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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

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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Chris Martin

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1 Answer

Answer by Shashank Prasanna 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.

4 Comments

Shashank Prasanna 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
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 2009.60959      4.21674  0.00268
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 2009.62329      4.21730  0.00258
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 2009.63698      4.21685  0.00276
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 2009.64246      4.21715  0.00242
 2009.64520      4.21928  0.00241
 2009.64794      4.21815  0.00264
 2009.65068      4.21679  0.00293
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 2009.65616      4.21837  0.00247
 2009.65890      4.21553  0.00259
 2009.66164      4.22324  0.00290
 2009.66438      4.21857  0.00280
 2009.66712      4.21990  0.00284
 2009.66986      4.21997  0.00257
 2009.67260      4.22210  0.00317
 2009.67534      4.21588  0.00288
 2009.67808      4.21821  0.00287
 2009.68082      4.21721  0.00295
 2009.68356      4.21789  0.00312
 2009.68630      4.21999  0.00248
 2009.68904      4.22012  0.00244
 2009.69178      4.21881  0.00248
 2009.69452      4.22078  0.00236
 2009.69726      4.21998  0.00256
 2009.70000      4.22221  0.00280
 2009.70274      4.22947  0.00341
 2009.70548      4.22126  0.00297
 2009.70822      4.21993  0.00264
 2009.71370      4.22160  0.00273
 2009.71644      4.22250  0.00257
 2009.71918      4.22157  0.00339
 2009.72192      4.22572  0.00372
 2009.72466      4.22117  0.00346
 2009.72740      4.21658  0.00294
 2009.73014      4.22233  0.00262
 2009.73287      4.22331  0.00262
 2009.73561      4.22184  0.00260
 2009.73835      4.22225  0.00274
 2009.74109      4.22232  0.00255
 2009.74383      4.22349  0.00253
 2009.74657      4.22204  0.00250
 2009.74931      4.22240  0.00269
 2009.75205      4.22372  0.00270
 2009.75479      4.22151  0.00262
 2009.75753      4.22255  0.00246
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 2009.76301      4.22377  0.00242
 2009.76575      4.22179  0.00262
 2009.76849      4.22164  0.00300
 2009.77123      4.22293  0.00331
 2009.77397      4.22347  0.00324
 2009.77671      4.22297  0.00272
 2009.77945      4.22272  0.00277
 2009.78219      4.22321  0.00252
 2009.78493      4.22449  0.00261
 2009.78767      4.22479  0.00294
 2009.79041      4.22234  0.00287
 2009.79315      4.22338  0.00290
 2009.79589      4.22442  0.00254
 2009.79863      4.22461  0.00277
 2009.80137      4.22366  0.00286
 2009.80411      4.22262  0.00241
 2009.80685      4.22481  0.00270
 2009.80959      4.22483  0.00342
 2009.81233      4.22374  0.00283
 2009.81507      4.22454  0.00249
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 2009.82055      4.22242  0.00252
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 2009.82877      4.22446  0.00243
 2009.83150      4.22487  0.00230
 2009.83424      4.22442  0.00232
 2009.83698      4.22439  0.00230
 2009.83972      4.22478  0.00237
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 2009.84520      4.22254  0.00245
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 2009.85890      4.22487  0.00287
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 2009.86986      4.22454  0.00243
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 2009.87534      4.22284  0.00287
 2009.87808      4.20700  0.00495
 2009.88082      4.22552  0.00244
 2009.88356      4.22554  0.00250
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 2009.97123      4.22680  0.00215
 2009.97397      4.22740  0.00220
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 2009.98493      4.22813  0.00216
 2009.98767      4.22771  0.00218
 2009.99041      4.22739  0.00217
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 2010.05068      4.23047  0.00279
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 2010.10000      4.22955  0.00223
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 2010.10548      4.22934  0.00219
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 2010.20959      4.23848  0.00234
 2010.21233      4.23756  0.00232
 2010.21507      4.23838  0.00219
 2010.21781      4.23648  0.00245
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 2010.23424      4.23815  0.00355
 2010.23698      4.24319  0.00336
 2010.23972      4.24030  0.00269
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 2010.24520      4.23970  0.00450
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 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
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 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
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 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
Chris Martin on 19 Jan 2013

please some one help me

Shashank Prasanna

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