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## HYBRID STRATEGY FOR VOLATILITY PREDICTION THAT RELIABLY BEATS GARCH(1,1)

We have six strategies with EXPONENTIAL GARCH(1,1) i.e. the model

$r_t = e^{h_t/2} z_t$ with $z_t \sim N(0,1)$ with $h_t$ following some GARCH type process as the benchmark.

The strategies are GARCH(1,1), GARCH(1,1)+AggVol, GARCH(5,1),GARCH(5,1)+AggVol, GARCH-MLF, GARCH-MLF+AggVol.  The hybrid strategy is simply to pick one of these based on lowest in-sample MAD error and compare the out-of-sample MAD error to GARCH and the best of 6.

The average improvement over GARCH(1,1) and the statistics of the strategy picked over train-test periods are:

error: 0.20816568315 std 0.429460284854
{‘G’: 12, ‘Gmlf’: 59, ‘GA’: 50, ‘GmlfA’: 25, ‘Gpq’: 27, ‘GpqA’: 49}

```in
[ 5.00322229  4.99335482  4.99302689  4.99330799  5.04856508  4.69094982]
out
Chose  5.11528387941 GmlfA best  5.11528387941 GmlfA
Improvement over GARCH(1,1): 0.09157082588
[ 5.20685471  5.41898385  5.41204648  5.4103377   5.3347274   5.11528388]
in
[ 4.94414533  4.94223409  4.93333856  4.93309792  5.01499511  6.41942232]
out
Chose  4.81599982007 GpqA best  4.81599982007 GpqA
Improvement over GARCH(1,1): 0.02077448222
[ 4.8367743   4.83870843  4.81611213  4.81599982  4.98492376  6.261753  ]
in
[ 4.68825969  4.68426829  4.67884959  4.67892997  4.78562853  7.7028841 ]
out
Chose  3.74966888273 Gpq best  3.74960394213 GpqA
Improvement over GARCH(1,1): 0.01349743702
[ 3.76316632  3.75835226  3.74966888  3.74960394  4.30822046  6.62960321]
in
[ 4.53280832  4.53234976  4.51266103  4.51287845  4.59418766  5.67152946]
out
Chose  5.48170473117 Gpq best  5.25505212614 Gmlf
Improvement over GARCH(1,1): 0.05771552511
[ 5.53942026  5.54050727  5.48170473  5.48245003  5.25505213  6.66544879]
in
[ 4.67569025  4.67108987  4.64229118  4.64257565  4.77089709  6.96423245]
out
Chose  4.36983118218 Gpq best  4.36983118218 Gpq
Improvement over GARCH(1,1): 0.01424010721
[ 4.38407129  4.37879607  4.36983118  4.37051867  4.63850819  6.55337767]
in
[ 4.63987003  4.63923802  4.63156776  4.63541575  4.76793833  4.57713332]
out
Chose  5.49237567336 GmlfA best  5.30320631658 Gmlf
Improvement over GARCH(1,1): 0.04477437331
[ 5.53715005  5.53583007  5.50437224  5.4995752   5.30320632  5.49237567]
in
[ 4.67211181  4.66869099  4.66856921  4.67185818  4.81029841  5.15689691]
out
Chose  5.3133662028 Gpq best  5.24307733042 Gmlf
Improvement over GARCH(1,1): 0.0181839017
[ 5.3315501   5.32853013  5.3133662   5.31378992  5.24307733  5.84604275]
in
[ 4.71316505  4.71186559  4.69449288  4.63735702  4.82174138  8.67630386]
out
Chose  4.66807672759 GpqA best  4.66807672759 GpqA
Improvement over GARCH(1,1): 0.33881512285
[ 5.00689185  5.00206704  4.98601457  4.66807673  4.99575383  8.81450457]
in
[ 4.95686774  4.95677679  4.94628149  4.93888116  5.05909652  8.79254303]
out
Chose  4.70198018327 GpqA best  4.70198018327 GpqA
Improvement over GARCH(1,1): 0.20940918285
[ 4.91138937  4.91123369  4.90505563  4.70198018  5.07771257  8.5620961 ]
in
[ 4.81585814  4.81600999  4.80057267  4.79973402  4.91228168  8.11733326]
out
Chose  4.99236588785 GpqA best  4.99236588785 GpqA
Improvement over GARCH(1,1): 0.07999549835
[ 5.07236139  5.07107671  5.00084377  4.99236589  5.09328287  8.25621568]
in
[ 4.91591227  4.91510241  4.88098157  4.88898506  4.97093024  7.61771195]
out
Chose  4.63353811091 Gpq best  4.63353811091 Gpq
Improvement over GARCH(1,1): 0.09578479145
[ 4.7293229   4.73097692  4.63353811  4.67039236  4.88819028  7.29815466]
in
[ 4.80812024  4.80266317  4.7532318   4.77325714  4.86541333  6.71372798]
out
Chose  4.77061263781 Gpq best  4.74576515087 GpqA
Improvement over GARCH(1,1): 0.02836985796
[ 4.7989825   4.78167533  4.77061264  4.74576515  4.8816717   6.62549715]
in
[ 4.78364832  4.78251617  4.75490442  4.75513619  4.84434459  6.46476148]
out
Chose  4.85542197151 Gpq best  4.84855464755 GpqA
Improvement over GARCH(1,1): 0.03270124269
[ 4.88812321  4.88611392  4.85542197  4.84855465  4.96869231  6.4961244 ]
in
[ 4.73884142  4.71556203  4.71692568  4.71861272  4.75586563  7.17352786]
out
Chose  4.78803998796 GA best  4.78803998796 GA
Improvement over GARCH(1,1): 0.00574468062
[ 4.79378467  4.78803999  4.80068504  4.81777544  4.88079045  7.21312106]
in
[ 4.77108267  4.75016534  4.72867512  4.72322687  4.86956486  8.56761375]
out
Chose  4.39247710319 GpqA best  4.32688092318 GA
Improvement over GARCH(1,1): 0.03225586452
[ 4.42473297  4.32688092  4.44845277  4.3924771   4.85495325  8.31088128]
in
[ 4.7380139   4.73345556  4.67215223  4.66929528  4.82367951  6.12655324]
out
Chose  inf GpqA best  inf G
Improvement over GARCH(1,1): nan
[ inf  inf  inf  inf  inf  inf]
in
[ 4.86470411  4.85714167  4.79730697  4.79848113  4.99891679  6.11602384]
out
Chose  4.7192210493 Gpq best  4.67716013216 GpqA
Improvement over GARCH(1,1): 0.02828124616
[ 4.7475023   4.7327547   4.71922105  4.67716013  4.98670525  5.9473419 ]
in
[ 4.89182646  4.89055092  4.85913752  4.83101014  5.00549909  5.45778283]
out
Chose  4.4575117124 GpqA best  4.4575117124 GpqA
Improvement over GARCH(1,1): 0.01119884088
[ 4.46871055  4.4746654   4.48839359  4.45751171  4.80682214  4.99666108]
in
[ 4.74441217  4.730875    4.72561116  4.7545891   4.93062058  6.75779869]
out
Chose  4.11548768037 Gpq best  4.08398650584 GpqA
Improvement over GARCH(1,1): 0.03584851828
[ 4.1513362   4.12476436  4.11548768  4.08398651  4.60579956  6.01034632]
in
[ 4.57239165  4.57003214  4.57439396  4.55928427  4.74498724  7.27043234]
out
Chose  4.47263936285 GpqA best  4.46310072743 GA
Improvement over GARCH(1,1): -0.00858904451
[ 4.46405032  4.46310073  4.47615627  4.47263936  4.70600855  7.00406277]
in
[ inf  inf  inf  inf  inf  inf]
out
Chose  7.8193307775 G best  4.08232361308 Gpq
Improvement over GARCH(1,1): 0.0
[ 7.81933078  7.81933078  4.08232361  4.08232361  7.30987     7.57141418]
in
[ 4.40767681  4.40622022  4.38259684  4.38087593  4.44901649  7.25337854]
out
Chose  4.36612932651 GpqA best  4.35345956253 GA
Improvement over GARCH(1,1): -0.01239869687
[ 4.35373063  4.35345956  4.36727248  4.36612933  4.45200564  7.08059247]
in
[ 4.32492557  4.3102127   4.31248041  4.31863428  4.38913333  6.49962469]
out
Chose  3.64036295532 GA best  3.64036295532 GA
Improvement over GARCH(1,1): 0.00979889541
[ 3.65016185  3.64036296  3.68862466  3.68973169  4.04768186  5.63162257]
in
[ 4.3236204   4.27334187  4.3151591   4.31507277  4.34985809  7.73488509]
out
Chose  4.28932602579 GA best  4.28932602579 GA
Improvement over GARCH(1,1): 0.10776897115
[ 4.397095    4.28932603  4.37561883  4.36666835  4.50452958  7.77900783]
in
[ 4.38272561  4.3495117   4.36866205  4.35587564  4.38597452  6.01643444]
out
Chose  4.52351893032 GA best  4.51895308779 Gmlf
Improvement over GARCH(1,1): 0.0413802063
[ 4.56489914  4.52351893  4.5460842   4.52787462  4.51895309  6.15842453]
in
[ 4.34021925  4.29171165  4.33890363  4.28207296  4.3719913   6.79096745]
out
Chose  4.60921420954 GpqA best  4.59558954939 GA
Improvement over GARCH(1,1): 0.0511133482
[ 4.66032756  4.59558955  4.67857243  4.60921421  4.68596736  7.15483992]
in
[ 4.33318184  4.28241741  4.3299502   4.26712177  4.3517512   7.51530444]
out
Chose  4.9387832683 GpqA best  4.91558811538 Gmlf
Improvement over GARCH(1,1): 0.28748850923
[ 5.22627178  5.05588077  5.24338475  4.93878327  4.91558812  8.45517111]
in
[ 4.41909737  4.37653266  4.40918175  4.40596007  4.43404811  6.36034445]
out
Chose  3.74814346221 GA best  3.74814346221 GA
Improvement over GARCH(1,1): 0.07045690438
[ 3.81860037  3.74814346  3.8514849   3.82634249  4.10300122  5.6247606 ]
in
[ 4.34191378  4.31880898  4.32312278  4.2810558   4.36486831  3.95315913]
out
Chose  3.89698978447 GmlfA best  3.89698978447 GmlfA
Improvement over GARCH(1,1): 0.34980999043
[ 4.24679977  4.24442219  4.24753689  4.23614956  4.36896375  3.89698978]
in
[ 4.34441216  4.25169751  4.33753085  4.28282863  4.39085837  6.7613605 ]
out
Chose  3.95494544572 GA best  3.95494544572 GA
Improvement over GARCH(1,1): 0.19861237281
[ 4.15355782  3.95494545  4.17136502  4.03234339  4.36211919  6.50215323]
in
[ 4.34113065  4.29329962  4.32617696  4.27705953  4.34775433  6.43291491]
out
Chose  4.05209834261 GpqA best  4.03266479906 GA
Improvement over GARCH(1,1): -0.00492626124
[ 4.04717208  4.0326648   4.05066957  4.05209834  4.22147783  6.07527973]
in
[ 4.26434178  4.22117588  4.2364334   4.19776708  4.30319957  5.73830296]
out
Chose  4.00727473064 GpqA best  4.00614923976 GA
Improvement over GARCH(1,1): 0.07245400698
[ 4.07972874  4.00614924  4.05914766  4.00727473  4.25339119  5.48468145]
in
[ 4.07115897  4.03061338  4.04979398  4.0318109   4.12113952  2.90252717]
out
Chose  2.563162896 GmlfA best  2.563162896 GmlfA
Improvement over GARCH(1,1): 1.05790257892
[ 3.62106547  3.55815264  3.58195177  3.56199154  3.94958712  2.5631629 ]
in
[ 4.10574189  4.07038297  4.09398034  4.05925012  4.15133414  3.37320113]
out
Chose  3.41031588964 GmlfA best  3.41031588964 GmlfA
Improvement over GARCH(1,1): 0.7156378633
[ 4.12595375  4.08222777  4.12088974  4.09761166  4.18139326  3.41031589]
in
[ 4.02152985  3.99591528  4.01760733  3.98914465  4.04855898  3.0733863 ]
out
Chose  3.2386743338 GmlfA best  3.2386743338 GmlfA
Improvement over GARCH(1,1): 0.88680207214
[ 4.12547641  4.13565734  4.13260072  4.13695529  4.1455256   3.23867433]
in
[ 4.00372119  3.98906293  3.99871554  3.95171712  4.04199686  2.94076451]
out
Chose  2.75475457144 GmlfA best  2.75475457144 GmlfA
Improvement over GARCH(1,1): 0.97259505385
[ 3.72734963  3.76592574  3.72988531  3.73555857  3.96499641  2.75475457]
in
[ 3.96663144  3.94038275  3.96294727  3.93336409  3.99497941  3.54518319]
out
Chose  4.34699254452 GmlfA best  4.34699254452 GmlfA
Improvement over GARCH(1,1): 0.42547554675
[ 4.77246809  4.72630477  4.76652535  4.71043422  4.40926516  4.34699254]
in
[ 4.04375835  4.02479048  4.03693506  4.01654352  4.05663279  3.37722821]
out
Chose  3.6339725347 GmlfA best  3.6339725347 GmlfA
Improvement over GARCH(1,1): 0.6551766736
[ 4.28914921  4.27387203  4.2769597   4.26153848  4.19637846  3.63397253]
in
[ 4.02646603  3.99869397  4.01567367  3.98714709  4.05268201  5.97749923]
out
Chose  3.90958630048 GpqA best  3.90958630048 GpqA
Improvement over GARCH(1,1): 0.05577679963
[ 3.9653631   3.91555492  3.94380475  3.9095863   4.04479762  5.86084112]
in
[ 4.01688497  3.99547153  4.01116998  3.98595127  4.02661216  5.91294784]
out
Chose  3.53241879439 GpqA best  3.51915999163 G
Improvement over GARCH(1,1): -0.01325880276
[ 3.51915999  3.5306694   3.52768397  3.53241879  3.78859313  5.33123523]
in
[ 3.98085214  3.92530844  3.96007701  3.90954553  3.97122     5.90594094]
out
Chose  4.18790678105 GpqA best  4.18199028976 Gmlf
Improvement over GARCH(1,1): 0.03602751061
[ 4.22393429  4.19521349  4.20040512  4.18790678  4.18199029  6.09245044]
in
[ 4.03877978  3.99457345  4.01721592  3.97312688  4.02412627  5.6855115 ]
out
Chose  4.53608640776 GpqA best  4.41262755533 Gmlf
Improvement over GARCH(1,1): 0.15766638936
[ 4.6937528   4.59861736  4.62644567  4.53608641  4.41262756  6.2780878 ]
in
[ 4.00469275  3.89363222  3.98347723  3.98393985  3.99317071  7.17076024]
out
Chose  4.29693756411 GA best  4.25502683619 Gmlf
Improvement over GARCH(1,1): 0.09453634843
[ 4.39147391  4.29693756  4.34225575  4.37498054  4.25502684  7.53343684]
in
[ 4.09359776  3.99019566  4.05646845  4.01014584  4.04042979  6.11358572]
out
Chose  4.02096795459 GA best  4.02096795459 GA
Improvement over GARCH(1,1): 0.20732448866
[ 4.22829244  4.02096795  4.16687036  4.08128162  4.13555188  6.13920623]
in
[ 4.08842365  3.99807769  4.06112799  3.94974538  4.05533247  7.42361687]
out
Chose  4.37199102381 GpqA best  4.37199102381 GpqA
Improvement over GARCH(1,1): 0.39816968591
[ 4.77016071  4.52753729  4.65480064  4.37199102  4.42108902  7.92013898]
in
[ 4.17323852  4.0942513   4.15948451  4.15544886  4.17252102  4.82517142]
out
Chose  4.53855384176 GA best  4.40321625917 Gmlf
Improvement over GARCH(1,1): 0.01252141492
[ 4.55107526  4.53855384  4.50538523  4.51693752  4.40321626  5.17697776]
in
[ 4.20647159  4.15096149  4.20011637  4.14478204  4.2505013   6.78157044]
out
Chose  4.21692692748 GpqA best  4.21692692748 GpqA
Improvement over GARCH(1,1): 0.06840727534
[ 4.2853342   4.22923569  4.27333767  4.21692693  4.31197569  6.77704175]
in
[ 4.17837657  4.18638254  4.18269333  4.20220476  4.24219795  4.48922484]
out
Chose  4.03904320963 G best  4.03904320963 G
Improvement over GARCH(1,1): 0.0
[ 4.03904321  4.31791246  4.26379078  4.63705963  4.51805269  4.92967639]
in
[ 4.27015278  4.2007048   4.26423008  4.2769717   4.30614931  5.7628836 ]
out
Chose  4.47535307639 GA best  4.47535307639 GA
Improvement over GARCH(1,1): 0.1099562587
[ 4.58530934  4.47535308  4.58575191  4.55558893  4.50536332  6.0125051 ]
in
[ 4.34670775  4.30276656  4.33431267  4.26794586  4.38459238  3.56479539]
out
Chose  3.92244020129 GmlfA best  3.92244020129 GmlfA
Improvement over GARCH(1,1): 0.75492856049
[ 4.67736876  4.61944526  4.68521227  4.61809579  4.62270463  3.9224402 ]
in
[ 4.35638557  4.28696301  4.3482961   4.29222241  4.41320023  7.61272803]
out
Chose  4.0932366521 GA best  4.06148423723 Gpq
Improvement over GARCH(1,1): 0.00253070748
[ 4.09576736  4.09323665  4.06148424  4.11226293  4.39096786  7.36624816]
in
[ 4.38534632  4.29912053  4.38045335  4.34836766  4.40933219  4.65900203]
out
Chose  4.42578727864 GA best  4.42578727864 GA
Improvement over GARCH(1,1): 0.21958253416
[ 4.64536981  4.42578728  4.63918654  4.62069925  4.58940795  4.92056146]
in
[ 4.41250344  4.37257979  4.40589624  4.39967935  4.45181574  6.43200272]
out
Chose  4.21469649654 GA best  4.21469649654 GA
Improvement over GARCH(1,1): 0.1132949109
[ 4.32799141  4.2146965   4.32570972  4.32197818  4.45966641  6.28729232]
in
[ 4.42467356  4.38215452  4.41461518  4.3629506   4.46512277  7.22822342]
out
Chose  4.20583771193 GpqA best  4.20583771193 GpqA
Improvement over GARCH(1,1): 0.12258469782
[ 4.32842241  4.20713657  4.32225863  4.20583771  4.47413028  7.05122662]
in
[ 4.44868003  4.36447359  4.43476538  4.41756869  4.45963349  4.90795768]
out
Chose  4.13052444798 GA best  4.13052444798 GA
Improvement over GARCH(1,1): 0.08642323613
[ 4.21694768  4.13052445  4.24204598  4.2509234   4.43599641  4.70688354]
in
[ 4.34575446  4.27867408  4.33874885  4.31195956  4.35267763  3.50174153]
out
Chose  3.44878181414 GmlfA best  3.44878181414 GmlfA
Improvement over GARCH(1,1): 0.83202873767
[ 4.28081055  4.05795843  4.27643755  4.24799156  4.33930807  3.44878181]
in
[ 4.31141352  4.26235896  4.30852183  4.29029182  4.32583531  5.0010667 ]
out
Chose  4.31711535038 GA best  4.25298094782 Gpq
Improvement over GARCH(1,1): -0.02092900312
[ 4.29618635  4.31711535  4.25298095  4.33408041  4.40865153  5.01813479]
in
[ 4.3149746   4.26522682  4.30645481  4.26790972  4.33948883  5.91623615]
out
Chose  4.02992109015 GA best  4.02992109015 GA
Improvement over GARCH(1,1): 0.12806906799
[ 4.15799016  4.02992109  4.15028639  4.16825278  4.33285604  5.78397507]
in
[ 4.25990335  4.22759366  4.25390451  4.21746751  4.27973892  4.13536097]
out
Chose  4.69548972947 GmlfA best  4.5992385915 Gmlf
Improvement over GARCH(1,1): 0.1573338658
[ 4.8528236   4.82915981  4.81609517  4.72962806  4.59923859  4.69548973]
in
[ 4.23345064  4.20116104  4.23084713  4.20552658  4.25396381  7.01231437]
out
Chose  4.77254713051 GA best  4.62732634875 Gmlf
Improvement over GARCH(1,1): 0.11294252444
[ 4.88548965  4.77254713  4.84377065  4.79184184  4.62732635  7.54677759]
in
[ 4.34705351  4.32704262  4.34200096  4.32778001  4.35093431  5.90215284]
out
Chose  4.19919855525 GA best  4.19845922008 GpqA
Improvement over GARCH(1,1): 0.07815593212
[ 4.27735449  4.19919856  4.27590121  4.19845922  4.32571043  5.7784869 ]
in
[ 4.39548042  4.38096417  4.36852621  4.34187803  4.37022511  7.18565076]
out
Chose  3.5369331257 GpqA best  3.37965310757 GA
Improvement over GARCH(1,1): -0.14735680847
[ 3.38957632  3.37965311  3.53624548  3.53693313  3.90037713  6.04555269]
in
[ 4.26911873  4.24413614  4.24155851  4.21771491  4.21647098  6.71688115]
out
Chose  3.54698157648 Gmlf best  2.96956533709 G
Improvement over GARCH(1,1): -0.57741623939
[ 2.96956534  2.97853913  3.08381977  3.09542793  3.54698158  5.27197804]
in
[ 4.13751082  4.09480545  4.13137105  4.1401182   4.17920316  8.2844851 ]
out
Chose  3.01401769201 GA best  3.01401769201 GA
Improvement over GARCH(1,1): 0.1190233653
[ 3.13304106  3.01401769  3.19086553  3.20105815  3.73607     7.08210769]
in
[ 4.06011501  4.00216524  4.05039999  4.00525738  4.01533649  5.546667  ]
out
Chose  3.70333185621 GA best  3.69660725359 G
Improvement over GARCH(1,1): -0.00672460262
[ 3.69660725  3.70333186  3.76981443  3.70391182  3.82374757  5.05750494]
in
[ 3.9122816   3.81473937  3.89706004  3.79168637  3.87104356  6.07976666]
out
Chose  3.38747203342 GpqA best  3.36846863951 GA
Improvement over GARCH(1,1): 0.1154644867
[ 3.50293652  3.36846864  3.5381413   3.38747203  3.64941553  5.44228896]
in
[ 3.82482816  3.6804399   3.80724004  3.69344805  3.81491796  6.94683786]
out
Chose  2.57940311915 GA best  2.57940311915 GA
Improvement over GARCH(1,1): 0.04107339486
[ 2.62047651  2.57940312  2.78275516  2.67292948  3.15350582  5.37248941]
in
[ 3.74179664  3.68876297  3.71140113  3.68644293  3.59222813  5.15633766]
out
Chose  3.56854627654 Gmlf best  3.56854627654 Gmlf
Improvement over GARCH(1,1): 0.08482247881
[ 3.65336876  3.60969622  3.64357709  3.61904894  3.56854628  5.00874319]
in
[ 3.75173081  3.7013027   3.72862246  3.69296566  3.56830287  6.27776992]
out
Chose  3.82063095296 Gmlf best  3.82063095296 Gmlf
Improvement over GARCH(1,1): 0.21455886291
[ 4.03518982  3.99036191  4.017458    3.99068965  3.82063095  6.56259306]
in
[ 3.7476179   3.69191046  3.74454718  3.72547208  3.5738533   5.21558193]
out
Chose  4.09562751139 Gmlf best  3.99241447873 GA
Improvement over GARCH(1,1): 0.21011991428
[ 4.30574743  3.99241448  4.42855426  4.52778793  4.09562751  6.16074986]
in
[ 3.84595641  3.81267331  3.74503328  3.73304692  3.60668487  5.08397124]
out
Chose  4.11536578731 Gmlf best  4.11536578731 Gmlf
Improvement over GARCH(1,1): 0.57560773952
[ 4.69097353  4.56486273  4.42901798  4.38095889  4.11536579  5.84409627]
in
[ 3.84617903  3.8162401   3.720351    3.74725844  3.67806536  3.45576281]
out
Chose  4.84046182009 GmlfA best  4.73089019887 Gmlf
Improvement over GARCH(1,1): 0.65789790002
[ 5.49835972  5.3176546   5.21320732  5.09347156  4.7308902   4.84046182]
in
[ 4.08082101  4.06340777  4.06137096  4.05889413  4.08265475  6.06236896]
out
Chose  4.54288302303 GpqA best  4.33413591165 G
Improvement over GARCH(1,1): -0.20874711138
[ 4.33413591  4.34409327  4.56593293  4.54288302  4.41015244  6.64794982]
in
[ 4.11717886  4.11490982  4.05516241  4.04052515  4.0432199   4.72919873]
out
Chose  3.95747860576 GpqA best  3.95747860576 GpqA
Improvement over GARCH(1,1): 0.03399065659
[ 3.99146926  3.98780213  3.97173909  3.95747861  3.97977862  4.55351196]
in
[ 4.05282434  4.05302074  3.99436447  3.99358785  4.03359513  4.6496316 ]
out
Chose  4.6787071833 GpqA best  4.45702098549 Gmlf
Improvement over GARCH(1,1): 0.12709319772
[ 4.80580038  4.80601309  4.6825172   4.67870718  4.45702099  5.42914502]
in
[ 4.17961654  4.17474261  4.13885469  4.12726009  4.15081822  5.96865676]
out
Chose  4.15153669892 GpqA best  4.15153669892 GpqA
Improvement over GARCH(1,1): 0.06656957089
[ 4.21810627  4.19229849  4.18113604  4.1515367   4.20744541  5.93704483]
in
[ 4.13035507  4.07409039  4.12445915  4.09954116  4.14979108  4.49819443]
out
Chose  4.37141604003 GA best  4.37141604003 GA
Improvement over GARCH(1,1): 0.06004832819
[ 4.43146437  4.37141604  4.41411266  4.50413535  4.40688736  4.90009139]
in
[ 4.03724468  3.96091474  4.01605203  3.94909652  4.04176081  6.05952772]
out
Chose  4.29746123045 GpqA best  4.29746123045 GpqA
Improvement over GARCH(1,1): 0.1740304457
[ 4.47149168  4.32741068  4.41312387  4.29746123  4.31493214  6.38189017]
in
[ 4.03944685  3.97454339  4.02174716  3.96495087  4.07556611  6.41500546]
out
Chose  3.72169085301 GpqA best  3.70825171965 GA
Improvement over GARCH(1,1): 0.04892537993
[ 3.77061623  3.70825172  3.78790716  3.72169085  3.97133779  6.0265125 ]
in
[ 4.16979074  4.06826838  4.12528761  4.09014374  4.19568631  6.74495951]
out
Chose  3.64626504194 GA best  3.64626504194 GA
Improvement over GARCH(1,1): 0.04518226015
[ 3.6914473   3.64626504  3.6894846   3.64872155  4.01479531  6.16557815]
in
[ 4.13020213  4.06515973  4.10856228  4.06345251  4.12895135  6.18129326]
out
Chose  4.37434393272 GpqA best  4.37434393272 GpqA
Improvement over GARCH(1,1): 0.1653860516
[ 4.53972998  4.42638224  4.48699349  4.37434393  4.38204882  6.47599855]
in
[ 4.19936167  4.1372167   4.17062091  4.13751167  4.20244796  5.66339808]
out
Chose  3.71793932723 GA best  3.71793932723 GA
Improvement over GARCH(1,1): 0.05083773375
[ 3.76877706  3.71793933  3.81892478  3.74739018  4.06031469  5.14771315]
in
[ 4.11008264  4.06699381  4.0814516   4.07593877  4.1397428   6.29874267]
out
Chose  4.39154520131 GA best  4.34056572141 GpqA
Improvement over GARCH(1,1): 0.06143867718
[ 4.45298388  4.3915452   4.40093194  4.34056572  4.39866907  6.52777843]
in
[ 4.09229737  4.03952292  4.06622193  4.07473628  4.13682432  6.49642689]
out
Chose  4.72203196364 GA best  4.53139674963 Gmlf
Improvement over GARCH(1,1): 0.13624485151
[ 4.85827682  4.72203196  4.66516733  4.62128497  4.53139675  7.10604368]
in
[ 4.15434871  4.13200071  4.13798488  4.14577794  4.19291468  5.42703625]
out
Chose  4.77532899716 GA best  4.58969893945 Gmlf
Improvement over GARCH(1,1): 0.03877358249
[ 4.81410258  4.775329    4.74138232  4.72252165  4.58969894  5.99895357]
in
[ 4.2723672   4.2597826   4.26952084  4.27225233  4.35993334  3.32970681]
out
Chose  3.36031811575 GmlfA best  3.36031811575 GmlfA
Improvement over GARCH(1,1): 0.90830193094
[ 4.26862005  4.26491694  4.26708436  4.26444162  4.36181619  3.36031812]
in
[ 4.27037421  4.25189841  4.26702106  4.25937451  4.33874695  4.10958734]
out
Chose  4.16255726516 GmlfA best  4.16255726516 GmlfA
Improvement over GARCH(1,1): 0.15556884629
[ 4.31812611  4.31417166  4.3151274   4.3078382   4.41000797  4.16255727]
in
[ 4.42995526  4.3595188   4.42329266  4.37758856  4.50205358  5.2046607 ]
out
Chose  4.24937014342 GA best  4.17398769592 Gpq
Improvement over GARCH(1,1): -0.03650328092
[ 4.21286686  4.24937014  4.1739877   4.24620227  4.46621247  5.02690546]
in
[ 4.44083058  4.37988426  4.43964702  4.38625949  4.49113667  4.4124186 ]
out
Chose  4.94884284643 GA best  4.83002401865 Gmlf
Improvement over GARCH(1,1): 0.0572357877
[ 5.00607863  4.94884285  4.99655906  4.94004136  4.83002402  4.98424949]
in
[ 4.47626043  4.3878796   4.47264886  4.47079715  4.54240483  8.09716196]
out
Chose  4.92321415542 GA best  4.79741973333 GpqA
Improvement over GARCH(1,1): 0.06440179722
[ 4.98761595  4.92321416  4.98929287  4.79741973  4.87101964  8.51928846]
in
[ 4.46251885  4.37858642  4.43072772  4.36233165  4.48605909  5.35938468]
out
Chose  5.10861663131 GpqA best  4.97520759976 Gmlf
Improvement over GARCH(1,1): 0.15081528289
[ 5.25943191  5.20524723  5.15525311  5.10861663  4.9752076   6.15970975]
in
[ 4.63523631  4.57844063  4.58683221  4.54084542  4.71332425  5.31428571]
out
Chose  5.13525982365 GpqA best  5.10142401421 Gmlf
Improvement over GARCH(1,1): 0.20989890591
[ 5.34515873  5.25744759  5.23393037  5.13525982  5.10142401  5.94021557]
in
[ 4.63969869  4.63303203  4.57361842  4.57176169  4.72764219  5.26789446]
out
Chose  4.54396799039 GpqA best  4.54396799039 GpqA
Improvement over GARCH(1,1): 0.04928955154
[ 4.59325754  4.58284584  4.5583719   4.54396799  4.75725703  5.13746672]
in
[ 4.70555528  4.69855092  4.64990594  4.62396189  4.77537365  6.44503731]
out
Chose  4.49991282675 GpqA best  4.49651693323 G
Improvement over GARCH(1,1): -0.00339589352
[ 4.49651693  4.50454787  4.52273445  4.49991283  4.71420112  6.16533335]
in
[ 4.56551966  4.54996415  4.55141859  4.53905701  4.67240382  6.7259939 ]
out
Chose  4.63997088556 GpqA best  4.62018981892 G
Improvement over GARCH(1,1): -0.01978106664
[ 4.62018982  4.64039228  4.63300249  4.63997089  4.74507033  6.76976486]
in
[ 4.82599381  4.82709     4.81164351  4.79771247  6.11759161  7.82615919]
out
Chose  4.88684714226 GpqA best  4.88684714226 GpqA
Improvement over GARCH(1,1): 0.0386995888
[ 4.92554673  4.93379791  4.91798623  4.88684714  6.17587164  7.82690457]
in
[ 4.90769419  4.90784063  4.88064595  4.88175049  6.18102686  5.35648208]
out
Chose  5.42248338957 Gpq best  5.42248338957 Gpq
Improvement over GARCH(1,1): 0.05500811776
[ 5.47749151  5.47741448  5.42248339  5.42255263  6.62576481  5.93032074]
in
[ 4.94618161  4.94479706  4.93837178  4.93890192  6.08146842  6.88368499]
out
Chose  5.92689794329 Gpq best  5.92689794329 Gpq
Improvement over GARCH(1,1): 0.03434018295
[ 5.96123813  5.95596463  5.92689794  5.93515492  6.85813364  7.93166271]
in
[ 5.18164687  5.17998745  5.17659576  5.17362636  6.3668242   6.97941332]
out
Chose  4.49869779734 GpqA best  4.00349203626 Gpq
Improvement over GARCH(1,1): -0.05211043459
[ 4.44658736  4.44332902  4.00349204  4.4986978   5.77259433  6.18596462]
in
[ 5.15324606  5.15334453  5.1264244   5.12695773  6.27949427  5.91103677]
out
Chose  4.79115644122 Gpq best  4.77798412131 GA
Improvement over GARCH(1,1): -0.01249081625
[ 4.77866562  4.77798412  4.79115644  4.7897297   5.9727024   5.4911113 ]
in
[ 5.07434251  5.06407883  5.04538521  5.05712298  6.22842814  7.70916872]
out
Chose  4.43400211296 Gpq best  4.43400211296 Gpq
Improvement over GARCH(1,1): 0.17200322675
[ 4.60600534  4.52109482  4.43400211  4.56314014  5.8698696   7.13424904]
in
[ 4.94918777  4.94815551  4.90133876  4.88612744  6.11539984  5.01714272]
out
Chose  5.3460495972 GpqA best  5.3460495972 GpqA
Improvement over GARCH(1,1): 0.07972960183
[ 5.4257792   5.43398515  5.36338284  5.3460496   6.42931006  5.50677929]
in
[ 4.75373592  4.74813676  4.73283314  4.7391957   5.74951684  4.86654672]
out
Chose  4.30088848764 Gpq best  4.25805573383 GA
Improvement over GARCH(1,1): -0.03830782683
[ 4.26258066  4.25805573  4.30088849  4.30248244  5.37062486  4.35512278]
in
[ 4.45659006  4.44103533  4.44945785  4.44684122  4.0905884   4.7674136 ]
out
Chose  4.32663937867 Gmlf best  4.32663937867 Gmlf
Improvement over GARCH(1,1): 0.46413877481
[ 4.79077815  4.78022928  4.79244127  4.79753822  4.32663938  5.13014727]
in
[ 4.49364805  4.48305142  4.48844904  4.48802251  4.15702013  6.32048167]
out
Chose  3.96040393736 Gmlf best  3.96040393736 Gmlf
Improvement over GARCH(1,1): 0.08989841967
[ 4.05030236  4.03605646  4.02932878  4.02978329  3.96040394  5.79145059]
in
[ 4.32163892  4.30587335  4.29225932  4.29639684  4.41066076  5.43833452]
out
Chose  3.36102588588 Gpq best  3.31689536181 GA
Improvement over GARCH(1,1): -0.04407510703
[ 3.31695078  3.31689536  3.36102589  3.37585204  3.92587684  4.43731949]
in
[ 4.2723597   4.26617681  4.24806778  4.24792433  4.33384427  5.60249408]
out
Chose  4.79504115092 GpqA best  4.69389856404 Gmlf
Improvement over GARCH(1,1): 0.06704245799
[ 4.86208361  4.83592714  4.8077679   4.79504115  4.69389856  6.16644387]
in
[ 4.18907403  4.18566478  4.18533325  4.18478383  4.22332979  6.09837414]
out
Chose  4.5099375303 GpqA best  4.44998017316 Gmlf
Improvement over GARCH(1,1): -0.00125671669
[ 4.50868081  4.4972317   4.50955819  4.50993753  4.44998017  6.39926789]
in
[ 4.27075785  4.26657174  4.2615341   4.26338085  4.27702904  6.25712873]
out
Chose  3.70372645031 Gpq best  3.67841921934 GA
Improvement over GARCH(1,1): -0.01203418854
[ 3.69169226  3.67841922  3.70372645  3.69197124  4.00743965  5.61266711]
in
[ 4.08204528  4.06938868  4.08042033  4.07289728  4.06882917  6.16608762]
out
Chose  4.6059237188 Gmlf best  4.6059237188 Gmlf
Improvement over GARCH(1,1): 0.23168997774
[ 4.8376137   4.8101763   4.83960922  4.81848386  4.60592372  6.907693  ]
in
[ 4.21150494  4.20291346  4.19627712  4.1957016   4.26534781  4.51256264]
out
Chose  4.95605590069 GpqA best  4.71950009573 Gmlf
Improvement over GARCH(1,1): 0.03876611391
[ 4.99482201  4.99243851  4.94964671  4.9560559   4.7195001   5.31732284]
in
[ 4.30475756  4.27563078  4.30283613  4.30085558  4.33882051  3.77758837]
out
Chose  3.60300878722 GmlfA best  3.60300878722 GmlfA
Improvement over GARCH(1,1): 0.55887188792
[ 4.16188068  4.13713957  4.13016068  4.15455166  4.283764    3.60300879]
in
[ 4.22067827  4.19219183  4.20356874  4.17069314  4.27177089  5.0180805 ]
out
Chose  4.69888284923 GpqA best  4.61947017224 Gmlf
Improvement over GARCH(1,1): 0.07364731562
[ 4.77253016  4.73947264  4.71193761  4.69888285  4.61947017  5.55571367]
in
[ 4.26764991  4.23851013  4.24490221  4.23186228  4.32825979  5.90467942]
out
Chose  5.28652603755 GpqA best  5.03050422006 Gmlf
Improvement over GARCH(1,1): 0.09200772413
[ 5.37853376  5.26091014  5.26514978  5.28652604  5.03050422  7.09202841]
in
[ 4.44050735  4.41801772  4.40333199  4.36714547  4.50118459  6.68818922]
out
Chose  4.15049859915 GpqA best  4.15049859915 GpqA
Improvement over GARCH(1,1): 0.09643091137
[ 4.24692951  4.22292147  4.21807411  4.1504986   4.40858838  6.36267693]
in
[ 4.41133255  4.3411823   4.38525871  4.34807987  4.46441084  5.46879634]
out
Chose  3.93447667437 GA best  3.93447667437 GA
Improvement over GARCH(1,1): 0.11050387879
[ 4.04498055  3.93447667  4.02970772  4.0312404   4.32379375  4.94473321]
in
[ 4.4117542   4.36218068  4.37108778  4.34407526  4.45815346  6.64277431]
out
Chose  4.56234738946 GpqA best  4.56234738946 GpqA
Improvement over GARCH(1,1): 0.0859725848
[ 4.64831997  4.59206411  4.58675415  4.56234739  4.63362049  6.83306396]
in
[ 4.50585524  4.46750247  4.49135683  4.49066153  4.55530365  7.29789687]
out
Chose  5.15472208231 GA best  5.05134497993 Gmlf
Improvement over GARCH(1,1): 0.03965761844
[ 5.1943797   5.15472208  5.14648877  5.14589967  5.05134498  8.00855284]
in
[ 4.56665372  4.52216469  4.53021195  4.53288141  4.60385197  7.25295985]
out
Chose  4.58038932787 GA best  4.55139888025 Gpq
Improvement over GARCH(1,1): 0.02645665455
[ 4.60684598  4.58038933  4.55139888  4.57744156  4.63324394  7.23685413]
in
[ 4.55274061  4.51787536  4.53630512  4.5411635   4.56231042  5.95156806]
out
Chose  4.70957891108 GA best  4.70957891108 GA
Improvement over GARCH(1,1): 0.06055126889
[ 4.77013018  4.70957891  4.75418314  4.75900287  4.74185055  6.14625475]
in
[ 4.52170291  4.52188975  4.48848913  4.48922797  4.56974197  7.50413256]
out
Chose  3.89240621347 Gpq best  3.8727087547 G
Improvement over GARCH(1,1): -0.01969745877
[ 3.87270875  3.87700227  3.89240621  3.89567822  4.14434408  6.45087389]
in
[ 4.51067098  4.53650285  4.41460283  4.41705165  4.57827865  7.34001884]
out
Chose  3.64210548905 Gpq best  3.5670451464 GA
Improvement over GARCH(1,1): -0.02509073421
[ 3.61701475  3.56704515  3.64210549  3.62805054  3.96653351  6.16127143]
in
[ 4.35323798  4.35496443  4.34631428  4.32739325  4.44084116  8.00218263]
out
Chose  3.97519803675 GpqA best  3.78400528753 GA
Improvement over GARCH(1,1): -0.19075021705
[ 3.78444782  3.78400529  4.06789213  3.97519804  4.53557024  7.97145308]
in
[ 4.43927601  4.38827052  4.42650812  4.43929389  4.43514827  5.91363943]
out
Chose  4.64603430495 GA best  4.59757228499 Gmlf
Improvement over GARCH(1,1): 0.06049866398
[ 4.70653297  4.6460343   4.67007467  4.6810892   4.59757228  6.14533362]
in
[ 4.40009139  4.36625698  4.35976809  4.35912244  4.44925316  8.439424  ]
out
Chose  3.74520813161 GpqA best  3.6799288557 GA
Improvement over GARCH(1,1): -0.05965524163
[ 3.68555289  3.67992886  3.74635576  3.74520813  4.18311855  7.73983383]
in
[ 4.34261663  4.31932962  4.31491024  4.2873726   4.39225518  6.51763576]
out
Chose  4.44027828877 GpqA best  4.44027828877 GpqA
Improvement over GARCH(1,1): 0.05347427196
[ 4.49375256  4.46160884  4.46757265  4.44027829  4.52984807  6.58024766]
in
[ 4.34131113  4.33051737  4.32619036  4.33209393  4.35061315  5.72372725]
out
Chose  4.51847697567 Gpq best  4.50552599331 Gmlf
Improvement over GARCH(1,1): 0.034574018
[ 4.55305099  4.51310342  4.51847698  4.51813322  4.50552599  5.87364174]
in
[ 4.4237877   4.4230291   4.40676041  4.41034656  4.43429822  5.37574038]
out
Chose  4.53049567057 Gpq best  4.52930578926 GpqA
Improvement over GARCH(1,1): 0.01949695802
[ 4.54999263  4.54923695  4.53049567  4.52930579  4.53118379  5.45942858]
in
[ 4.35898589  4.35720798  4.32864961  4.33047365  4.38698469  5.29915119]
out
Chose  4.25972643638 Gpq best  4.25972643638 Gpq
Improvement over GARCH(1,1): 0.01900419905
[ 4.27873064  4.27826565  4.25972644  4.2600569   4.36263357  5.17733857]
in
[ 4.29081677  4.28946675  4.28271903  4.28302765  4.34814277  6.56987734]
out
Chose  4.79026786678 Gpq best  4.77184078675 Gmlf
Improvement over GARCH(1,1): -0.0003367756
[ 4.78993109  4.77568512  4.79026787  4.78565264  4.77184079  7.07972358]
in
[    4.28416935     4.28455641  3671.07665008     4.26460639     4.41446976
6.40632672]
out
Chose  4.09113013626 GpqA best  4.09113013626 GpqA
Improvement over GARCH(1,1): 0.16169654494
[ 4.25282668  4.25291198  7.15515541  4.09113014  4.42571995  6.24993081]
in
[ 4.33735315  4.33690537  4.29504687  4.29499302  4.50995878  3.44831338]
out
Chose  3.13841608581 GmlfA best  3.13841608581 GmlfA
Improvement over GARCH(1,1): 0.63413667174
[ 3.77255276  3.77074705  3.62982925  3.6316469   4.24226422  3.13841609]
in
[ 4.85099376  4.84718291  4.68260511  4.68236216  5.97526843  7.77512592]
out
Chose  3.46629527514 GpqA best  3.46629527514 GpqA
Improvement over GARCH(1,1): 0.15379958677
[ 3.62009486  3.63791569  3.46740757  3.46629528  4.7842984   5.68797154]
in
[ 4.89769953  4.64827933  4.8001089   4.80015862  5.78802318  6.85185826]
out
Chose  3.26210202257 GA best  3.26210202257 GA
Improvement over GARCH(1,1): 1.43107075983
[ 4.69317278  3.26210202  4.63787977  4.64491998  5.58193162  6.5926653 ]
in
[ 4.85709265  4.81502417  4.70892304  4.71666855  5.75190215  6.97661634]
out
Chose  4.72129150341 Gpq best  4.72129150341 Gpq
Improvement over GARCH(1,1): 0.14389295049
[ 4.86518445  4.81620921  4.7212915   4.73154616  5.73673874  6.92027763]
in
[ 4.74651971  4.72732216  4.62446939  4.62448092  5.59792356  6.21092673]
out
Chose  5.19125160632 Gpq best  5.1844755747 GpqA
Improvement over GARCH(1,1): 0.18415677602
[ 5.37540838  5.33351612  5.19125161  5.18447557  6.09120026  6.91174191]
in
[ 4.77131729  4.76449791  4.6552226   4.64885714  5.61226205  5.84489054]
out
Chose  4.86158329748 GpqA best  4.86158329748 GpqA
Improvement over GARCH(1,1): 0.11164610918
[ 4.97322941  4.95057969  4.87289219  4.8615833   5.7773421   6.06765216]
in
[ 4.40456226  4.26288951  4.30916593  4.319232    3.84612489  4.76100954]
out
Chose  4.19308888364 Gmlf best  3.83846055227 GA
Improvement over GARCH(1,1): 0.72163427772
[ 4.91472316  3.83846055  4.96657009  4.96733428  4.19308888  5.47124728]
in
[ 4.31722203  4.30636294  4.25935508  4.25312436  3.98265413  3.14025043]
out
Chose  3.53616050025 GmlfA best  3.53616050025 GmlfA
Improvement over GARCH(1,1): 1.17815134782
[ 4.71431185  4.69991574  4.69556161  4.69000368  4.20474771  3.5361605 ]
in
[ 4.34301249  4.33326364  4.27984892  4.27825164  4.05264242  5.57748733]
out
Chose  4.20209041599 Gmlf best  4.20209041599 Gmlf
Improvement over GARCH(1,1): 0.39288405334
[ 4.59497447  4.5908454   4.58677903  4.5547017   4.20209042  5.83128701]
in
[ 4.24025201  4.23763397  4.17333353  4.1321721   4.33885554  2.59075151]
out
Chose  2.95473415809 GmlfA best  2.95473415809 GmlfA
Improvement over GARCH(1,1): 1.61810956363
[ 4.57284372  4.57161615  4.57542632  4.53234592  4.54357759  2.95473416]
in
[ 4.19923664  4.16586954  4.1411663   4.14718061  4.22874095  4.5526211 ]
out
Chose  4.68616825237 Gpq best  4.53816785493 Gmlf
Improvement over GARCH(1,1): -0.00051431168
[ 4.68565394  4.64109431  4.68616825  4.60284083  4.53816785  5.00375122]
in
[ 4.14519061  4.12641534  4.1074864   4.10040048  4.23273318  1.72406587]
out
Chose  1.99909610643 GmlfA best  1.99909610643 GmlfA
Improvement over GARCH(1,1): 2.46701704185
[ 4.46611315  4.4458847   4.46348477  4.46008521  4.39584125  1.99909611]
in
[ 4.18055028  4.16072049  4.14702257  4.14718424  4.28894458  5.13697301]
out
Chose  4.58543243314 Gpq best  4.51600726056 GA
Improvement over GARCH(1,1): -0.01113112672
[ 4.57430131  4.51600726  4.58543243  4.58255489  4.54030227  5.51680756]
in
[ 4.14708679  4.12317632  4.13734413  4.12647649  4.19237098  5.14412586]
out
Chose  5.08510359225 GA best  4.83372577068 Gmlf
Improvement over GARCH(1,1): 0.03912346864
[ 5.12422706  5.08510359  5.13498049  5.16353308  4.83372577  6.17836738]
in
[ 4.29605747  4.28312964  4.26422224  4.25702211  4.32614894  5.75215176]
out
Chose  4.77703901416 GpqA best  4.66941761906 Gmlf
Improvement over GARCH(1,1): 0.05872785641
[ 4.83576687  4.81658395  4.7821994   4.77703901  4.66941762  6.28238122]
in
[ 4.33425013  4.32100495  4.28849756  4.29044775  4.37769182  8.49160757]
out
Chose  3.66466878112 Gpq best  3.66466878112 Gpq
Improvement over GARCH(1,1): 0.09017163124
[ 3.75484041  3.76037179  3.66466878  3.66704332  4.16713581  7.75989333]
in
[ 4.31483891  4.31484232  4.28653904  4.28881864  4.36946201  6.37720737]
out
Chose  4.24529854843 Gpq best  4.24529854843 Gpq
Improvement over GARCH(1,1): 0.00707040054
[ 4.25236895  4.25239874  4.24529855  4.25260974  4.45729678  6.1548883 ]
in
[ 4.41662362  4.41607885  4.39445119  4.39388003  4.50671143  9.09745035]
out
Chose  4.46411957092 GpqA best  4.43836378565 G
Improvement over GARCH(1,1): -0.02575578527
[ 4.43836379  4.44002417  4.46148448  4.46411957  4.59082064  9.05207573]
in
[ 4.52180955  4.52048892  4.45731996  4.45657035  4.58486652  8.87684826]
out
Chose  4.54795255113 GpqA best  4.54795255113 GpqA
Improvement over GARCH(1,1): 0.04376978944
[ 4.59172234  4.59042527  4.54880757  4.54795255  4.6863828   8.78835429]
in
[ 4.45123531  4.45116126  4.39768248  4.3978131   4.50768016  8.93693024]
out
Chose  5.26242108164 Gpq best  5.19212451103 Gmlf
Improvement over GARCH(1,1): 0.02947869085
[  5.29189977   5.29283634   5.26242108   5.2637968    5.19212451
10.19721296]
in
[ 4.53920515  4.53917466  4.49516339  4.49486375  4.58481291  8.83929196]
out
Chose  4.55516991798 GpqA best  4.55516991798 GpqA
Improvement over GARCH(1,1): 0.0098693785
[ 4.5650393   4.56567331  4.5565052   4.55516992  4.65722124  8.81483366]
in
[ 4.51116124  4.46909489  4.45899005  4.4552071   4.49761277  4.20904712]
out
Chose  4.23100725142 GmlfA best  4.23100725142 GmlfA
Improvement over GARCH(1,1): 0.25183690717
[ 4.48284416  4.35479151  4.53056709  4.52506796  4.54192124  4.23100725]
in
[ 4.57507617  4.55776523  4.53209264  4.52456242  4.63612115  6.32147322]
out
Chose  3.74919445231 GpqA best  3.74919445231 GpqA
Improvement over GARCH(1,1): 0.07072296672
[ 3.81991742  3.78008619  3.77196922  3.74919445  4.23771627  5.38700996]
in
[ 4.56314429  4.55098332  4.5326884   4.51909883  4.56370937  6.20542516]
out
Chose  3.96681175227 GpqA best  3.89931164048 G
Improvement over GARCH(1,1): -0.06750011179
[ 3.89931164  3.91152986  3.97068023  3.96681175  4.23940498  5.44518122]
in
[ 4.51904396  4.52731661  4.49500473  4.49811377  4.54221491  7.50887814]
out
Chose  3.65225418782 Gpq best  3.55227181945 GA
Improvement over GARCH(1,1): -0.04541985981
[ 3.60683433  3.55227182  3.65225419  3.63024849  4.01945994  6.27451955]
in
[ 4.3355465   4.29776467  4.31338995  4.30655656  4.35774411  5.7978668 ]
out
Chose  4.08806128286 GA best  4.08806128286 GA
Improvement over GARCH(1,1): 0.01613564907
[ 4.10419693  4.08806128  4.11115572  4.1127946   4.26864771  5.45147996]
in
[ 4.26941085  4.21876555  4.23749784  4.23635798  4.32086474  7.05497299]
out
Chose  4.47795735116 GA best  4.34641216901 Gpq
Improvement over GARCH(1,1): -0.08017808666
[ 4.39777926  4.47795735  4.34641217  4.3554123   4.49107079  7.21673125]
in
[ 4.1330645   4.10818034  4.13344813  4.13081636  4.17300995  7.43441487]
out
Chose  4.13698395704 GA best  3.97182622703 G
Improvement over GARCH(1,1): -0.16515773001
[ 3.97182623  4.13698396  4.07932349  4.06738566  4.21076202  7.33685623]
in
[ 4.10506004  4.02988157  4.09557368  4.08725455  4.14872282  7.12318492]
out
Chose  2.75841529753 GA best  2.55086043853 GpqA
Improvement over GARCH(1,1): 0.03433646432
[ 2.79275176  2.7584153   3.13769656  2.55086044  3.43264068  5.60202919]
in
[ 4.05629282  4.00777144  4.04956237  4.018077    4.08487743  5.88980305]
out
Chose  3.75879462326 GA best  3.75879462326 GA
Improvement over GARCH(1,1): 0.04972525679
[ 3.80851988  3.75879462  3.81304811  3.78529272  3.94413073  5.4715495 ]
in
[ 4.08986734  4.03588047  4.08659008  4.04006659  4.14690297  5.68506025]
out
Chose  4.0462914517 GA best  4.0462914517 GA
Improvement over GARCH(1,1): 0.0160738732
[ 4.06236532  4.04629145  4.05299766  4.05598199  4.18554095  5.64540035]
in
[ 4.03266163  3.93989398  4.02606608  3.92730733  4.08233464  6.85169147]
out
Chose  4.16205133326 GpqA best  4.16205133326 GpqA
Improvement over GARCH(1,1): 0.11591826716
[ 4.2779696   4.16907627  4.33274206  4.16205133  4.27237226  7.07738467]
in
[ 4.04768614  3.88014166  4.02006822  4.00807615  3.80668732  7.22999942]
out
Chose  4.29765862638 Gmlf best  3.61502395098 GA
Improvement over GARCH(1,1): 0.40788453535
[ 4.70554316  3.61502395  4.464366    4.39265766  4.29765863  8.0600099 ]
in
[ 4.13053959  4.06264194  4.12066539  4.12676109  3.84209093  6.28208174]
out
Chose  4.46628557966 Gmlf best  4.46628557966 Gmlf
Improvement over GARCH(1,1): 0.58865572985
[ 5.05494131  4.92963997  5.02522712  5.01956458  4.46628558  7.31585204]
in
[ 4.31031123  4.26172989  4.28287089  4.26549632  4.29543053  4.38324306]
out
Chose  5.30153806259 GA best  5.02152579112 Gmlf
Improvement over GARCH(1,1): 0.10899648132
[ 5.41053454  5.30153806  5.49449967  5.46481075  5.02152579  5.66750105]
in
[ 4.43858131  4.39424993  4.41748777  4.38973586  4.4018427   6.8060722 ]
out
Chose  4.20932094576 GpqA best  4.17147608059 GA
Improvement over GARCH(1,1): 0.0032257996
[ 4.21254675  4.17147608  4.23045388  4.20932095  4.28352037  6.47370127]
in
[ 4.43069808  4.38441233  4.41297522  4.41767489  4.40744165  7.91250175]
out
Chose  4.11946758333 GA best  4.11946758333 GA
Improvement over GARCH(1,1): 0.07244107335
[ 4.19190866  4.11946758  4.21169448  4.22406547  4.36735557  7.58035502]
in
[ 4.32131724  4.28559686  4.30283969  4.27115863  4.36719367  6.61059543]
out
Chose  4.64242547698 GpqA best  4.64242547698 GpqA
Improvement over GARCH(1,1): 0.07768164273
[ 4.72010712  4.64359324  4.71084692  4.64242548  4.69152471  7.00293153]
in
[ 4.31173583  4.25374442  4.26788174  4.21361185  4.33832324  5.52024558]
out
Chose  4.7649314651 GpqA best  4.69521937128 Gmlf
Improvement over GARCH(1,1): 0.19944357495
[ 4.96437504  4.90140151  4.83308733  4.76493147  4.69521937  6.12945219]
in
[ 4.34429825  4.29002628  4.31656745  4.24983881  4.32690677  6.76680543]
out
Chose  3.76402041692 GpqA best  3.71269345662 GA
Improvement over GARCH(1,1): 0.00053256219
[ 3.76455298  3.71269346  3.81565165  3.76402042  4.04030216  6.05948371]
in
[ 4.13100572  4.06507499  4.10450954  4.0403048   4.08280166  5.39080641]
out
Chose  3.93099098969 GpqA best  3.92402696381 GA
Improvement over GARCH(1,1): 0.04265933288
[ 3.97365032  3.92402696  3.98309985  3.93099099  4.0284119   5.17753259]
in
[ 4.07836974  4.02313043  4.04799248  4.03000307  4.04257212  4.14631632]
out
Chose  3.14054544492 GA best  3.14054544492 GA
Improvement over GARCH(1,1): 0.02258314721
[ 3.16312859  3.14054544  3.27486769  3.22724383  3.59651785  3.19304706]
in
[ 3.95380863  3.90250395  3.91404681  3.86638262  3.91661127  5.75050417]
out
Chose  3.97487184371 GpqA best  3.97487184371 GpqA
Improvement over GARCH(1,1): 0.08536397202
[ 4.06023582  4.02055029  4.01420718  3.97487184  4.01929883  5.7925692 ]
in
[ 3.94122497  3.91546965  3.92891102  3.88957215  3.94235928  6.04054082]
out
Chose  4.17127181429 GpqA best  4.17127181429 GpqA
Improvement over GARCH(1,1): 0.02427392435
[ 4.19554574  4.22047773  4.25087475  4.17127181  4.17286664  6.33102032]
in
[ 3.89116123  3.86439588  3.8745704   3.86702475  3.89910592  4.99303404]
out
Chose  4.07370088416 GA best  4.05639291561 GpqA
Improvement over GARCH(1,1): 0.03626407328
[ 4.10996496  4.07370088  4.08824708  4.05639292  4.065553    5.1384015 ]
in
[ 3.9878663   3.95072407  3.97434589  3.96029679  3.99891968  5.01293958]
out
Chose  4.43730113862 GA best  4.38554451111 Gmlf
Improvement over GARCH(1,1): 0.14362647787
[ 4.58092762  4.43730114  4.53240152  4.50796706  4.38554451  5.57889598]
in
[ 4.01522859  3.98732975  4.01115683  4.0552517   4.04074777  6.93038092]
out
Chose  4.67006831108 GA best  4.47609802265 Gmlf
Improvement over GARCH(1,1): 0.03156619402
[ 4.70163451  4.67006831  4.66780105  4.64702279  4.47609802  7.58936929]
in
[ 4.23698214  4.22870926  4.23278367  4.25408539  4.2570007   5.12280726]
out
Chose  4.61426210353 GA best  4.45616524043 Gmlf
Improvement over GARCH(1,1): 0.0110925105
[ 4.62535461  4.6142621   4.60143588  4.58477923  4.45616524  5.44800125]
in
[ 4.24862366  4.22709709  4.2411598   4.23878331  4.26785669  5.86237106]
out
Chose  4.30114902932 GA best  4.30114902932 GA
Improvement over GARCH(1,1): 0.02818526354
[ 4.32933429  4.30114903  4.33219978  4.30437489  4.38061986  5.87060417]
in
[ 4.22439848  4.20024786  4.21871236  4.21886792  4.24631885  6.90556144]
out
Chose  5.00558458668 GA best  4.71526483754 Gmlf
Improvement over GARCH(1,1): -0.02104292572
[ 4.98454166  5.00558459  4.97381975  4.98465554  4.71526484  7.67702583]
in
[ 4.31936183  4.30829219  4.31048514  4.28843499  4.32745752  5.3401953 ]
out
Chose  4.69038218854 GpqA best  4.59383639881 Gmlf
Improvement over GARCH(1,1): 0.04624295226
[ 4.73662514  4.72949472  4.71401202  4.69038219  4.5938364   5.72178801]
in
[ 4.35996093  4.35211727  4.35858369  4.35948108  4.41956044  4.20417668]
out
Chose  4.03026052316 GmlfA best  4.03026052316 GmlfA
Improvement over GARCH(1,1): 0.00585467042
[ 4.03611519  4.05275362  4.0316128   4.163146    4.39345604  4.03026052]
in
[ 4.39165957  4.37983438  4.37888575  4.36257071  4.45207146  1.82763864]
out
Chose  1.8754081865 GmlfA best  1.8754081865 GmlfA
Improvement over GARCH(1,1): 2.6276305075
[ 4.50303869  4.49481722  4.50219599  4.48322346  4.53304558  1.87540819]
in
[ 4.39231907  4.37170711  4.36489978  4.34665896  4.45235706  1.72593775]
out
Chose  2.15121185748 GmlfA best  2.15121185748 GmlfA
Improvement over GARCH(1,1): 2.80342856384
[ 4.95464042  4.91388733  4.9860233   4.94744856  4.75695705  2.15121186]
in
[ 4.5102842   4.50705455  4.45815665  4.4308662   4.54000141  1.61991355]
out
Chose  1.80578741323 GmlfA best  1.80578741323 GmlfA
Improvement over GARCH(1,1): 2.44929963875
[ 4.25508705  3.95194013  3.91233194  4.21788666  4.45288656  1.80578741]
in
[ 4.45926604  4.39544559  4.44703269  4.39239186  4.49169839  3.00800077]
out
Chose  2.9621769006 GmlfA best  2.9621769006 GmlfA
Improvement over GARCH(1,1): 1.43696431015
[ 4.39914121  4.34671035  4.38753659  4.32410759  4.53523587  2.9621769 ]
in
[ 4.40434378  4.33203769  4.39426227  4.3396199   4.40600171  3.86940593]
out
Chose  4.37508124265 GmlfA best  4.37508124265 GmlfA
Improvement over GARCH(1,1): 0.53661653051
[ 4.91169777  4.84193287  4.89522163  4.82684143  4.6630122   4.37508124]
in
[ 4.40167227  4.37507856  4.38523941  4.37085817  4.40449046  3.99402766]
out
Chose  4.33699401686 GmlfA best  4.33699401686 GmlfA
Improvement over GARCH(1,1): 0.37353840871
[ 4.71053243  4.6948003   4.7023771   4.70648832  4.58420907  4.33699402]
in
[ 4.44365374  4.43210696  4.41386023  4.40981623  4.44704277  7.84426238]
out
Chose  4.51142579677 GpqA best  4.51142579677 GpqA
Improvement over GARCH(1,1): 0.07661526394
[ 4.58804106  4.56895747  4.52701883  4.5114258   4.60397567  7.86530002]
in
[ 4.70565878  4.70705247  4.64337196  4.64331675  5.66460316  7.5408189 ]
out
Chose  4.81438711739 GpqA best  4.80818815961 Gpq
Improvement over GARCH(1,1): 0.00185087985
[ 4.816238    4.82201077  4.80818816  4.81438712  5.81212207  7.63395581]
in
[ 4.66537442  4.66507018  4.56723499  4.56551336  5.53956257  6.46746069]
out
Chose  5.66512224122 GpqA best  5.66512224122 GpqA
Improvement over GARCH(1,1): 0.23657337364
[ 5.90169561  5.90106344  5.67510917  5.66512224  6.44448361  7.72953893]
in
[ 4.87650285  4.87209621  4.77636926  4.76872033  5.82994878  8.69303676]
out
Chose  5.0298974347 GpqA best  5.0298974347 GpqA
Improvement over GARCH(1,1): 0.06211259799
[ 5.09201003  5.10564989  5.03461542  5.02989743  6.02726202  8.86076959]
in
[ 4.91630867  4.9126365   4.87291447  4.8703277   5.86033919  7.25124036]
out
Chose  4.40919281817 GpqA best  4.40919281817 GpqA
Improvement over GARCH(1,1): 0.11285070183
[ 4.52204352  4.5211312   4.42247321  4.40919282  5.49988822  6.59916607]
in
[ 4.90781138  4.87923279  4.88377215  4.8812754   5.91995622  6.78360684]
out
Chose  3.28765363436 GA best  3.22758004527 Gpq
Improvement over GARCH(1,1): -0.01803781959
[ 3.26961581  3.28765363  3.22758005  3.24272685  4.88989655  5.31134746]
in
[ 4.81508049  4.80490205  4.79808978  4.80127001  5.94108681  6.90796229]
out
Chose  3.36311315302 Gpq best  3.35029723289 GA
Improvement over GARCH(1,1): -0.0045545488
[ 3.3585586   3.35029723  3.36311315  3.35397912  4.71945183  5.17937911]
in
[ 4.56546611  4.56498525  4.5474798   4.54948241  5.703687    7.25704404]
out
Chose  3.80317018112 Gpq best  3.80317018112 Gpq
Improvement over GARCH(1,1): 0.00521171041
[ 3.80838189  3.80862969  3.80317018  3.80432797  4.94390016  6.11046785]
in
[ 4.2457479   4.25062106  4.23256108  4.2345316   5.26875054  6.96360325]
out
Chose  4.7279852282 Gpq best  4.7279852282 Gpq
Improvement over GARCH(1,1): 0.12149382011
[ 4.84947905  4.87657215  4.72798523  4.73391881  5.86500868  7.69182823]
in
[ 4.23591752  4.22990794  4.21062865  4.21268308  5.17061927  5.74874248]
out
Chose  4.54193865887 Gpq best  4.54193865887 Gpq
Improvement over GARCH(1,1): 0.03249075627
[ 4.57442942  4.57361899  4.54193866  4.54731311  5.41626861  6.0839777 ]
in
[ 4.08854478  4.09291417  4.07630172  4.0602318   5.0401847   6.80077685]
out
Chose  3.38566600829 GpqA best  3.38566600829 GpqA
Improvement over GARCH(1,1): 0.05657260567
[ 3.44223861  3.4456973   3.43418696  3.38566601  4.43158605  5.82563342]
in
[ 4.03764612  3.98311589  4.01121109  4.05860942  3.61201031  6.59233484]
out
Chose  3.54841202626 Gmlf best  3.54841202626 Gmlf
Improvement over GARCH(1,1): 0.29520333952
[ 3.84361537  3.73794511  3.87284309  3.9073256   3.54841203  6.26178313]
in
[ 4.06623932  4.00641713  4.06513838  4.00922256  3.66197739  5.94314839]
out
Chose  4.02020487589 Gmlf best  4.02020487589 Gmlf
Improvement over GARCH(1,1): 0.50269424731
[ 4.52289912  4.45064271  4.54290435  4.47105694  4.02020488  6.39924431]
in
[ 4.1484478   4.10965344  4.12146021  4.09614892  3.72969014  6.13405239]
out
Chose  4.32353975701 Gmlf best  4.32353975701 Gmlf
Improvement over GARCH(1,1): 0.68978976062
[ 5.01332952  4.95887606  4.94764542  4.95890103  4.32353976  7.15711921]
in
[ 4.19265041  4.17101877  4.15444714  4.15319395  3.7464373   5.89408674]
out
Chose  3.96920266015 Gmlf best  3.96920266015 Gmlf
Improvement over GARCH(1,1): 0.35819663132
[ 4.32739929  4.29019838  4.29988294  4.29736611  3.96920266  5.92958856]
in
[ 4.20122504  4.19540795  4.16712171  4.15805998  3.72369822  4.44166285]
out
Chose  3.34035618463 Gmlf best  3.34035618463 Gmlf
Improvement over GARCH(1,1): 0.06631494228
[ 3.40667113  3.3918395   3.53112114  3.51263551  3.34035618  3.56475555]
in
[ 4.17515046  4.17195086  4.12232357  4.11960531  3.70377132  6.01972611]
out
Chose  3.95788676516 Gmlf best  3.95788676516 Gmlf
Improvement over GARCH(1,1): 0.35419273377
[ 4.3120795   4.29797209  4.27463584  4.24367758  3.95788677  6.02115796]
in
[ 4.31480527  4.31226434  4.24895331  4.2514274   5.21710026  6.78260811]
out
Chose  4.22838261978 Gpq best  4.22838261978 Gpq
Improvement over GARCH(1,1): 0.32841887983
[ 4.5568015   4.59350379  4.22838262  4.4894627   5.43779853  6.99996504]
in
[ 4.32537308  4.32118652  4.24948608  4.25095047  5.22768159  7.55617199]
out
Chose  3.31690201728 Gpq best  3.31215917323 GpqA
Improvement over GARCH(1,1): 0.26137445629
[ 3.57827647  3.54049067  3.31690202  3.31215917  4.60586778  6.48924104]
in
[ 4.10221135  4.10133961  4.02384309  4.02467089  4.98987673  5.98650647]
out
Chose  3.92090492531 Gpq best  3.92090492531 Gpq
Improvement over GARCH(1,1): 0.04885966735
[ 3.96976459  3.96241733  3.92090493  3.92107503  4.89844978  5.75642102]
in
[ 3.96440946  3.96464417  3.88499319  3.88275085  4.84979306  6.17224666]
out
Chose  4.0738755169 GpqA best  4.07277360884 Gpq
Improvement over GARCH(1,1): 0.10884155659
[ 4.18271707  4.18251523  4.07277361  4.07387552  4.99728151  6.2558224 ]
in
[ 4.07393422  4.07396457  4.02660965  4.02641837  5.06886377  5.05283942]
out
Chose  4.21263076496 GpqA best  4.16688307331 Gpq
Improvement over GARCH(1,1): -0.01629289158
[ 4.19633787  4.19774097  4.16688307  4.21263076  5.16721522  5.19439511]
in
[ 3.99932433  3.99790839  3.9728706   3.9680199   3.64514603  4.97524062]
out
Chose  3.85049699162 Gmlf best  3.85049699162 Gmlf
Improvement over GARCH(1,1): 0.33277892571
[ 4.18327592  4.17997513  4.1721944   4.1599238   3.85049699  5.18073042]
in
[ 3.94489408  3.94426989  3.94258274  3.92869456  3.60300731  5.61549935]
out
Chose  3.81108348104 Gmlf best  3.81108348104 Gmlf
Improvement over GARCH(1,1): 0.31518519674
[ 4.12626868  4.13124948  4.13814103  4.13246734  3.81108348  5.76976827]
in
[ 4.10742894  4.10113661  4.02547133  4.0054547   4.95355305  5.32572338]
out
Chose  3.82131197779 GpqA best  3.82131197779 GpqA
Improvement over GARCH(1,1): 0.0387052975
[ 3.86001728  3.8496175   3.83118153  3.82131198  4.73726022  4.94022562]
in
[ 4.02614349  4.02610013  4.01414952  4.02139425  3.64613201  3.6789071 ]
out
Chose  3.67142614757 Gmlf best  3.67142614757 Gmlf
Improvement over GARCH(1,1): 0.43655478301
[ 4.10798093  4.10827782  4.09598107  4.10180933  3.67142615  3.741256  ]
in
[ 4.03203807  4.03107405  4.01025118  4.00831184  3.65015331  5.06178418]
out
Chose  3.6440530336 Gmlf best  3.6440530336 Gmlf
Improvement over GARCH(1,1): 0.31436832778
[ 3.95842136  3.95731044  3.9454646   3.94295544  3.64405303  4.92823896]
in
[ 3.89714747  3.86519167  3.99758839  3.88167195  3.6184664   5.08266795]
out
Chose  3.94863515486 Gmlf best  3.72577273637 Gpq
Improvement over GARCH(1,1): 0.40427747564
[ 4.35291263  4.32156782  3.72577274  4.37504196  3.94863515  5.59566968]
in
[ 3.89018682  3.87841111  3.89750705  3.89675441  3.65136927  6.31513623]
out
Chose  4.24273139552 Gmlf best  4.24273139552 Gmlf
Improvement over GARCH(1,1): 0.40330208784
[ 4.64603348  4.65822812  4.64244297  4.63853266  4.2427314   7.15562685]
in
[ 3.87931369  3.87930993  3.83854542  3.83615741  3.7331423   4.66501972]
out
Chose  4.57470225342 Gmlf best  4.57470225342 Gmlf
Improvement over GARCH(1,1): 0.62702503789
[ 5.20172729  5.20172788  5.04133461  4.99187829  4.57470225  5.97697223]
in
[ 4.06618962  4.06297548  3.98490805  4.0100601   4.06972627  4.37398115]
out
Chose  4.27672687376 Gpq best  4.27672687376 Gpq
Improvement over GARCH(1,1): 0.01831201815
[ 4.29503889  4.29006072  4.27672687  4.30441381  4.30088343  4.52945193]
in
[ 4.13660863  4.11338067  4.12071113  4.11127598  4.25895521  6.27146128]
out
Chose  5.13200785004 GpqA best  4.91503179831 Gmlf
Improvement over GARCH(1,1): 0.02518226021
[ 5.15719011  5.12497747  5.22571122  5.13200785  4.9150318   7.30827922]
in
[ 4.32125013  4.30258724  4.27633674  4.26651141  4.48346063  7.96036714]
out
Chose  4.56993830062 GpqA best  4.56993830062 GpqA
Improvement over GARCH(1,1): 1.11051516944
[ 5.68045347  5.62173273  5.64384932  4.5699383   5.32529417  9.20958911]
```