In [ ]:
from google.colab import drive
drive.mount('/content/drive')

Mounted at /content/drive
In [ ]:
%cd '/content/drive/MyDrive/CS460 ML Project /CODES/EXPERIMENTS/Data sets'

/content/drive/MyDrive/CS460 ML Project /CODES/EXPERIMENTS/Data sets
In [ ]:
import matplotlib.pyplot as plt
import csv
import pandas as pd
import numpy as np
from statsmodels.tsa.statespace.varmax import VARMAX
# from pmdarima import auto_arima

/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.
  import pandas.util.testing as tm
In [ ]:
# log transform
tol = 1e-4
ltr = lambda x: np.log(x + tol)
# inverse
iltr = lambda  y: np.exp(y) - tol

DATA

In [ ]:
df = pd.read_csv('ker.csv',index_col='Date',parse_dates=True)
df=df.dropna()
df = df.drop('State', axis =1)
df
Out[ ]:
Confirmed Recovered Deceased Other Tested First Dose Administered Second Dose Administered Total Doses Administered Active cases Active tested Active Vaccinated Active Tested
Date
2020-02-02 2 0 0 0 0.0 0.0 0.0 0.0 2 0.0 0.0 0.0
2020-02-03 3 0 0 0 0.0 0.0 0.0 0.0 3 0.0 0.0 0.0
2020-02-14 3 3 0 0 0.0 0.0 0.0 0.0 0 0.0 0.0 0.0
2020-03-02 3 3 0 0 0.0 0.0 0.0 0.0 0 0.0 0.0 0.0
2020-03-03 3 3 0 0 0.0 0.0 0.0 0.0 0 0.0 0.0 0.0
... ... ... ... ... ... ... ... ... ... ... ... ...
2021-10-17 4854321 4739270 26865 529 36802640.0 25079316.0 12171427.0 37250743.0 88186 73157.0 13055.0 73157.0
2021-10-18 4860997 4750293 26925 529 36871308.0 25106712.0 12314762.0 37421474.0 83779 68668.0 170731.0 68668.0
2021-10-19 4868640 4760781 27002 529 36953716.0 25115770.0 12364284.0 37480054.0 80857 82408.0 58580.0 82408.0
2021-10-20 4879790 4769373 27084 529 37047867.0 25130853.0 12437190.0 37568043.0 83333 94151.0 87989.0 94151.0
2021-10-21 4888523 4779228 27202 529 37134170.0 25153284.0 12564537.0 37717821.0 82093 86303.0 149778.0 86303.0

602 rows × 12 columns

In [ ]:
df['Active cases'].plot()
Out[ ]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f309b865d90>
In [ ]:
l = int(df.shape[0]*0.15)
train = df.iloc[:-l]
test = df.iloc[-l:-1]
train = train.astype(np.float64)
test = test.astype(np.float64)
In [ ]:
# en = train.drop(['TESTED'], axis=1)
ens = ['Recovered', 'Deceased', 'Total Doses Administered', 'Active Tested']
del ens[2:]
en = train[['Active cases'] + ens]
exs = ['Active Tested']
ex= train[exs]
ext = test[exs]
In [ ]:
en
Out[ ]:
Active cases Recovered Deceased
Date
2020-02-02 2.0 0.0 0.0
2020-02-03 3.0 0.0 0.0
2020-02-14 0.0 3.0 0.0
2020-03-02 0.0 3.0 0.0
2020-03-03 0.0 3.0 0.0
... ... ... ...
2021-07-19 122202.0 3033258.0 15408.0
2021-07-20 126894.0 3045310.0 15512.0
2021-07-21 130138.0 3059441.0 15618.0
2021-07-22 129381.0 3072895.0 15739.0
2021-07-23 135700.0 3083962.0 15871.0

512 rows × 3 columns

MODEL

In [ ]:
model = VARMAX(en, order=(4, 8), exog = ex)
model_fit = model.fit()

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/varmax.py:159: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.
  EstimationWarning)
/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  ' ignored when e.g. forecasting.', ValueWarning)
In [ ]:
y = model_fit.forecast(steps=len(test), exog = ext)

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/varmax.py:159: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.
  EstimationWarning)
/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:576: ValueWarning: No supported index is available. Prediction results will be given with an integer index beginning at `start`.
  ValueWarning)
In [ ]:
y.index = test.index
y.columns += [' pred']*y.shape[1]
y
Out[ ]:
Active cases pred Recovered pred Deceased pred
Date
2021-07-24 140929.921766 3.138534e+06 16166.115606
2021-07-25 130839.920256 3.010455e+06 15654.214862
2021-07-26 121727.112982 2.889253e+06 15162.524484
2021-07-27 151523.496392 3.171290e+06 16439.036754
2021-07-28 154969.857623 3.161123e+06 16440.817568
... ... ... ...
2021-10-16 152226.430991 8.500018e+05 5517.362008
2021-10-17 148691.996281 8.333241e+05 5428.229524
2021-10-18 143940.109332 8.054055e+05 5289.982377
2021-10-19 143392.886188 8.162696e+05 5323.870715
2021-10-20 145556.316690 8.506807e+05 5463.237305

89 rows × 3 columns

In [ ]:
plt.matshow(y.corr())
plt.colorbar()
plt.show()
In [ ]:
# train['ACTIVE'].plot(legend = True)
test['Active cases'].plot(legend = True)
y['Active cases pred'].plot(legend = True)
Out[ ]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f6cc8dbebd0>
In [ ]:
pr = model_fit.predict(2, len(df)-2, exog = ext)

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/varmax.py:159: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.
  EstimationWarning)
/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:576: ValueWarning: No supported index is available. Prediction results will be given with an integer index beginning at `start`.
  ValueWarning)
In [ ]:
pr.index = df.iloc[1:len(df)-2].index
# pr.columns += [' pred']*pr.shape[1]
train['Active cases'].plot(label = 'Active cases', legend = True)
test['Active cases'].plot(legend = True, label = 'Actual')
pr['Active cases'].iloc[:-l].plot(style = '--',label = 'Fit', legend = True)
pr['Active cases'].iloc[-l:].plot(style = '--',label = 'Forecast', legend = True)

# y['ACTIVE pred'].plot(legend = True)
Out[ ]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f6cc94fec50>
In [ ]:
model_fit.plot_diagnostics(variable=0, lags=20, fig=None, figsize= (9,7))
Out[ ]:
In [ ]:
plt.matshow(model_fit.cov_params())
plt.show()
In [ ]:
model_fit.summary().tables[4]
Out[ ]:
Results for equation DEATH
coef std err z P>|z| [0.025 0.975]
intercept -209.3012 1.707 -122.639 0.000 -212.646 -205.956
L1.ACTIVE -0.0073 0.001 -6.935 0.000 -0.009 -0.005
L1.RECOVERED -0.0284 0.001 -28.884 0.000 -0.030 -0.026
L1.DEATH 7.2504 0.161 45.108 0.000 6.935 7.565
L2.ACTIVE 0.0033 0.001 3.323 0.001 0.001 0.005
L2.RECOVERED 0.0284 0.001 30.019 0.000 0.027 0.030
L2.DEATH -6.4510 0.162 -39.827 0.000 -6.768 -6.134
L1.e(ACTIVE) 0.0246 0.001 23.220 0.000 0.023 0.027
L1.e(RECOVERED) 0.0231 0.002 13.438 0.000 0.020 0.027
L1.e(DEATH) -5.7875 0.162 -35.674 0.000 -6.105 -5.470
L2.e(ACTIVE) -0.0196 0.001 -31.251 0.000 -0.021 -0.018
L2.e(RECOVERED) -0.0287 0.001 -20.475 0.000 -0.031 -0.026
L2.e(DEATH) 6.7048 0.095 70.693 0.000 6.519 6.891
beta.Active Tested 0.0206 0.004 4.801 0.000 0.012 0.029
In [ ]:
model_fit.cov_params()
Out[ ]:
intercept.ACTIVE intercept.RECOVERED intercept.DEATH L1.ACTIVE.ACTIVE L1.RECOVERED.ACTIVE L1.DEATH.ACTIVE L2.ACTIVE.ACTIVE L2.RECOVERED.ACTIVE L2.DEATH.ACTIVE L1.ACTIVE.RECOVERED L1.RECOVERED.RECOVERED L1.DEATH.RECOVERED L2.ACTIVE.RECOVERED L2.RECOVERED.RECOVERED L2.DEATH.RECOVERED L1.ACTIVE.DEATH L1.RECOVERED.DEATH L1.DEATH.DEATH L2.ACTIVE.DEATH L2.RECOVERED.DEATH L2.DEATH.DEATH L1.e(ACTIVE).ACTIVE L1.e(RECOVERED).ACTIVE L1.e(DEATH).ACTIVE L2.e(ACTIVE).ACTIVE L2.e(RECOVERED).ACTIVE L2.e(DEATH).ACTIVE L1.e(ACTIVE).RECOVERED L1.e(RECOVERED).RECOVERED L1.e(DEATH).RECOVERED L2.e(ACTIVE).RECOVERED L2.e(RECOVERED).RECOVERED L2.e(DEATH).RECOVERED L1.e(ACTIVE).DEATH L1.e(RECOVERED).DEATH L1.e(DEATH).DEATH L2.e(ACTIVE).DEATH L2.e(RECOVERED).DEATH L2.e(DEATH).DEATH beta.Active Tested.ACTIVE beta.Active Tested.RECOVERED beta.Active Tested.DEATH sqrt.var.ACTIVE sqrt.cov.ACTIVE.RECOVERED sqrt.var.RECOVERED sqrt.cov.ACTIVE.DEATH sqrt.cov.RECOVERED.DEATH sqrt.var.DEATH
intercept.ACTIVE -6.390369e-04 2.726122e-04 -0.054603 0.001184 0.000517 -0.001630 -0.001199 -4.811624e-04 -0.004768 0.006019 0.006187 0.002392 -0.005946 -0.006187 0.002676 2.836880e-05 2.833080e-05 -0.000372 -2.816697e-05 -2.816133e-05 0.000367 -9.830560e-04 2.098003e-04 -0.000855 0.000026 -4.358434e-05 -1.926002e-04 -0.004828 0.001937 7.676587e-05 0.000068 -0.000761 2.041483e-05 -2.422498e-05 6.978804e-06 0.000384 -1.070530e-06 -4.134842e-06 0.000219 -1.687376e-04 -0.001018 -4.534963e-06 5.126742e-04 2.134241e-06 2.986266e-04 -1.020647e-02 0.000366 -0.000289
intercept.RECOVERED -1.374139e-04 5.858796e-05 -0.011735 0.000251 0.000120 -0.000267 -0.000246 -1.120203e-04 -0.000943 0.001340 0.001345 0.000503 -0.001232 -0.001333 0.000564 6.256374e-06 6.221872e-06 -0.000086 -5.809183e-06 -6.134817e-06 0.000085 -1.993122e-04 3.840592e-05 -0.000184 0.000003 -8.813398e-06 -3.836670e-05 -0.001038 0.000348 1.622561e-05 0.000034 -0.000157 4.190045e-06 -5.137932e-06 1.171339e-06 0.000088 -1.547690e-07 -8.731450e-07 0.000050 -6.754988e-05 -0.000580 -2.562068e-06 1.103608e-04 4.171437e-07 6.441478e-05 -2.188269e-03 0.000047 -0.000062
intercept.DEATH 3.410714e-02 -1.454189e-02 2.912632 -0.062478 -0.029683 0.067453 0.061321 2.769083e-02 0.235179 -0.332096 -0.333781 -0.124989 0.306114 0.330868 -0.140143 -1.551812e-03 -1.542854e-03 0.021182 1.444451e-03 1.521671e-03 -0.021045 4.968561e-02 -9.604812e-03 0.045732 -0.000639 2.192188e-03 9.550610e-03 0.257626 -0.087072 -4.029621e-03 -0.008311 0.039015 -1.041661e-03 1.276403e-03 -2.939202e-04 -0.021762 3.925582e-05 2.169722e-04 -0.012383 1.648497e-02 0.140754 6.216539e-04 -2.739083e-02 -1.041519e-04 -1.598486e-02 5.432469e-01 -0.012328 0.015430
L1.ACTIVE.ACTIVE -4.874211e-04 1.722479e-04 -0.033384 0.016557 -0.002129 -0.046954 -0.016382 2.698958e-03 -0.049249 0.004924 0.003797 0.005711 -0.000766 -0.002901 0.005964 9.621304e-05 -6.251871e-06 0.002795 -7.807086e-05 1.223022e-05 -0.003169 -1.773861e-02 1.384264e-03 -0.000335 -0.006250 4.990034e-04 -1.451984e-04 -0.002620 -0.004390 1.727489e-05 0.001543 -0.003311 1.769735e-05 -9.299482e-05 2.883914e-06 -0.003156 -1.692062e-05 -1.415005e-06 -0.002262 -2.059758e-03 -0.017671 -7.927547e-05 3.568751e-04 4.125420e-06 1.833452e-04 -7.625194e-03 0.007524 -0.000876
L1.RECOVERED.ACTIVE -9.938776e-05 5.111707e-05 -0.010554 -0.002305 0.003284 0.022111 0.002406 -3.431453e-03 0.021460 0.001483 0.002337 -0.001805 -0.000057 -0.001510 -0.001770 -6.580603e-06 2.187245e-05 -0.000747 1.280999e-05 -1.901049e-05 0.000893 4.769975e-03 -7.463705e-04 -0.000206 0.000196 4.996136e-06 2.020091e-04 -0.001468 -0.003978 -3.474905e-06 -0.000035 0.001876 -1.127145e-05 1.395782e-05 -2.355292e-05 0.000969 -5.985095e-07 6.000389e-06 0.000394 -1.345423e-03 -0.015423 -6.773962e-05 9.487083e-05 8.603308e-06 1.141697e-05 -3.828554e-03 0.009446 0.000048
L1.DEATH.ACTIVE 2.103535e-03 -7.419232e-04 0.143390 -0.049737 0.020739 0.296400 0.052860 -2.343443e-02 0.305524 -0.005655 -0.006943 -0.035014 0.030004 0.009387 -0.035996 -2.128828e-04 3.084590e-05 0.004989 3.252185e-04 -3.153030e-05 -0.002946 6.305078e-02 -8.830449e-03 0.001567 0.008342 1.442742e-04 2.501537e-03 0.008904 -0.031239 -2.286051e-04 -0.003260 0.025397 -1.451958e-04 2.737416e-04 -1.452498e-04 -0.003428 1.193523e-05 1.105175e-04 -0.001474 -7.240979e-03 -0.081204 -3.581812e-04 -1.481705e-03 5.306347e-05 -1.152021e-03 1.524538e-02 0.055484 -0.000566
L2.ACTIVE.ACTIVE 4.499465e-04 -1.602050e-04 0.031053 -0.016342 0.002250 0.050071 0.016860 -2.789659e-03 0.052123 -0.000942 -0.002584 -0.006099 0.004419 0.002293 -0.006337 -7.854804e-05 1.015963e-05 -0.002432 9.410896e-05 -1.358071e-05 0.002824 1.773836e-02 -1.687084e-03 0.000294 0.005787 -5.182536e-04 3.189890e-04 0.002364 0.001067 -2.670062e-05 -0.000696 0.002719 -3.214879e-05 9.047323e-05 -1.573822e-05 0.002783 1.840568e-05 -2.344867e-07 0.002077 1.629643e-04 -0.003125 -1.227336e-05 -3.225219e-04 -2.863556e-06 -1.742615e-04 6.646045e-03 -0.005024 0.000368
L2.RECOVERED.ACTIVE 6.938535e-05 -4.055794e-05 0.008507 0.002900 -0.003415 -0.024746 -0.002971 3.599199e-03 -0.024240 -0.001037 -0.002053 0.002124 0.000058 0.001334 0.002102 1.074028e-05 -2.100508e-05 0.000710 -1.506645e-05 1.872026e-05 -0.000874 -5.444618e-03 8.000136e-04 0.000181 -0.000405 -1.134999e-05 -2.038332e-04 0.001316 0.003866 4.738029e-06 0.000171 -0.002305 1.032077e-05 -1.718163e-05 2.318963e-05 -0.000942 4.200632e-07 -7.792376e-06 -0.000390 1.140413e-03 0.013241 5.811916e-05 -7.243702e-05 -8.784480e-06 2.151600e-06 3.446691e-03 -0.009448 -0.000202
L2.DEATH.ACTIVE 2.397828e-03 -8.658413e-04 0.168170 -0.050335 0.020342 0.296278 0.053347 -2.306194e-02 0.306900 -0.008992 -0.010076 -0.035965 0.031821 0.012319 -0.037080 -2.284952e-04 1.677897e-05 0.005055 3.342227e-04 -1.839558e-05 -0.003013 6.344211e-02 -8.765122e-03 0.001935 0.008526 9.031692e-05 2.518581e-03 0.011288 -0.030209 -2.535473e-04 -0.003369 0.024954 -1.520258e-04 2.856080e-04 -1.403695e-04 -0.003539 1.264186e-05 1.085230e-04 -0.001481 -6.713888e-03 -0.075305 -3.323934e-04 -1.717615e-03 4.834423e-05 -1.268706e-03 2.080216e-02 0.050542 0.000037
L1.ACTIVE.RECOVERED -2.992134e-04 1.075506e-04 -0.021160 0.000909 0.000719 0.013604 0.002802 -5.311032e-04 0.011873 0.023469 0.007337 -0.001465 0.018652 -0.004018 -0.001371 9.530065e-05 3.578468e-05 -0.000671 8.963009e-05 -2.161172e-05 0.000766 7.038674e-04 -1.786473e-03 -0.000442 0.000133 -1.277413e-04 8.803474e-04 -0.001858 -0.019823 -5.179828e-05 0.006168 -0.001286 -6.518721e-05 -5.107149e-06 -8.979195e-05 0.000547 2.583702e-05 -8.608252e-06 0.000636 -1.039955e-02 -0.117639 -5.170256e-04 2.689768e-04 -1.039078e-05 1.859193e-04 -2.964584e-03 -0.006581 -0.000101
L1.RECOVERED.RECOVERED -1.418238e-03 5.992526e-04 -0.119940 0.002080 0.002500 0.009038 -0.001100 -2.395735e-03 0.001856 0.018536 0.015888 0.003660 -0.006788 -0.014254 0.004291 8.320212e-05 7.442797e-05 -0.000181 -3.176234e-05 -6.733522e-05 0.000248 -6.059829e-04 -4.881179e-04 -0.001864 -0.000941 4.033321e-05 2.819179e-05 -0.011168 -0.005276 1.280760e-04 0.001513 -0.000329 1.552650e-05 -5.129413e-05 -2.458453e-05 0.000342 2.996118e-08 -1.355532e-06 0.000073 -4.197943e-03 -0.046159 -2.026792e-04 1.148044e-03 1.487458e-05 6.064413e-04 -2.524989e-02 0.014899 -0.002381
L1.DEATH.RECOVERED -1.104417e-04 3.515447e-05 -0.006617 0.004194 -0.002088 -0.027653 -0.004685 2.309541e-03 -0.028048 -0.001341 -0.000524 0.003068 -0.003342 -0.000016 0.003120 1.009605e-05 -7.689545e-06 -0.000588 -3.115155e-05 6.366034e-06 0.000399 -5.564493e-03 9.265435e-04 -0.000049 -0.000512 -3.863822e-05 -2.893312e-04 -0.000155 0.004490 1.987180e-05 -0.000051 -0.002405 1.609020e-05 -2.079225e-05 1.975810e-05 0.000434 -1.569544e-06 -1.096205e-05 0.000230 1.460724e-03 0.016557 7.280022e-05 6.883310e-05 -6.634351e-06 7.659541e-05 2.913436e-04 -0.007453 0.000410
L2.ACTIVE.RECOVERED -2.883735e-04 8.966969e-05 -0.017163 0.003831 0.001017 0.011082 0.000088 -7.483724e-04 0.009154 0.023153 0.007980 -0.001498 0.022005 -0.004113 -0.001353 1.168781e-04 1.828221e-05 0.003518 8.217874e-05 -1.514200e-06 -0.003490 -2.316841e-03 -1.803202e-03 -0.000144 -0.002812 7.799389e-05 1.134454e-03 -0.002624 -0.023454 -7.722434e-05 0.003983 -0.001326 -8.447098e-05 -3.581113e-05 -8.550836e-05 -0.003390 5.567839e-06 3.980438e-06 -0.002033 -1.124259e-02 -0.126093 -5.537564e-04 2.432069e-04 2.895834e-05 -3.504281e-05 -1.142295e-02 0.040911 -0.004655
L2.RECOVERED.RECOVERED 1.345784e-03 -5.763790e-04 0.115544 -0.001115 -0.001636 -0.006553 0.000738 1.639858e-03 0.000170 -0.014677 -0.013826 -0.003994 0.010116 0.013657 -0.004598 -6.333090e-05 -6.221324e-05 0.000224 4.329444e-05 6.148483e-05 -0.000279 3.507689e-04 5.935663e-05 0.001796 -0.000186 -7.060992e-05 2.370411e-04 0.010620 -0.000189 -1.465505e-04 -0.000228 -0.000951 -4.003394e-05 4.795938e-05 7.760314e-07 -0.000344 1.373303e-06 -3.612681e-06 -0.000155 1.250659e-03 0.012739 5.586463e-05 -1.085667e-03 -1.199094e-05 -5.921634e-04 2.335188e-02 -0.009740 0.000952
L2.DEATH.RECOVERED -1.200335e-04 3.906297e-05 -0.007394 0.004259 -0.002090 -0.027748 -0.004748 2.312659e-03 -0.028194 -0.001266 -0.000424 0.003107 -0.003386 -0.000114 0.003167 1.139879e-05 -8.358428e-06 -0.000356 -3.226651e-05 7.050045e-06 0.000165 -5.650387e-03 9.319870e-04 -0.000055 -0.000559 -3.190217e-05 -2.889709e-04 -0.000246 0.004464 2.119662e-05 -0.000100 -0.002363 1.675491e-05 -2.250373e-05 2.078285e-05 0.000206 -2.011703e-06 -1.015938e-05 0.000096 1.463084e-03 0.016597 7.300163e-05 7.616572e-05 -5.836526e-06 7.697530e-05 -2.877105e-05 -0.006551 0.000310
L1.ACTIVE.DEATH -2.691719e-06 9.056542e-07 -0.000175 0.000080 -0.000009 -0.000125 -0.000063 1.225590e-05 -0.000139 0.000107 0.000042 0.000014 0.000085 -0.000024 0.000016 1.112130e-06 -2.470451e-07 0.000092 -2.535084e-07 3.313591e-07 -0.000094 -8.667754e-05 6.006469e-07 -0.000001 -0.000032 2.041405e-06 3.626645e-06 -0.000016 -0.000091 8.117683e-08 0.000020 -0.000016 -7.656650e-08 -8.617782e-07 9.249580e-08 -0.000094 -6.425631e-08 1.867354e-07 -0.000053 -4.960309e-05 -0.000535 -2.354993e-06 2.086332e-06 1.106117e-07 5.547836e-07 -6.530275e-05 0.000159 -0.000039
L1.RECOVERED.DEATH -6.925896e-06 2.996894e-06 -0.000602 -0.000013 0.000023 0.000103 0.000016 -2.290040e-05 0.000068 0.000091 0.000079 0.000013 -0.000053 -0.000068 0.000015 -3.654512e-08 9.649118e-07 -0.000118 1.727302e-07 -9.230434e-07 0.000120 3.537645e-05 -6.654455e-06 -0.000012 0.000015 -1.332730e-06 -3.034126e-07 -0.000051 -0.000035 3.115540e-07 0.000028 -0.000003 -1.118671e-07 4.038254e-07 -7.400783e-07 0.000119 1.835364e-07 -3.200792e-07 0.000067 -2.566070e-05 -0.000294 -1.299359e-06 5.758256e-06 -1.835072e-07 4.330020e-06 -6.821477e-05 -0.000222 0.000014
L1.DEATH.DEATH 2.525715e-04 -1.141693e-04 0.023096 0.002553 -0.000894 0.004540 -0.002183 8.561304e-04 0.005684 -0.002995 -0.001847 -0.001473 0.005905 0.001898 -0.001349 8.211937e-05 -1.253763e-04 0.025835 -6.306754e-05 1.255579e-04 -0.026030 -4.879478e-03 4.619882e-04 0.000824 -0.003888 3.109504e-04 2.760935e-04 0.000985 0.000064 4.273685e-05 -0.004218 0.001271 2.748842e-05 -1.234989e-04 1.263592e-04 -0.025706 -3.734004e-05 7.286673e-05 -0.014651 4.160311e-04 0.006419 3.010236e-05 -2.219964e-04 5.327081e-05 -3.989752e-04 -7.896479e-03 0.061486 -0.006788
L2.ACTIVE.DEATH 1.847730e-07 -6.894978e-08 0.000012 -0.000059 0.000017 0.000238 0.000076 -1.786426e-05 0.000237 0.000097 0.000025 -0.000028 0.000095 -0.000011 -0.000029 -1.667211e-07 4.515097e-07 -0.000074 9.998339e-07 -4.008178e-07 0.000076 7.925870e-05 -1.628266e-05 -0.000001 0.000018 -2.183999e-06 5.267540e-06 -0.000003 -0.000098 -6.308123e-07 0.000023 0.000004 -5.759040e-07 6.578083e-07 -8.276661e-07 0.000075 1.870955e-07 -1.922086e-07 0.000043 -4.522500e-05 -0.000531 -2.327856e-06 1.024282e-07 -1.708134e-08 1.318043e-08 5.381583e-07 0.000005 0.000016
L2.RECOVERED.DEATH 6.495319e-06 -2.854715e-06 0.000575 0.000020 -0.000020 -0.000103 -0.000020 2.039561e-05 -0.000071 -0.000074 -0.000069 -0.000013 0.000067 0.000065 -0.000015 1.360305e-07 -9.116424e-07 0.000118 -1.374243e-07 8.978953e-07 -0.000120 -3.912228e-05 5.152443e-06 0.000011 -0.000020 1.171109e-06 1.368332e-06 0.000048 0.000012 -3.781914e-07 -0.000022 -0.000004 9.125923e-09 -4.328852e-07 6.439354e-07 -0.000119 -1.788911e-07 2.929410e-07 -0.000067 1.289512e-05 0.000150 6.662393e-07 -5.402275e-06 1.952113e-07 -4.213484e-06 5.857110e-05 0.000244 -0.000021
L2.DEATH.DEATH -2.354111e-04 1.080801e-04 -0.021918 -0.002955 0.001028 -0.002471 0.002603 -1.009237e-03 -0.003538 0.002930 0.001767 0.001223 -0.005726 -0.001806 0.001089 -8.485303e-05 1.264448e-04 -0.026023 6.629932e-05 -1.266670e-04 0.026236 5.380496e-03 -5.316544e-04 -0.000815 0.003962 -3.095275e-04 -2.610426e-04 -0.000897 -0.000307 -4.524420e-05 0.004237 -0.001086 -2.868309e-05 1.269699e-04 -1.286161e-04 0.025906 3.776624e-05 -7.263145e-05 0.014764 -4.565863e-04 -0.006906 -3.225759e-05 2.099000e-04 -5.349880e-05 3.929163e-04 8.172281e-03 -0.061789 0.006900
L1.e(ACTIVE).ACTIVE 4.131925e-04 -1.362605e-04 0.025998 -0.017751 0.004618 0.060752 0.017785 -5.272903e-03 0.062587 -0.002702 -0.002097 -0.006852 0.001569 0.001899 -0.007097 -1.008666e-04 2.929965e-05 -0.005077 9.551532e-05 -3.271894e-05 0.005555 2.166019e-02 -1.831553e-03 0.000150 0.006468 -6.019303e-04 2.961426e-04 0.001800 0.002157 -2.145686e-05 -0.000920 0.003683 -3.216043e-05 1.150691e-04 -2.560013e-05 0.005612 1.985446e-05 -2.586249e-06 0.003418 6.687820e-04 0.000661 4.758569e-06 -2.849961e-04 -4.053459e-06 -1.437526e-04 6.187572e-03 -0.007359 0.002076
L1.e(RECOVERED).ACTIVE -9.188382e-05 3.640944e-05 -0.007170 0.001432 -0.000701 -0.008473 -0.001740 7.520126e-04 -0.008784 -0.000942 0.000004 0.001247 -0.002717 -0.000441 0.001292 4.249562e-06 -4.541513e-06 0.000485 -2.023139e-05 2.995958e-06 -0.000551 -1.869139e-03 9.554686e-04 -0.000109 -0.000350 -4.955646e-04 -2.177340e-04 -0.000008 0.009465 5.312529e-05 -0.001121 -0.006577 -9.268863e-06 -9.848211e-06 4.501380e-05 -0.000606 -6.970406e-06 -2.730453e-05 -0.000265 1.023952e-03 0.013495 5.877044e-05 6.568317e-05 -8.589688e-07 4.720151e-05 -1.006760e-03 -0.001850 -0.000440
L1.e(DEATH).ACTIVE -1.170546e-04 4.839982e-05 -0.009644 0.000518 0.000021 -0.001504 -0.000516 -3.502391e-07 -0.002098 0.001029 0.001144 0.000533 -0.000870 -0.001123 0.000592 7.500642e-06 2.555096e-06 0.000419 -6.738440e-06 -2.380042e-06 -0.000434 -5.685113e-04 5.261152e-05 -0.000126 -0.000218 1.820164e-05 -2.088111e-05 -0.000953 0.000064 1.204021e-05 -0.000177 -0.000044 3.503789e-06 -8.183241e-06 2.445740e-06 -0.000402 -1.818258e-06 1.087441e-06 -0.000262 -3.362350e-05 -0.000272 -1.105071e-06 9.168319e-05 3.695557e-06 3.619691e-05 -2.575684e-03 0.004069 -0.000494
L2.e(ACTIVE).ACTIVE -2.043027e-05 2.622421e-05 -0.005781 -0.006150 0.000230 0.008111 0.005690 -4.349374e-04 0.008104 0.000493 -0.000512 -0.000374 -0.003111 -0.000608 -0.000405 -3.003505e-05 1.667931e-05 -0.003924 1.647861e-05 -2.192770e-05 0.003997 6.384495e-03 -3.329107e-04 -0.000258 0.013487 -5.648254e-04 -1.990757e-04 -0.000119 0.002767 1.657263e-05 0.000492 0.006420 3.523715e-05 2.906431e-05 -9.734233e-06 0.004293 5.772229e-05 8.491337e-06 0.003396 2.388254e-03 0.019042 8.615056e-05 3.214125e-05 -2.524328e-05 1.550790e-04 5.134088e-03 -0.031656 0.008128
L2.e(RECOVERED).ACTIVE 3.524639e-05 -1.405477e-05 0.002779 0.000461 -0.000016 0.000102 -0.000480 9.507403e-06 0.000199 -0.000451 -0.000203 -0.000162 0.000405 0.000173 -0.000170 5.891434e-07 -2.413368e-06 0.000313 -7.105425e-07 2.251916e-06 -0.000313 -5.709181e-04 -4.996871e-04 0.000073 -0.000560 6.754621e-04 6.831636e-05 -0.000209 -0.006766 -3.514551e-05 0.000822 0.007154 2.731363e-05 -3.318134e-06 -2.809619e-05 -0.000276 1.838703e-06 3.308777e-05 -0.000344 -2.544118e-05 -0.001130 -4.737864e-06 -2.763893e-05 2.998833e-07 -1.892043e-05 4.510952e-04 0.000701 0.000340
L2.e(DEATH).ACTIVE -1.827327e-04 7.635029e-05 -0.015260 0.000346 0.000375 0.001409 -0.000157 -3.566835e-04 0.000461 0.002700 0.002175 0.000413 -0.000398 -0.001875 0.000496 1.262305e-05 9.643159e-06 0.000102 -2.521690e-06 -8.345360e-06 -0.000094 -1.144052e-04 -1.361206e-04 -0.000228 -0.000201 4.598703e-05 3.793023e-05 -0.001506 -0.001647 1.162726e-05 0.000266 0.000404 1.357753e-06 -7.546022e-06 -6.815197e-06 -0.000070 1.083694e-07 2.188232e-06 -0.000081 -7.670816e-04 -0.008718 -3.819878e-05 1.478278e-04 3.446458e-06 6.945118e-05 -3.604463e-03 0.003914 -0.000507
L1.e(ACTIVE).RECOVERED -1.635429e-04 6.792413e-05 -0.013542 0.001211 -0.000586 -0.007039 -0.001242 6.574818e-04 -0.007659 0.001638 0.001011 0.001280 -0.002312 -0.001101 0.001334 9.823995e-06 7.870772e-06 -0.001019 -1.302701e-05 -7.952070e-06 0.000979 -1.437743e-03 7.545968e-04 -0.000291 0.000134 -4.835246e-04 -1.966257e-04 -0.000243 0.007773 5.507510e-05 0.000395 -0.006281 -8.292879e-06 -3.472459e-06 3.049112e-05 0.000818 1.273322e-06 -3.020526e-05 0.000654 -6.243240e-05 0.001297 4.873667e-06 1.311307e-04 -1.394347e-05 1.510072e-04 7.011847e-04 -0.016920 0.000853
L1.e(RECOVERED).RECOVERED -6.898061e-04 3.087427e-04 -0.061903 -0.004094 -0.003634 -0.028060 0.000724 3.499805e-03 -0.029947 -0.013184 -0.001639 0.007006 -0.030722 -0.003902 0.007288 -6.292719e-05 -1.932380e-05 0.000292 -1.288748e-04 -3.459923e-06 -0.000501 1.928609e-03 9.448526e-03 -0.001236 0.002629 -6.727781e-03 -2.323391e-03 0.001715 0.120674 6.423499e-04 -0.015383 -0.078028 -1.600600e-04 1.037690e-05 5.307832e-04 -0.001002 -6.851775e-05 -3.448616e-04 0.000830 1.282267e-02 0.167632 7.302365e-04 5.107520e-04 -1.033137e-05 4.094650e-04 -6.971801e-03 -0.026010 -0.004557
L1.e(DEATH).RECOVERED 7.734463e-06 -3.122543e-06 0.000622 -0.000052 -0.000021 0.000035 0.000039 1.863119e-05 0.000081 -0.000154 -0.000110 -0.000021 -0.000039 0.000084 -0.000024 -5.463279e-07 -8.294308e-07 0.000077 -2.718868e-07 7.143262e-07 -0.000077 3.728542e-05 3.969698e-05 0.000008 0.000013 -3.050831e-05 -7.453716e-06 0.000092 0.000535 2.091471e-06 -0.000070 -0.000343 -8.948610e-07 2.138084e-07 2.724951e-06 -0.000084 -3.083516e-07 -1.332728e-06 -0.000037 6.045005e-05 0.000782 3.408357e-06 -6.268857e-06 -1.559192e-07 -2.717979e-06 1.556496e-04 -0.000228 -0.000014
L2.e(ACTIVE).RECOVERED -7.876081e-04 3.325533e-04 -0.066615 0.002995 0.000568 -0.005048 -0.002124 -3.849160e-04 -0.008891 0.013634 0.008754 0.002814 -0.002928 -0.007402 0.003106 5.536114e-05 6.090880e-05 -0.004608 -9.633086e-06 -5.473752e-05 0.004622 -2.128593e-03 -9.042187e-04 -0.001231 0.000435 7.753819e-04 1.159508e-05 -0.005462 -0.013538 2.291897e-05 0.006218 0.008252 5.068563e-05 -1.486833e-05 -7.923608e-05 0.004332 2.797526e-05 2.512272e-05 0.002504 -4.116954e-03 -0.048436 -2.129567e-04 6.519481e-04 -3.790372e-05 5.751506e-04 -3.825806e-03 -0.044095 0.003844
L2.e(RECOVERED).RECOVERED 6.103610e-04 -2.259523e-04 0.044118 -0.003884 0.001530 0.024389 0.003308 -1.962539e-03 0.026465 -0.006708 -0.004242 -0.004471 0.004238 0.002979 -0.004680 -3.977372e-05 -2.042070e-05 0.001276 2.853014e-05 1.354752e-05 -0.001107 4.152347e-03 -6.633596e-03 0.000898 0.006504 7.148996e-03 8.067798e-04 -0.001609 -0.078576 -4.220307e-04 0.009146 0.090533 3.360726e-04 5.345263e-06 -3.422784e-04 -0.000353 7.263122e-05 4.006423e-04 -0.001500 1.892445e-03 0.001750 1.345705e-05 -4.603463e-04 -9.135713e-06 -2.322029e-04 1.071597e-02 -0.008562 0.010749
L2.e(DEATH).RECOVERED 1.805404e-05 -7.443271e-06 0.001484 -0.000032 -0.000029 -0.000033 0.000016 2.557511e-05 0.000056 -0.000246 -0.000200 -0.000054 0.000066 0.000172 -0.000061 -9.706481e-07 -1.109417e-06 0.000045 1.944615e-07 9.828772e-07 -0.000046 9.254667e-06 -1.753823e-05 0.000024 0.000035 2.959577e-05 9.672831e-07 0.000121 -0.000229 -2.763912e-06 0.000024 0.000377 1.511312e-06 3.909911e-07 -7.803245e-07 -0.000045 2.963248e-07 1.773917e-06 -0.000030 6.561810e-05 0.000658 2.912346e-06 -1.446235e-05 -3.374220e-07 -6.835843e-06 3.519425e-04 -0.000373 0.000080
L1.e(ACTIVE).DEATH 1.459495e-06 -4.480730e-07 0.000084 -0.000078 0.000017 0.000199 0.000076 -1.889472e-05 0.000206 -0.000009 -0.000011 -0.000022 -0.000015 0.000010 -0.000024 -8.333189e-07 6.056637e-07 -0.000132 7.037584e-07 -6.216609e-07 0.000135 1.022875e-04 -6.643217e-06 -0.000002 0.000030 -4.562859e-06 -2.632963e-07 0.000013 0.000035 -2.342573e-07 0.000014 -0.000016 -3.314868e-07 1.120492e-06 -5.315569e-07 0.000132 2.159418e-07 -4.221140e-07 0.000075 9.748470e-07 -0.000014 -6.352582e-08 -9.132881e-07 -2.794600e-07 8.776588e-07 8.036518e-05 -0.000331 0.000046
L1.e(RECOVERED).DEATH -2.054157e-06 8.913855e-07 -0.000177 0.000003 -0.000023 -0.000133 -0.000016 2.214913e-05 -0.000137 -0.000070 -0.000015 0.000027 -0.000108 -0.000009 0.000029 1.770512e-07 -7.005879e-07 0.000127 -9.229823e-07 6.027684e-07 -0.000129 -2.584631e-05 4.485391e-05 -0.000002 -0.000010 -2.793702e-05 -9.099195e-06 0.000012 0.000530 3.063400e-06 -0.000086 -0.000340 -5.496566e-07 -6.069015e-07 2.966255e-06 -0.000133 -4.857034e-07 -1.170417e-06 -0.000068 5.788442e-05 0.000761 3.325916e-06 1.351139e-06 1.923897e-07 7.635314e-08 -6.767923e-05 0.000161 -0.000061
L1.e(DEATH).DEATH -2.518911e-04 1.141441e-04 -0.023099 -0.002922 0.001115 -0.002945 0.002542 -1.087459e-03 -0.004128 0.002863 0.001982 0.001316 -0.005778 -0.001993 0.001195 -8.385333e-05 1.262295e-04 -0.025701 6.470076e-05 -1.263065e-04 0.025909 5.420961e-03 -5.840186e-04 -0.000808 0.004256 -2.730227e-04 -2.465795e-04 -0.001186 -0.000786 -4.998428e-05 0.003930 -0.000338 -2.708480e-05 1.235093e-04 -1.323439e-04 0.026320 3.788572e-05 -6.892932e-05 0.014648 -4.052679e-04 -0.006115 -2.866840e-05 2.211489e-04 -4.888318e-05 3.759040e-04 6.912941e-03 -0.056342 0.008579
L2.e(ACTIVE).DEATH -2.408280e-06 1.072410e-06 -0.000217 -0.000011 0.000001 0.000002 0.000013 -1.458723e-06 -0.000010 0.000050 0.000026 0.000008 -0.000015 -0.000024 0.000008 5.025458e-08 3.009329e-07 -0.000039 8.426372e-08 -2.939714e-07 0.000039 1.524558e-05 -6.091438e-06 -0.000005 0.000058 1.617806e-06 -2.812545e-07 -0.000016 -0.000061 -3.844659e-08 0.000030 0.000069 3.400323e-07 1.220607e-07 -4.603753e-07 0.000040 3.937551e-07 1.711930e-07 0.000024 -8.265543e-06 -0.000143 -6.135748e-07 2.073733e-06 -2.644377e-07 2.570565e-06 2.047409e-05 -0.000311 0.000055
L2.e(RECOVERED).DEATH 3.136914e-06 -1.218307e-06 0.000240 -0.000004 0.000004 0.000105 0.000003 -6.021865e-06 0.000116 -0.000037 -0.000022 -0.000022 0.000033 0.000017 -0.000022 6.145841e-08 -4.091665e-07 0.000073 -6.337203e-08 3.823451e-07 -0.000073 -1.935291e-07 -2.758726e-05 0.000006 0.000009 3.305876e-05 4.294473e-06 -0.000006 -0.000348 -1.745340e-06 0.000030 0.000401 1.559160e-06 -3.141222e-07 -1.182458e-06 -0.000069 1.925512e-07 1.964790e-06 -0.000048 8.109507e-06 0.000013 8.729116e-08 -2.453167e-06 1.100770e-07 -2.034668e-06 2.112202e-05 0.000137 0.000019
L2.e(DEATH).DEATH -1.316469e-04 6.155318e-05 -0.012511 -0.002146 0.000470 -0.001184 0.001957 -4.650074e-04 -0.001752 0.001853 0.000913 0.000694 -0.003296 -0.001002 0.000616 -4.776004e-05 7.038920e-05 -0.014645 3.785288e-05 -7.078372e-05 0.014762 3.323432e-03 -2.551425e-04 -0.000478 0.003376 -3.420128e-04 -1.774289e-04 -0.000405 0.000931 -1.905635e-05 0.002279 -0.001483 -2.008921e-05 7.015344e-05 -6.782896e-05 0.014644 2.331407e-05 -4.787308e-05 0.008995 -9.708273e-05 -0.001971 -9.767192e-06 1.185250e-04 -3.237012e-05 2.337198e-04 5.108848e-03 -0.037651 0.005731
beta.Active Tested.ACTIVE 2.278402e-04 -7.979971e-05 0.015608 -0.002213 -0.001452 -0.007725 0.000323 1.248136e-03 -0.006393 -0.012154 -0.005383 0.000792 -0.009406 0.002445 0.000713 -5.733883e-05 -3.085336e-05 0.000399 -3.712186e-05 1.813282e-05 -0.000446 7.932959e-04 1.012540e-03 0.000284 0.002418 -2.965308e-05 -6.216736e-04 0.001484 0.012699 3.387451e-05 -0.003765 0.001848 5.083349e-05 7.721609e-06 5.727913e-05 -0.000391 -6.744838e-06 7.900180e-06 -0.000093 7.453257e-03 0.082763 3.643228e-04 -1.975153e-04 -8.155040e-07 -9.386517e-05 4.083284e-03 -0.005047 0.001930
beta.Active Tested.RECOVERED 2.071696e-03 -6.868373e-04 0.133361 -0.018999 -0.016351 -0.085384 -0.001732 1.417781e-02 -0.072507 -0.132840 -0.056461 0.010763 -0.110176 0.023126 0.010097 -6.022145e-04 -3.388103e-04 0.006270 -4.604724e-04 1.951234e-04 -0.006812 1.743406e-03 1.339546e-02 0.002477 0.019304 -1.166018e-03 -7.458232e-03 0.014719 0.166551 5.517775e-04 -0.045380 0.001372 5.302771e-04 4.460843e-05 7.560143e-04 -0.005995 -1.293763e-04 1.147035e-05 -0.001936 8.276396e-02 0.954032 4.188156e-03 -1.833746e-03 -2.084934e-07 -8.607139e-04 3.658185e-02 -0.049861 0.018112
beta.Active Tested.DEATH 9.140385e-06 -3.036266e-06 0.000590 -0.000085 -0.000072 -0.000377 -0.000006 6.225772e-05 -0.000320 -0.000584 -0.000248 0.000047 -0.000483 0.000102 0.000044 -2.651237e-06 -1.499005e-06 0.000029 -2.017623e-06 8.675918e-07 -0.000032 9.550235e-06 5.832834e-05 0.000011 0.000087 -4.897309e-06 -3.263759e-05 0.000064 0.000725 2.390824e-06 -0.000199 0.000012 2.346909e-06 1.951855e-07 3.302597e-06 -0.000028 -5.553512e-07 7.942949e-08 -0.000010 3.643326e-04 0.004188 1.839086e-05 -8.090861e-06 8.223087e-09 -3.849995e-06 1.592905e-04 -0.000208 0.000081
sqrt.var.ACTIVE -1.182769e-05 5.047251e-06 -0.001012 0.000008 0.000025 0.000130 0.000004 -2.392453e-05 0.000072 0.000180 0.000136 0.000025 -0.000048 -0.000119 0.000030 6.967962e-07 7.720862e-07 -0.000025 -1.200972e-07 -7.011294e-07 0.000027 1.082305e-05 -6.611084e-06 -0.000017 0.000003 -4.194132e-07 4.758944e-07 -0.000088 -0.000059 1.066117e-06 0.000035 -0.000002 1.208644e-07 -2.531324e-07 -3.828482e-07 0.000025 1.389131e-07 -7.674968e-08 0.000015 -4.803901e-05 -0.000537 -2.363296e-06 9.728719e-06 -1.135684e-07 6.340766e-06 -1.598912e-04 -0.000152 0.000010
sqrt.cov.ACTIVE.RECOVERED -2.968577e-05 1.253911e-05 -0.002508 0.000062 0.000032 -0.000025 -0.000060 -3.047226e-05 -0.000175 0.000278 0.000300 0.000104 -0.000236 -0.000294 0.000118 1.476587e-06 1.117384e-06 0.000037 -1.285772e-06 -1.085358e-06 -0.000038 -5.232638e-05 7.919650e-06 -0.000036 -0.000027 -1.652392e-06 -5.457971e-06 -0.000238 0.000064 3.361949e-06 -0.000034 -0.000046 6.068288e-07 -1.412810e-06 4.554656e-07 -0.000032 -3.184743e-07 -8.566416e-08 -0.000023 -1.522432e-05 -0.000125 -5.423656e-07 2.362822e-05 6.726644e-07 1.079097e-05 -6.011060e-04 0.000699 -0.000082
sqrt.var.RECOVERED 8.654803e-06 -3.122834e-06 0.000606 -0.000050 -0.000042 -0.000173 0.000045 4.154643e-05 -0.000112 -0.000014 -0.000129 -0.000006 -0.000068 0.000115 -0.000014 -9.560941e-07 7.584339e-07 -0.000276 5.356306e-07 -8.182658e-07 0.000278 5.326894e-05 6.039274e-07 -0.000007 0.000139 -2.071368e-06 -1.175061e-05 0.000139 0.000040 -2.561798e-07 0.000214 0.000054 1.168230e-06 1.844659e-06 -1.068302e-06 0.000253 1.472077e-06 -5.506541e-07 0.000169 5.566104e-07 -0.000042 -2.327687e-07 -5.863606e-06 -3.029888e-06 1.202538e-05 7.998654e-04 -0.003550 0.000355
sqrt.cov.ACTIVE.DEATH 7.206985e-03 -3.045945e-03 0.609218 -0.014658 -0.008055 0.003201 0.013870 7.629799e-03 0.039464 -0.069013 -0.073056 -0.024879 0.056290 0.071359 -0.028249 -3.603081e-04 -2.798232e-04 -0.007810 3.031797e-04 2.707954e-04 0.007899 1.194234e-02 -1.703117e-03 0.008875 0.006151 3.950251e-04 1.279647e-03 0.057565 -0.013725 -8.107033e-04 0.006976 0.010782 -1.462480e-04 3.344602e-04 -9.673613e-05 0.006706 6.981351e-05 2.217691e-05 0.004878 4.642701e-03 0.041388 1.803664e-04 -5.744559e-03 -1.516452e-04 -2.682195e-03 1.434651e-01 -0.156455 0.018630
sqrt.cov.RECOVERED.DEATH -2.949703e-04 -7.480436e-06 0.005808 0.007467 0.009520 0.057070 -0.004989 -9.536313e-03 0.051350 -0.004697 0.015564 -0.006741 0.038689 -0.010445 -0.005751 1.663611e-04 -2.198196e-04 0.061633 -3.701418e-06 2.412785e-04 -0.061920 -7.305441e-03 -1.884400e-03 0.003646 -0.031708 7.231029e-04 3.656907e-03 -0.018783 -0.026244 -1.937097e-04 -0.044889 -0.008215 -3.470348e-04 -3.378942e-04 1.604707e-04 -0.056485 -3.139222e-04 1.390774e-04 -0.037722 -4.950659e-03 -0.049023 -2.040960e-04 1.429858e-05 6.678430e-04 -3.437261e-03 -1.522014e-01 0.791018 -0.078483
sqrt.var.DEATH 2.242475e-04 -7.408849e-05 0.014170 -0.001037 -0.000065 -0.001107 0.000538 -8.693661e-05 0.000362 -0.001996 -0.003643 -0.000311 -0.002666 0.002225 -0.000499 -4.688794e-05 8.338323e-06 -0.006809 2.499596e-05 -1.501090e-05 0.006914 2.207216e-03 -4.517386e-04 -0.000150 0.008161 3.347985e-04 -3.484035e-04 0.002523 -0.004684 -4.301253e-05 0.004230 0.010696 6.382988e-05 5.350031e-05 -6.211821e-05 0.008596 5.622327e-05 1.845470e-05 0.005736 1.928014e-03 0.018094 8.111191e-05 -1.509560e-04 -6.626762e-05 2.527860e-04 1.795964e-02 -0.078585 0.050387
In [ ]:
print(model_fit.mse)

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-122-2bd19a1963b9> in <module>()
----> 1 print(model_fit.mse)

/usr/local/lib/python3.7/dist-packages/statsmodels/base/wrapper.py in __getattribute__(self, attr)
     33             pass
     34 
---> 35         obj = getattr(results, attr)
     36         data = results.model.data
     37         how = self._wrap_attrs.get(attr)

AttributeError: 'VARMAXResults' object has no attribute 'mse'
In [ ]:
from sklearn import metrics
In [ ]:
metrics.mean_squared_error(test['Active cases'], y['Active cases pred'])
Out[ ]:
1443436507.881272
In [ ]:
metrics.mean_absolute_error(test['ACTIVE'], y['ACTIVE pred'])
In [ ]:
model_fit.self.mse
In [ ]:

With vaccination¶

In [ ]:
In [ ]:
# en = train.drop(['TESTED'], axis=1)
ens = ['Recovered', 'Deceased', 'Total Doses Administered', 'Active Tested']
del ens[3:]
en = train[['Active cases'] + ens]
exs = ['Active Tested']
ex= train[exs]
ext = test[exs]
In [ ]:
en
Out[ ]:
Active cases Recovered Deceased Total Doses Administered
Date
2020-02-02 2.0 0.0 0.0 0.0
2020-02-03 3.0 0.0 0.0 0.0
2020-02-14 0.0 3.0 0.0 0.0
2020-03-02 0.0 3.0 0.0 0.0
2020-03-03 0.0 3.0 0.0 0.0
... ... ... ... ...
2021-07-19 122202.0 3033258.0 15408.0 17059082.0
2021-07-20 126894.0 3045310.0 15512.0 17329411.0
2021-07-21 130138.0 3059441.0 15618.0 17427963.0
2021-07-22 129381.0 3072895.0 15739.0 17709527.0
2021-07-23 135700.0 3083962.0 15871.0 17976323.0

512 rows × 4 columns

MODEL

In [ ]:
model = VARMAX(en, order=(5, 9), exog = ex)
model_fit = model.fit()

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/varmax.py:159: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.
  EstimationWarning)
/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  ' ignored when e.g. forecasting.', ValueWarning)
/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:512: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  "Check mle_retvals", ConvergenceWarning)
In [ ]:
y = model_fit.forecast(steps=len(test), exog = ext)

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/varmax.py:159: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.
  EstimationWarning)
/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:576: ValueWarning: No supported index is available. Prediction results will be given with an integer index beginning at `start`.
  ValueWarning)
In [ ]:
model_fit.get_forecast(len(test), exog = ext)

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/varmax.py:159: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.
  EstimationWarning)
/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:576: ValueWarning: No supported index is available. Prediction results will be given with an integer index beginning at `start`.
  ValueWarning)
Out[ ]:
<statsmodels.tsa.statespace.mlemodel.PredictionResultsWrapper at 0x7f8f3fa29110>
In [ ]:
print(f)

<statsmodels.tsa.statespace.mlemodel.PredictionResultsWrapper object at 0x7f8f442d8290>
In [ ]:
y.index = test.index
y.columns += [' pred']*y.shape[1]
y
Out[ ]:
Active cases pred Recovered pred Deceased pred Total Doses Administered pred
Date
2021-07-24 120722.295746 2.936559e+06 15251.444337 1.799726e+07
2021-07-25 136279.926804 3.087144e+06 15943.610878 1.903589e+07
2021-07-26 116821.951333 2.869757e+06 15017.063522 1.770858e+07
2021-07-27 128265.631180 2.947657e+06 15390.719040 1.753981e+07
2021-07-28 139531.853199 3.028345e+06 15772.208342 1.749127e+07
... ... ... ... ...
2021-10-16 107030.922107 1.416993e+06 8284.166900 6.897209e+06
2021-10-17 103154.849162 1.399609e+06 8216.596288 6.864710e+06
2021-10-18 98439.651819 1.373752e+06 8112.219620 6.784352e+06
2021-10-19 97233.958201 1.379015e+06 8146.156181 6.801438e+06
2021-10-20 98351.791926 1.403967e+06 8267.528219 6.829014e+06

89 rows × 4 columns

In [ ]:
plt.matshow(y.corr())
plt.colorbar()
plt.show()
In [ ]:
# train['ACTIVE'].plot(legend = True)
test['Active cases'].plot(legend = True)
y['Active cases pred'].plot(legend = True)
Out[ ]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f8f3f8da6d0>
In [ ]:
test['Recovered'].plot(legend = True)
y['Recovered pred'].plot(legend = True)
Out[ ]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f6cca16bc10>
In [ ]:
pr = model_fit.predict(2, len(df)-2, exog = ext)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-1-c8da972cea17> in <module>()
----> 1 pr = model_fit.predict(2, len(df)-2, exog = ext)

NameError: name 'model_fit' is not defined
In [ ]:
pr.index = df.iloc[1:len(df)-2].index
# pr.columns += [' pred']*pr.shape[1]
train['Active cases'].plot(label = 'Active cases', legend = True)
test['Active cases'].plot(legend = True, label = 'Actual')
pr['Active cases'].iloc[:-l].plot(style = '--',label = 'Fit', legend = True)
pr['Active cases'].iloc[-l:].plot(style = '--',label = 'Forecast', legend = True)

# y['ACTIVE pred'].plot(legend = True)
Out[ ]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f6cc9fa6e90>
In [ ]:
# /pr.index = df.iloc[1:len(df)-2].index
# pr.columns += [' pred']*pr.shape[1]
train['Recovered'].plot(label = 'Active cases', legend = True)
test['Recovered'].plot(legend = True, label = 'Actual')
pr['Recovered'].iloc[:-l].plot(style = '--',label = 'Fit', legend = True)
pr['Recovered'].iloc[-l:].plot(style = '--',label = 'Forecast', legend = True)
plt.show()

# y['ACTIVE pred'].plot(legend = True)

train['Deceased'].plot(label = 'Active cases', legend = True)
test['Deceased'].plot(legend = True, label = 'Actual')
pr['Deceased'].iloc[:-l].plot(style = '--',label = 'Fit', legend = True)
pr['Deceased'].iloc[-l:].plot(style = '--',label = 'Forecast', legend = True)
Out[ ]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f6cc99b0690>
In [ ]:
In [ ]:
model_fit.plot_diagnostics(variable=0, lags=20, fig=None, figsize= (9,7))
Out[ ]:
In [ ]:
metrics.mean_squared_error(test['Active cases'], y['Active cases pred'])
Out[ ]:
210008334.1936363
In [ ]:
plt.matshow(model_fit.cov_params())
plt.show()
In [ ]:
model_fit.summary().tables[4]

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:1286: RuntimeWarning: invalid value encountered in sqrt
  bse_ = np.sqrt(np.diag(self.cov_params()))
Out[ ]:
Results for equation Deceased
coef std err z P>|z| [0.025 0.975]
intercept -95.7981 0.709 -135.027 0.000 -97.189 -94.408
L1.Active cases 0.0190 0.002 9.141 0.000 0.015 0.023
L1.Recovered -0.0045 0.002 -2.503 0.012 -0.008 -0.001
L1.Deceased 1.2488 0.326 3.833 0.000 0.610 1.887
L2.Active cases -0.0662 0.004 -17.511 0.000 -0.074 -0.059
L2.Recovered -0.0470 0.002 -20.906 0.000 -0.051 -0.043
L2.Deceased 12.0318 0.293 41.039 0.000 11.457 12.606
L3.Active cases 0.0642 0.003 19.737 0.000 0.058 0.071
L3.Recovered 0.0752 0.003 29.573 0.000 0.070 0.080
L3.Deceased -18.2712 0.449 -40.662 0.000 -19.152 -17.391
L4.Active cases -0.0175 0.002 -8.700 0.000 -0.021 -0.014
L4.Recovered -0.0238 0.002 -14.815 0.000 -0.027 -0.021
L4.Deceased 5.9133 0.312 18.934 0.000 5.301 6.525
L1.e(Active cases) -0.0190 0.002 -8.887 0.000 -0.023 -0.015
L1.e(Recovered) -0.0031 0.003 -0.953 0.341 -0.009 0.003
L1.e(Deceased) 1.0837 0.329 3.296 0.001 0.439 1.728
L2.e(Active cases) 0.0229 0.003 8.491 0.000 0.018 0.028
L2.e(Recovered) 0.0292 0.002 15.877 0.000 0.026 0.033
L2.e(Deceased) -7.1395 0.301 -23.680 0.000 -7.730 -6.549
L3.e(Active cases) -0.0104 0.002 -6.608 0.000 -0.013 -0.007
L3.e(Recovered) -0.0109 0.002 -5.392 0.000 -0.015 -0.007
L3.e(Deceased) 2.6659 0.211 12.627 0.000 2.252 3.080
L4.e(Active cases) 0.0107 0.001 11.074 0.000 0.009 0.013
L4.e(Recovered) 0.0085 0.002 5.079 0.000 0.005 0.012
L4.e(Deceased) -2.2079 0.176 -12.549 0.000 -2.553 -1.863
L5.e(Active cases) -0.0057 0.001 -5.863 0.000 -0.008 -0.004
L5.e(Recovered) -0.0085 0.001 -7.788 0.000 -0.011 -0.006
L5.e(Deceased) 1.9984 0.057 35.037 0.000 1.887 2.110
L6.e(Active cases) 0.0080 0.000 29.846 0.000 0.007 0.008
L6.e(Recovered) 0.0130 0.001 9.614 0.000 0.010 0.016
L6.e(Deceased) -3.1298 0.063 -49.759 0.000 -3.253 -3.007
L7.e(Active cases) -0.0043 0.000 -9.020 0.000 -0.005 -0.003
L7.e(Recovered) 0.0074 0.001 8.138 0.000 0.006 0.009
L7.e(Deceased) -0.8855 0.055 -16.224 0.000 -0.992 -0.779
L8.e(Active cases) 0.0347 0.001 26.203 0.000 0.032 0.037
L8.e(Recovered) -0.0078 0.003 -2.940 0.003 -0.013 -0.003
L8.e(Deceased) 1.0492 0.087 12.019 0.000 0.878 1.220
beta.Active Tested 0.0096 0.001 6.635 0.000 0.007 0.012