 4.13957 0.00274 2006.76301 4.13522 0.00255 2006.76575 4.13853 0.00260 2006.76849 4.14028 0.00283 2006.77123 4.14113 0.00257 2006.77397 4.13912 0.00267 2006.77671 4.13922 0.00320 2006.77945 4.13982 0.00288 2006.78219 4.13967 0.00268 2006.78493 4.13310 0.00389 2006.78767 4.14119 0.00288 2006.79041 4.14028 0.00289 2006.79315 4.14058 0.00290 2006.79589 4.14202 0.00247 2006.79863 4.14100 0.00248 2006.80137 4.13902 0.00314 2006.80411 4.14170 0.00286 2006.80685 4.14224 0.00227 2006.80959 4.14280 0.00239 2006.81233 4.14167 0.00257 2006.81507 4.14369 0.00242 2006.81781 4.14359 0.00235 2006.82055 4.14287 0.00241 2006.82329 4.14303 0.00254 2006.83424 4.14134 0.00271 2006.83698 4.14050 0.00349 2006.84794 4.14336 0.00249 2006.85068 4.14202 0.00236 2006.85342 4.14292 0.00242 2006.85616 4.14384 0.00270 2006.85890 4.14389 0.00250 2006.86164 4.14373 0.00263 2006.86438 4.14133 0.00228 2006.86712 4.14184 0.00221 2006.86986 4.14225 0.00237 2006.87260 4.14387 0.00234 2006.87534 4.14154 0.00226 2006.87808 4.14372 0.00244 2006.88082 4.14239 0.00233 2006.88356 4.14371 0.00246 2006.88630 4.14397 0.00233 2006.88904 4.14281 0.00210 2006.89178 4.14430 0.00223 2006.89452 4.14408 0.00224 2006.89726 4.14310 0.00245 2006.90000 4.14452 0.00237 2006.90274 4.14305 0.00254 2006.90548 4.14314 0.00219 2006.90822 4.14339 0.00220 2006.91096 4.14361 0.00215 2006.91370 4.14501 0.00211 2006.91644 4.14455 0.00207 2006.91918 4.14494 0.00216 2006.92192 4.14740 0.00239 2006.92466 4.14450 0.00226 2006.92740 4.14489 0.00209 2006.93014 4.14512 0.00220 2006.93287 4.14407 0.00208 2006.93561 4.14510 0.00215 2006.93835 4.14521 0.00210 2006.94109 4.14312 0.00214 2006.94383 4.14483 0.00229 2006.94657 4.14334 0.00249 2006.94931 4.14512 0.00222 2006.95205 4.14468 0.00210 2006.95479 4.14611 0.00210 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2009.92192 4.22591 0.00216 2009.92466 4.22613 0.00216 2009.92740 4.22485 0.00226 2009.93014 4.22671 0.00232 2009.93287 4.22500 0.00270 2009.93561 4.22521 0.00260 2009.93835 4.22618 0.00263 2009.94109 4.22684 0.00258 2009.94383 4.22744 0.00265 2009.94657 4.22586 0.00257 2009.94931 4.22736 0.00260 2009.95205 4.22678 0.00260 2009.95479 4.22769 0.00253 2009.95753 4.22786 0.00241 2009.96027 4.22986 0.00219 2009.96301 4.22776 0.00226 2009.96575 4.22677 0.00238 2009.96849 4.22702 0.00216 2009.97123 4.22680 0.00215 2009.97397 4.22740 0.00220 2009.97671 4.22857 0.00227 2009.97945 4.22789 0.00245 2009.98219 4.22836 0.00223 2009.98493 4.22813 0.00216 2009.98767 4.22771 0.00218 2009.99041 4.22739 0.00217 2009.99315 4.22755 0.00238 2009.99589 4.22637 0.00259 2009.99863 4.22539 0.00260 2010.00137 4.22623 0.00251 2010.00411 4.22532 0.00250 2010.00685 4.22680 0.00248 2010.00959 4.22798 0.00223 2010.01233 4.23021 0.00220 2010.01507 4.22843 0.00221 2010.01781 4.22925 0.00219 2010.02055 4.23070 0.00218 2010.02329 4.23228 0.00229 2010.02603 4.23098 0.00222 2010.02877 4.23261 0.00221 2010.03150 4.22880 0.00219 2010.03424 4.22700 0.00230 2010.03698 4.22800 0.00226 2010.03972 4.22947 0.00224 2010.04246 4.22996 0.00229 2010.04520 4.22910 0.00259 2010.04794 4.22991 0.00235 2010.05068 4.23047 0.00279 2010.05342 4.22906 0.00226 2010.05616 4.22968 0.00228 2010.05890 4.22932 0.00218 2010.06164 4.22988 0.00217 2010.06438 4.22964 0.00212 2010.06712 4.22978 0.00226 2010.06986 4.22887 0.00221 2010.07260 4.22957 0.00219 2010.07808 4.22864 0.00223 2010.08082 4.23074 0.00217 2010.08356 4.23087 0.00214 2010.08904 4.23054 0.00224 2010.09178 4.23082 0.00223 2010.09452 4.22963 0.00218 2010.09726 4.23036 0.00217 2010.10000 4.22955 0.00223 2010.10274 4.22875 0.00213 2010.10548 4.22934 0.00219 2010.10822 4.23025 0.00225 2010.11096 4.23292 0.00228 2010.11370 4.23590 0.00236 2010.11918 4.23580 0.00252 2010.12192 4.23360 0.00264 2010.12740 4.23607 0.00239 2010.13014 4.23450 0.00241 2010.13561 4.23299 0.00235 2010.13835 4.23400 0.00237 2010.14109 4.23384 0.00214 2010.14383 4.23398 0.00226 2010.14657 4.23454 0.00243 2010.14931 4.23374 0.00253 2010.15205 4.23468 0.00248 2010.15479 4.23394 0.00235 2010.15753 4.23511 0.00226 2010.16027 4.23580 0.00221 2010.16301 4.23544 0.00237 2010.16575 4.23408 0.00307 2010.16849 4.23377 0.00270 2010.17123 4.23411 0.00242 2010.17397 4.23488 0.00244 2010.17671 4.23567 0.00261 2010.17945 4.23552 0.00240 2010.18219 4.23518 0.00245 2010.18493 4.23863 0.00242 2010.18767 4.23552 0.00231 2010.19041 4.23677 0.00256 2010.19315 4.23806 0.00231 2010.19589 4.23849 0.00240 2010.19863 4.23918 0.00269 2010.20137 4.24009 0.00268 2010.20411 4.23813 0.00244 2010.20685 4.23783 0.00228 2010.20959 4.23848 0.00234 2010.21233 4.23756 0.00232 2010.21507 4.23838 0.00219 2010.21781 4.23648 0.00245 2010.22055 4.23680 0.00250 2010.22329 4.23754 0.00308 2010.22603 4.23869 0.00293 2010.22877 4.24069 0.00294 2010.23150 4.23758 0.00275 2010.23424 4.23815 0.00355 2010.23698 4.24319 0.00336 2010.23972 4.24030 0.00269 2010.24246 4.24093 0.00367 2010.24520 4.23970 0.00450 2010.24794 4.23772 0.00330 2010.25068 4.23617 0.00346 2010.25342 4.24180 0.00397 2010.25616 4.24238 0.00344 2010.25890 4.23842 0.00328 2010.26164 4.24107 0.00295 2010.26438 4.24192 0.00241 2010.26712 4.24158 0.00265 2010.26986 4.24251 0.00294 2010.27260 4.23897 0.00306 2010.27534 4.24120 0.00311 2010.27808 4.24344 0.00318 2010.28082 4.24052 0.00329 2010.28356 4.23537 0.00328 2010.28630 4.24350 0.00279 2010.28904 4.23929 0.00249 2010.29178 4.24290 0.00271 2010.29452 4.24401 0.00274 2010.29726 4.24488 0.00349 2010.30000 4.23938 0.00301 2010.30274 4.23901 0.00351 2010.30548 4.23991 0.00329 2010.30822 4.24150 0.00350 2010.31096 4.24510 0.00371 2010.31370 4.24437 0.00365 2010.31644 4.24390 0.00357 2010.31918 4.24265 0.00259 2010.32192 4.24071 0.00249 2010.32466 4.24064 0.00280 2010.33014 4.23988 0.00242 2010.33287 4.24411 0.00255 2010.33561 4.24049 0.00266 2010.33835 4.24281 0.00310 2010.34109 4.24229 0.00266 2010.34383 4.24255 0.00251 2010.34657 4.24129 0.00330 2010.34931 4.24401 0.00269 2010.35205 4.24167 0.00299 2010.35479 4.24044 0.00331 2010.35753 4.24066 0.00474 2010.36027 4.23824 0.00494 2010.36575 4.23963 0.00478 2010.36849 4.24281 0.00334 2010.37123 4.24171 0.00330 2010.37397 4.24408 0.00281 2010.37671 4.24032 0.00268 2010.37945 4.24417 0.00286 2010.38219 4.24101 0.00348 2010.38493 4.24263 0.00350
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