# Fixtures model_selection # ============================================================================== import numpy as np import pandas as pd # Fixtures _backtesting_forecaster_no_refit Series (skforecast==0.5.1) # np.random.seed(123) # y = np.random.rand(50) # exog = np.random.rand(50) # out_sample_residuals = np.random.rand(50) y = pd.Series( np.array([0.69646919, 0.28613933, 0.22685145, 0.55131477, 0.71946897, 0.42310646, 0.9807642 , 0.68482974, 0.4809319 , 0.39211752, 0.34317802, 0.72904971, 0.43857224, 0.0596779 , 0.39804426, 0.73799541, 0.18249173, 0.17545176, 0.53155137, 0.53182759, 0.63440096, 0.84943179, 0.72445532, 0.61102351, 0.72244338, 0.32295891, 0.36178866, 0.22826323, 0.29371405, 0.63097612, 0.09210494, 0.43370117, 0.43086276, 0.4936851 , 0.42583029, 0.31226122, 0.42635131, 0.89338916, 0.94416002, 0.50183668, 0.62395295, 0.1156184 , 0.31728548, 0.41482621, 0.86630916, 0.25045537, 0.48303426, 0.98555979, 0.51948512, 0.61289453])) exog = pd.Series( np.array([0.12062867, 0.8263408 , 0.60306013, 0.54506801, 0.34276383, 0.30412079, 0.41702221, 0.68130077, 0.87545684, 0.51042234, 0.66931378, 0.58593655, 0.6249035 , 0.67468905, 0.84234244, 0.08319499, 0.76368284, 0.24366637, 0.19422296, 0.57245696, 0.09571252, 0.88532683, 0.62724897, 0.72341636, 0.01612921, 0.59443188, 0.55678519, 0.15895964, 0.15307052, 0.69552953, 0.31876643, 0.6919703 , 0.55438325, 0.38895057, 0.92513249, 0.84167 , 0.35739757, 0.04359146, 0.30476807, 0.39818568, 0.70495883, 0.99535848, 0.35591487, 0.76254781, 0.59317692, 0.6917018 , 0.15112745, 0.39887629, 0.2408559 , 0.34345601]), name='exog') out_sample_residuals = np.array([ 0.51312815, 0.66662455, 0.10590849, 0.13089495, 0.32198061, 0.66156434, 0.84650623, 0.55325734, 0.85445249, 0.38483781, 0.3167879 , 0.35426468, 0.17108183, 0.82911263, 0.33867085, 0.55237008, 0.57855147, 0.52153306, 0.00268806, 0.98834542, 0.90534158, 0.20763586, 0.29248941, 0.52001015, 0.90191137, 0.98363088, 0.25754206, 0.56435904, 0.80696868, 0.39437005, 0.73107304, 0.16106901, 0.60069857, 0.86586446, 0.98352161, 0.07936579, 0.42834727, 0.20454286, 0.45063649, 0.54776357, 0.09332671, 0.29686078, 0.92758424, 0.56900373, 0.457412 , 0.75352599, 0.74186215, 0.04857903, 0.7086974 , 0.83924335 ]) if pd.__version__ < '2.2.0': freq = "H" else: freq = "h" y_feature_selection = pd.Series( np.array([ -1.58530369e-01, 3.63524919e+01, 8.86770772e+01, -2.08096884e+01, 3.76744792e+01, 5.42039264e+01, 2.49951079e+01, 5.96497621e+01, -3.64029383e+01, -8.99068703e+01, -5.31841523e-01, -9.03290403e+01, 4.56887850e+01, -2.49293880e+01, -6.18020819e+01, 4.81618954e+01, 3.26310898e+01, -2.44143206e+01, 6.87147394e+00, 1.38394053e+02, -6.67347231e+01, -1.44324564e+01, 6.32450871e+01, -1.74927315e+01, -6.50498732e+01, 1.26871769e+00, -4.62944202e+00, -4.94827228e+01, 1.01249089e+01, 1.53308277e+01, -3.69715718e+01, -2.21622729e+01, 3.11725914e+00, -3.83302883e+01, 2.16908072e+01, -2.10268226e+01, 6.78497270e+01, 1.42683679e+01, 6.36213242e+01, 1.00853462e+01, -1.21032085e+02, 5.30171567e+01, -8.01331471e+01, 1.81492924e+01, 2.68676263e+01, 5.97301700e+01, 3.82119310e+01, -4.55420580e+01, 6.94521006e+00, -4.73468973e+01, -1.48148761e+02, 2.29818323e+01, -9.68532806e+00, 2.76546139e+00, -1.40197169e+01, -1.79977212e+01, 2.90915247e+01, -5.81317655e+01, 6.26341927e+01, -4.31587829e+01, 6.11486861e+01, 5.62691011e+01, 1.44680330e+02, -4.88822314e+01, -2.30270910e+01, -1.94277591e+01, 1.10160891e+02, -4.37123011e+01, 8.14983289e+00, 5.22837112e+01, 2.86575456e+01, 2.29161213e+01, -3.79674889e+01, 1.67458893e+02, -1.77894011e+01, -1.03118676e+02, -1.06301190e+01, -4.95821365e+01, 8.34199592e+01, -4.68179051e+01, 9.02512187e+01, 6.50321794e+00, -2.36988588e+01, -5.93556794e+01, 8.66356531e+01, -4.21331617e-01, -1.33358686e+01, 8.85688491e-01, -7.91775647e+01, -3.91874049e+01, 1.02938351e+02, -1.39356598e+02, -2.71242014e+01, 4.94413982e+00, 2.51210850e+01, -1.14021678e+02, -9.83043793e+00, -2.46791536e+01, 1.26197536e+02, 7.07296471e+01, -1.48490792e+01, -3.81572592e+01, 3.36228174e+00, 5.02254997e+01, 4.83905762e+01, -1.22854727e+01, -3.72298171e+00, 9.69243121e+01, 1.83230387e+01, 4.79080121e+01, -5.02785237e+01, 5.30605069e+00, 9.11735636e+00, 1.20992097e+02, 5.07724189e+01, -6.61957621e+01, -1.18758527e+02, 4.38121898e+01, 4.71145746e+01, -9.59096663e+01, 8.17362884e+01, 2.78323605e+01, -1.49768202e+02, -9.50435221e+01, 1.52499279e+01, 9.75031543e+01, 2.99590420e+01, 8.14841118e+01, -9.09235317e+01, 2.24549649e+01, -1.39351580e+01, -8.54523328e+01, 6.51813430e+01, 7.06275842e+01, 7.22721475e+01, 5.06527546e+01, 3.17631845e+01, -1.09067190e+02, 2.10858128e+01, 1.37894317e+02, -1.50063653e+02, -5.60100981e+01, 3.19259485e+01, 2.03014087e+00, -1.45944905e+02, 9.16632722e+00, -1.58914631e+01, -3.51276089e+01, -1.18339557e+02, 6.39648686e+01, -2.03190494e+02, 3.80745266e+01, -1.65838317e+01, -1.26060286e+01, 1.27181499e+01, -3.43827585e+01, 1.15694826e+01, -4.18745607e+01, 4.46593188e+01, -3.14665665e+01, 4.11450856e+01, 3.40144660e+01, 1.69260611e+01, 2.50389041e+01, -6.52338599e+01, 2.95550204e+01, 2.66243247e+01, 8.03162342e+00, 1.07299060e+02, -4.26300248e+01, -9.22817018e+01, 2.92342723e+01, -3.14167515e+01, 1.21750220e+02, -1.28273407e+02, 5.69996760e+01, -5.94722717e+01, -3.70135231e+01, -1.50875044e+01, 1.24349786e+01, 2.93546274e+01, 5.58450165e+01, -6.09614358e+01, 1.50686444e+02, -6.60876062e+01, 3.27308282e+00, -8.11195367e+01, 1.48781142e+02, -4.64665781e+01, -4.43740691e+01, 4.42086791e+00, -1.71807931e-01, -1.38476803e+01, 9.38533531e+01, -6.34257208e+00, -5.32379520e+01, -6.56385902e+01, -6.88319920e+01, 1.88616758e+01, -3.78665080e+01, 9.03362210e+01, -6.12345585e+01, 3.62391684e+01, 2.27791810e+01, 2.61787409e+01, 7.10670027e+01, -1.69782866e+02, 5.46516427e+01, 7.31752893e+01, 3.70983828e+01, 2.57014914e+01, 4.51903037e+01, 1.54271333e+01, -7.22404048e+01, 8.49674160e+01, -3.80708514e+01, -8.21965516e+01, -9.90222813e+01, 5.04291554e+01, 6.71092487e+01, -2.54028468e+01, 6.19285727e+00, 3.37506382e+01, 1.06194107e+01, -4.78360905e+00, 3.05097535e+01, 4.66097713e-01, -2.89461229e+01, -1.07559559e+02, -1.53063506e+00, -5.17377380e+01, -6.44892938e+01, 3.31164284e+01, -1.39741794e+02, 9.72383726e+00, -4.88859146e+01, -6.63388661e+00, 2.34625297e+01, 1.43717916e+01, -2.03500132e+01, 3.59241238e+01, 8.91049005e+01, -5.47449496e+01, 2.83063982e+01, 1.13304321e+02, 8.41522649e+00, -8.55949044e+01, 4.79462422e+01, -4.73253784e+01, 7.88875784e+01, 1.18269469e+01, -3.31065216e+01, -6.65618970e+01, 5.38478238e+01, 1.67286335e+02, 1.46898179e+00, 6.56125553e+01, 1.67152856e+02, 6.73137469e+01, 5.32219913e+01, -6.10516845e+01, -8.83475557e+01, -2.27319938e+01, 5.23392275e+01, -5.29282171e+01, -1.76494319e+02, -1.17055662e+01, -1.97459504e+01, 8.28942756e+01, -1.80294321e+02, -5.71667714e+01, -9.74097242e+01, 1.17080425e+01, 1.30820406e+02, 4.21402873e+01, -1.90580400e+01, 3.99124025e+01, 6.18856985e+01, -3.51700998e+01, 1.22602432e+02, 5.70271630e+01, 6.46144109e+01, 2.41557719e+01, -1.13501557e+02, 2.72631676e+01, 7.28722423e+00, 1.99883252e+01, 3.97109357e+01, -1.82895115e+01, -1.34488088e+01, -4.45549253e+00, -5.16386483e+01, -3.60900727e+01, -1.00785722e+02, -7.73251591e+01, 7.34002993e+01, -7.21196198e+01, 5.79606980e+01, 6.10317661e+01, -6.78061440e+00, -4.82356605e+00, -7.69245853e+01, -3.68793781e+00, 1.93437107e+01, -2.56196808e+01, -3.12889013e+01, 4.45856649e-01, -6.28395977e+01, 2.18249188e+01, 1.18199214e+02, 6.54885658e+01, -7.83002701e-01, -1.62080961e+01, 1.09051247e+01, 9.25203200e+01, 6.06691665e+01, -1.03088078e+02, -5.02757262e+01, -2.11197834e+02, 1.27696530e+02, 5.39775830e+01, 4.81178428e+01, 5.00059133e+01, 1.88753514e+01, -1.33122181e+02, 1.07492127e+01, -1.04563731e+01, 1.70051212e+01, -3.23902317e+01, 6.69411654e+01, 5.87355465e+01, 5.56736869e+01, 6.89323640e+01, -6.36684030e+01, -1.48232105e+01, 1.32566589e+02, -7.38290450e+01, 8.45840735e+01, 3.35485475e+01, 7.71060524e+01, 1.15895368e+02, 8.95113757e+01, -3.89877898e-01, 2.13564322e+01, 4.03131907e+01, 1.74257217e+01, 1.85306243e+01, -1.47089948e+01, -8.24139743e+01, 5.32703970e+00, 1.98902106e+01, 1.16746208e+02, -2.05999632e+01, 4.99095473e+01, 4.74790837e+01, 4.77497101e+01, 4.03050347e+01, 9.23570820e+01, -6.65499759e-01, -3.51158530e+01, -6.15051737e+01, -4.64955502e+00, 2.42430061e+01, 5.70394277e+01, -6.09160013e+01, 1.35328480e+02, 4.48620109e-01, -2.18721016e+01, -2.47251019e+01, -4.49132916e+00, -2.69264608e+01, -7.96576990e-01, -2.08657724e+01, 4.92066290e+01, -8.79475031e+00, 8.09279500e+01, 1.66006628e+01, -6.78466032e+01, 2.51119307e+01, -3.72633493e+01, 4.46930239e+01, -1.52321323e+02, -2.03679319e+00, -5.48379080e+01, -4.01161247e+01, -3.24045965e+01, 2.48064082e+01, -2.91570756e+01, 3.43471176e+01, 5.01819045e+01, -1.06422259e+02, 4.70568897e+01, 2.66706126e+01, 4.11062263e+01, -6.80674230e+00, -9.65621562e+00, -1.79955672e+02, -8.32369474e+01, -1.91848651e+01, 7.03384798e+01, -4.78190796e+00, 9.66764662e+01, -3.99982128e+01, -3.25128359e+01, -3.03416068e+01, 1.27989184e+01, -1.37599472e+01, 3.58854723e+01, 1.59619407e+02, 9.76405555e+01, -6.62951356e+01, -1.41575566e+02, -5.38353046e+01, -7.42682810e+01, 1.10029273e+02, -6.41307606e+01, -8.52456829e-01, -1.09195991e+02, -7.49118428e+01, 9.94697250e+00, -9.02804015e+01, -3.14899975e+01, -1.47491245e+01, 7.33591244e+01, 3.52933611e+01, 1.66384393e+02, -1.50976922e+01, -3.03651222e+01, -5.63948670e+01, 1.38138220e+02, -9.06866916e+01, -3.15184584e+01, 8.07650183e+01, -8.56152312e+01, -3.02473589e+01, 9.00588150e+01, -1.45606729e+01, -6.66530802e-01, 5.58943997e+01, -9.40965691e+01, 4.88185243e+01, -1.40645937e+01, 5.77229615e+01, 3.47658520e+01, 1.96878564e+01, 2.70791473e+01, -3.95351689e+00, 1.36884690e+01, 3.00670972e+00, 1.32772960e+01, 4.95438485e+01, -2.49057858e+00, -8.41864474e+01, -1.26661898e+02, 1.56209571e+02, 4.87353348e+01, 2.99994948e+01, 1.44968040e+01, -8.33124743e+01, 3.33386434e+01, -2.59072771e+01, -2.01548017e+00, -1.22220956e+02, 5.04636930e+01, -6.38434192e+01, -5.10596603e+01, 5.63684109e+01, -1.16439418e+02, 3.49362857e+01, 1.58135023e+02, -1.06270368e+02, -1.83927457e+01, -5.80986004e+01, 6.79312268e+01, -1.18349740e+02, -4.29282772e+01, -4.00610877e+01, 2.58717848e+01, 1.50695089e+02, 3.11986902e+01, -8.00308714e+01, 1.09791672e+02, 2.62532586e+00, 8.72201086e+01, -4.94596849e+01, 4.94959321e+00, 2.09457431e-01, 1.04281270e+01, -6.40634325e+01, 2.09727662e+01, -1.84245723e+01, -5.57535945e+01, 3.84932111e+01, 6.24541727e+01, 1.11414165e+01, -7.28150550e+01, -7.81017553e+01, -1.29776897e+02, -1.31206072e+00, -5.03490895e+01 ]), index=pd.date_range(start='2020-01-01', periods=500, freq=freq) ) exog_feature_selection = pd.DataFrame( np.array([ [ 9.12687936e-01, -6.30618391e-01, 2.75341863e-01, -1.39437511e+00, -1.27357024e+00], [-5.98731767e-01, 1.44890361e+00, -3.93293346e-02, -1.87039748e+00, 9.83033396e-01], [ 1.49564414e+00, 8.90706391e-01, 1.06931597e+00, 1.75488618e+00, 1.06939267e+00], [ 3.21254276e-01, -1.98252429e-02, -3.34325312e-01, -1.53906585e+00, -1.39380664e+00], [-2.29426629e-01, 1.44857659e+00, -1.73912222e-02, 8.92200085e-01, -4.49667602e-01], [-1.89382188e-01, 1.50092262e+00, 2.32036972e-01, 4.91957128e-01, 5.99431927e-02], [ 1.37725748e+00, 5.53856166e-01, 1.67942295e-01, -5.30674560e-01, -1.43175974e-01], [-1.14752541e+00, 1.59592117e+00, 2.79943571e-01, 5.85318030e-01, 5.33510818e-01], [-2.39669947e-01, 5.75848362e-01, -8.53944819e-01, 1.95473356e+00, 7.68735860e-01], [ 3.21686576e-01, -1.10004311e+00, -9.97321469e-01, -7.56437209e-01, 7.60949393e-01], [ 2.16396568e-01, -2.33503993e-01, 9.41528855e-02, 1.33063078e+00, 1.25546432e+00], [-6.99877235e-01, -2.79858911e+00, -2.55619371e-01, -1.77153310e+00, 9.27462432e-01], [-8.32408826e-01, 3.74366421e-01, 5.88206408e-01, 1.04109692e+00, 1.46017154e-01], [ 1.62953419e+00, -1.25683381e+00, 1.42990028e-01, 2.61989197e-01, 6.58062825e-02], [ 1.32026832e+00, 7.74000002e-01, -1.36000768e+00, -1.05705578e+00, -1.00326528e-02], [ 3.11581503e-01, 5.12982850e-01, 5.67880067e-01, -2.69225906e-02, -1.42050727e-01], [ 1.00405390e+00, 2.20593008e+00, -4.34351276e-01, 2.18678609e+00, 3.86186399e-01], [-6.00584865e-01, -2.17923506e-01, -3.06435381e-01, 1.44199915e+00, -3.12644023e-01], [ 4.26146640e-01, 1.79549485e-01, 3.41421289e-02, -1.86197571e+00, -1.60540974e+00], [-2.45165068e-01, 1.64249834e+00, 1.55757372e+00, -5.27091942e-01, -1.66430542e+00], [-5.68685746e-01, -7.61404530e-02, -1.06661274e+00, 2.20714791e-01, 6.13274991e-01], [-1.40068720e-01, 9.07105196e-01, -6.37751502e-01, -1.42868070e+00, -8.61754896e-01], [ 9.78736006e-01, 2.39236527e+00, -1.18304945e-02, 4.12912160e-01, 2.23814334e+00], [-1.70966090e+00, -2.99330718e-01, -1.56446138e-01, 1.26025679e+00, -9.61805342e-01], [ 1.25872130e+00, -2.47621379e-01, -9.63253686e-01, -2.63143804e+00, 6.00175236e-01], [ 5.94070255e-01, 1.03247972e+00, -4.34166520e-01, 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4.63487255e-01, -4.47440164e-01, 3.92493258e-01, 2.60009682e-01], [ 1.86625720e-01, -4.71891730e-01, 1.41737520e+00, -1.49147867e+00, -7.94643718e-01], [ 1.26593626e+00, -2.42667924e+00, 1.65143654e+00, -4.28912629e-01, -8.66740402e-01], [-1.66768923e+00, -5.36094601e-02, 2.76660307e+00, -4.34004738e-01, 5.02219248e-02], [ 1.02390550e+00, -1.10638591e+00, 2.38760672e-01, 3.66732198e-01, -2.10056413e-01], [ 5.19611147e-01, -1.66528042e+00, 2.33407312e-01, -3.66081695e-01, 2.05809293e+00], [-9.07591995e-01, -1.32567447e-01, -8.71281197e-01, 8.85841112e-01, 5.21137514e-01], [-7.14880775e-01, 2.75040151e-01, 2.15608564e+00, -1.74343681e-01, 9.85282566e-01], [-1.49290942e-01, -7.59835089e-01, -1.16012966e+00, -6.54381086e-01, 1.98676304e+00], [ 1.86284938e-01, 2.81117663e-02, -5.31996585e-01, -1.08229436e+00, -3.81271461e-01], [ 9.93806707e-01, 1.49245539e+00, 6.73648934e-01, 9.86474019e-01, 2.04187588e-02], [-1.32907883e+00, -1.65369784e+00, -6.82538154e-01, 1.25333595e+00, 2.78033712e-01], [-9.99380749e-01, 5.67594726e-01, -7.48827466e-01, 7.18150543e-01, 4.74898323e-01], [-2.20292465e-01, 4.95180889e-01, 1.26642930e+00, -5.14240391e-01, 1.86156412e+00], [-1.36038857e-02, -2.48655850e-01, -1.30444689e-01, -6.69647148e-01, 6.86200686e-01], [ 5.72842819e-01, 2.72824942e-01, -1.31240319e-01, 1.81974128e-01, -8.39112705e-01], [ 1.31092370e+00, 7.86903222e-01, 5.74621429e-01, 2.73073188e-01, -6.81004547e-02], [ 8.47517370e-01, 1.62670626e-01, -1.62295356e+00, -5.21305606e-01, -5.28400755e-01], [-4.80100622e-01, -1.09078443e+00, 1.28559172e+00, 1.99611039e-02, -9.23415197e-01], [ 2.87620713e-01, -8.56649877e-01, 1.45716855e-01, -1.17684832e+00, -6.38061937e-01], [ 8.07308186e-01, -6.88868984e-01, 1.25523737e+00, 1.66095249e+00, -3.14758147e-01], [-4.69550013e-01, -2.15410489e-01, 6.68087321e-01, 1.85978589e-01, 4.72396137e-02], [-1.81188023e-01, 1.03716203e+00, -1.32576755e-01, -1.51832631e+00, -2.83365746e+00], [ 2.00660009e-01, 3.61203060e-01, 2.87214281e-01, 1.08319880e+00, -8.53201516e-01], [ 7.04474074e-01, -1.93963871e-01, 2.03159982e-02, 1.34026793e-01, 6.65653438e-01], [-3.73745028e-01, -4.22114730e-01, 4.11718831e-01, -7.73805905e-01, -3.46720291e-01], [ 2.84469557e-01, 1.57564975e+00, -6.44925458e-01, 7.53276212e-01, 2.04860319e-01], [ 7.42372588e-01, -8.86004489e-01, 6.09407319e-01, -1.26386180e-01, 6.25430326e-01], [ 1.09411010e+00, 7.96667868e-01, 4.65623814e-01, -8.37083388e-01, -1.66797491e-01], [-1.46511622e+00, 6.30488030e-01, -3.18956989e-01, -2.15249344e+00, 3.63445562e-01], [-5.29988864e-01, 7.28535401e-01, -1.70899178e+00, -9.87598059e-02, -2.44307579e+00], [ 1.07611274e+00, 1.45194681e-01, -2.15211508e+00, 2.31228126e-01, -3.58749383e+00], [ 1.60659681e+00, 3.49025641e-02, 2.55985023e+00, 2.32649658e-01, 1.68722267e-01], [ 8.64209271e-01, -1.56943204e+00, 1.49519203e+00, 1.13101627e-01, -6.27750196e-01], [-1.32081431e+00, -4.10510463e-01, 6.75503781e-01, -9.64200035e-01, -4.44703779e-01], [ 9.45876984e-01, 9.31529613e-01, -1.71596005e-01, 3.85066103e-01, 6.13067728e-01], [ 8.44334606e-01, 4.08625561e-01, -1.55357818e+00, -1.01164375e+00, -2.87784364e-01], [ 4.95728916e-01, 8.10325597e-01, 1.92448761e-01, 1.16799059e+00, -1.13195653e+00], [-6.37692139e-01, -1.26254374e+00, 1.29385524e-01, -1.40298909e+00, -3.26517647e-01], [-4.97568783e-01, -7.85719399e-01, 3.13091930e-01, -7.03838361e-02, 2.55177521e-01], [-5.23860010e-01, -6.78373811e-01, -1.71590149e+00, 1.47440502e+00, -1.35982402e-01], [ 5.53774608e-01, 1.57323963e+00, 1.38501464e-01, 1.27002488e+00, -2.15944165e+00], [-4.39672205e-01, -7.17485837e-01, -7.36263934e-01, -9.72556324e-01, 1.08822048e+00], [ 8.11145045e-01, -8.89911057e-01, -4.49514671e-01, 2.79216715e-01, -1.25977171e+00], [ 6.48562899e-01, 2.89795599e-01, 8.01544172e-01, -4.03713105e-01, -1.54344391e+00], [-6.69205605e-01, 2.96358656e-01, -2.05021768e+00, 5.65396564e-01, 4.32505429e-02], [ 1.43324013e+00, 5.28141973e-01, 3.43164157e-01, 9.85833246e-01, 1.31022893e+00], [ 1.44424506e+00, 2.17205091e+00, 1.64960973e+00, -6.19832034e-01, -1.57782779e+00], [-7.98062735e-01, -1.03878821e+00, -1.29408532e+00, 1.74371223e+00, 2.96832303e-02], [-1.54205311e-01, -4.30417758e-02, -2.84247098e-01, -5.28014827e-02, -1.67877227e-01], [ 3.77704564e-01, 8.29547144e-01, -1.32343627e+00, -7.61528587e-01, -1.18743326e+00], [ 1.80443632e+00, -9.20093108e-01, 1.52544424e+00, -6.24024850e-01, -2.50601446e-02], [ 1.18411875e+00, -6.89640164e-01, -1.64711570e+00, 1.67806871e+00, -7.11572671e-01], [-3.56663061e-01, -4.47771425e-01, -5.10342874e-01, 9.37850297e-01, -1.89517559e+00], [ 2.60374659e-01, 4.96712400e-02, -6.82331046e-01, -1.74762917e+00, -1.03552842e+00], [-3.66568075e-01, 5.86579680e-01, 1.67971561e-01, 1.01240024e+00, -6.14836787e-02], [-1.87469173e-03, 1.58806789e+00, 1.78435680e+00, 1.12644172e-01, 6.31948284e-01], [ 9.78559078e-01, 6.20277356e-01, 2.40936864e-01, -2.59341634e-01, -1.27674575e-01], [ 4.24243386e-01, -1.27027612e+00, -7.59475102e-01, 4.46491416e-01, 8.00220882e-01], [ 4.97555942e-01, 6.37492602e-01, 1.52901431e+00, 2.11713340e+00, -2.31291944e-01], [-7.01750520e-01, -3.26651702e-01, 1.87257576e-01, -1.05197042e+00, 4.67550474e-01], [ 1.53591757e+00, -7.17890892e-01, 1.75431226e+00, -8.23192038e-01, 1.30774005e+00], [-1.88849238e+00, -9.57581839e-01, -3.93310852e-01, 2.05646734e+00, -1.12833055e+00], [ 2.85650196e-01, -1.78012614e-01, 1.60059793e-01, 3.42205404e-01, -2.36286411e+00], [-5.68139293e-01, -9.25466973e-01, 4.11367752e-01, 4.38430903e-01, -7.20391314e-01], [ 3.71187505e-01, -1.55900181e-01, 2.40631191e-01, -5.01817103e-01, 5.25028054e-01], [-7.20600982e-02, 9.84827487e-01, -1.49021343e+00, -4.64034254e-01, -1.05268356e-01], [-8.82828988e-01, -1.00750880e+00, 7.89828035e-01, -1.30578587e+00, -3.46090034e-01], [-7.28077864e-01, 1.40817707e+00, -9.24420198e-01, 6.18716810e-01, -1.87115353e-02], [-1.51501351e+00, -1.69175117e+00, -1.73473635e-01, 3.67705494e-01, -8.11269834e-01], [ 3.03787931e-01, 1.49933828e-01, 5.68504207e-01, 5.49642596e-01, 2.43765761e-01], [-1.11252931e+00, -1.56844005e+00, 1.72092032e+00, -4.80141918e-02, -6.47449515e-02], [-1.24607797e+00, 6.37380986e-01, -9.72613193e-02, 5.11604056e-01, 4.72785023e-01], [-1.92614986e-01, -1.75540184e+00, -4.26689770e-01, -3.48607515e-01, 4.49135613e-01], [ 1.60293721e-01, -1.20004328e+00, -7.58628423e-01, 9.74132435e-01, -7.92091951e-01], [ 1.94513083e-01, -6.30065218e-01, -1.86175975e+00, -1.70035827e-02, 2.79197117e+00], [-4.09241617e-01, -1.09635351e+00, 4.61605393e-01, -8.77618277e-01, -2.04813502e-01], [ 1.25870044e+00, -9.87571530e-01, -3.94754919e-01, 6.82132899e-02, 3.51798274e-02] ]), index = pd.date_range(start='2020-01-01', periods=500, freq=freq), columns=[f"exog_{i}" for i in range(5)] )