De entre las series de tiempo para cada enfermedad en el periodo descrito, no todas contienen información de casos reportados durante el periodo de tiempo establecido para la investigación, por lo que se extraen los que reportan al menos la mitad del periodo (260 semanas)
# https://stackoverflow.com/a/16916611
print('Iniciales {}'.format(len(cie)))
cie = cie.filter(lambda x: x['sem'].count() >= 260 )
cie.reset_index(drop=True, inplace=True)
cie = cie.groupby('cie')
print('Restantes {}'.format(len(cie)))Iniciales 138
Restantes 40
print('Iniciales {}'.format(len(cieG)))
cieG = cieG.filter(lambda x: x['sem'].count() >= 260 )
cieG.reset_index(drop=True, inplace=True)
cieG = cieG.groupby(cieG.cie.str[0])
print('Restantes {}'.format(len(cieG)))Iniciales 22
Restantes 12
Así, de 138 series de tiempo de enfermedades, se obtienen 40 en las que al menos se cuenta con datos semanales de 5 años. Para dichas enfermedades se obtienen los pesos de la regresión lineal y se obtiene la serie de tiempo sin la tendencia y las autocorrelaciones (eliminando la a92.3 porque viene vacía)
from scipy import signal
from statsmodels.graphics.tsaplots import plot_pacf, plot_acf
from statsmodels.tsa.stattools import acf
ciesF = [] # CIEs Características
ciesTSt = [] # CIEs Series de tiempo
for name, group in cie:
if name == 'a92.3':
continue
# https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.detrend.html
detrended = signal.detrend(group.casos)
a, b, r, p, e = stats.linregress(group['sem'], group.casos)
print("y = f(x) = {} x + {}".format(a, b))
print("error", e)
print("p = ", p)
print("pendiente {:s}significativa".format("no " if p >= 0.05 else ""))
print("R^2", r**2)
plt.figure(figsize=(12, 2))
plt.plot(group['sem'], group.casos)
plt.plot(group['sem'], detrended, c='black')
plt.plot(group['sem'], (a * group['sem'] + b), label = 'y = {:.1f}x + {:.0f}'.format(a, b), color = 'red', linewidth = 3)
plt.title(name)
plt.xlabel("Semana")
plt.ylabel("Casos normalizados")
plt.show()
# https://stackoverflow.com/questions/48497756/time-series-distance-metric
plt.figure(figsize=(12, 2))
# https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.cumsum.html
plt.plot(group['sem'], group.casos.cumsum(), c='green')
plt.title(name)
plt.xlabel("Semana")
plt.ylabel("Acumulado de Casos normalizados")
plt.show()
# https://machinelearningmastery.com/gentle-introduction-autocorrelation-partial-autocorrelation/
plot_acf(detrended, lags=52)
# https://www.statsmodels.org/dev/generated/statsmodels.tsa.stattools.acf.html
plt.title(name)
plt.xlabel("Retraso en semanas")
plt.ylabel('Correlación')
plt.show()
temp = [a, b]
# https://stackoverflow.com/a/3748071
temp.extend(acf(detrended, nlags=52))
temp.append(name)
ciesF.append(temp)
temp2 = list(group.casos)
#temp2.append(name)
ciesTSt.append(temp2)y = f(x) = 4.2687498879775535e-11 x + -5.61276490864389e-09
error 2.0113605583063735e-11
p = 0.03438325581830106
pendiente significativa
R^2 0.010390302941758996
y = f(x) = -1.7653075450894884e-06 x + 0.0019754909758688734
error 1.215881678974069e-07
p = 1.0774404716157897e-37
pendiente significativa
R^2 0.3765563116502911
y = f(x) = -3.0752338979568535e-09 x + 1.2904965711605356e-05
error 8.36749265385657e-10
p = 0.0002687345236732541
pendiente significativa
R^2 0.03144815483703095
y = f(x) = -1.0785666679174943e-08 x + 6.155839207125693e-06
error 3.564598970127455e-10
p = 3.9269145731807006e-112
pendiente significativa
R^2 0.6622135065357393
y = f(x) = -9.213574424729245e-09 x + 1.2957954379028175e-05
error 6.75300549213463e-10
p = 4.863591366039641e-36
pendiente significativa
R^2 0.2798612445705242
y = f(x) = -3.831012274635742e-09 x + 4.559110665311131e-06
error 2.056660576324692e-10
p = 2.1083769747172313e-58
pendiente significativa
R^2 0.4247090552255535
y = f(x) = -1.4627725963638185e-11 x + 4.5153183905681134e-08
error 8.6165080095987e-12
p = 0.09023493838847157
pendiente no significativa
R^2 0.006068835261027791
y = f(x) = -1.7642681104091792e-10 x + 6.894953499860091e-07
error 6.403728082254567e-11
p = 0.0061121040534305735
pendiente significativa
R^2 0.01699628644380042
y = f(x) = 3.8938781393720075e-11 x + 4.4324399670136904e-08
error 2.301537019363991e-11
p = 0.09131901816285937
pendiente no significativa
R^2 0.00590350974760678
y = f(x) = 2.3434709729609935e-13 x + -3.6003147872535345e-11
error 1.478629682740248e-13
p = 0.1136746875979033
pendiente no significativa
R^2 0.005407586602284264
y = f(x) = -3.4234098194666664e-11 x + 1.8622107713377432e-08
error 7.415007265413988e-12
p = 4.945787391949576e-06
pendiente significativa
R^2 0.040422588588555235
y = f(x) = 2.725400812299939e-10 x + 1.9471946148640167e-08
error 7.110945660238779e-11
p = 0.00014458146666075644
pendiente significativa
R^2 0.031274848966871695
y = f(x) = -4.255464112013022e-09 x + 2.7470903702510135e-06
error 3.3548559373967543e-10
p = 6.366969283108536e-32
pendiente significativa
R^2 0.25462455709847065
y = f(x) = -1.0744562226275755e-10 x + 5.3269706349552e-08
error 6.010845348981309e-11
p = 0.07452781641973526
pendiente no significativa
R^2 0.007081769917450651
y = f(x) = -4.51442956629053e-11 x + 5.003109663849265e-08
error 8.825884482273087e-12
p = 4.625709147491021e-07
pendiente significativa
R^2 0.05414963353204715
y = f(x) = -2.8757621426513095e-09 x + 8.65805695809489e-06
error 2.5195362618720955e-09
p = 0.25425697912167106
pendiente no significativa
R^2 0.002603944949826924
y = f(x) = -1.4644681914017878e-07 x + 0.00011211051217541277
error 1.1228826202874234e-08
p = 2.0750705342062423e-33
pendiente significativa
R^2 0.2653193213169377
y = f(x) = -2.722125710622442e-10 x + 1.262294141156984e-07
error 1.588658069624221e-11
p = 7.30165010543899e-51
pendiente significativa
R^2 0.3985877970692943
y = f(x) = -7.433434732564669e-09 x + 6.901511580636186e-06
error 4.809110869935852e-10
p = 3.1523565347787724e-42
pendiente significativa
R^2 0.3841635208468614
y = f(x) = -1.2411343091809244e-10 x + 2.1160165305354125e-07
error 2.468137006599137e-11
p = 7.217507598355145e-07
pendiente significativa
R^2 0.05458192227303572
y = f(x) = 4.306189172696877e-11 x + 4.5311776302657916e-07
error 4.983732447188263e-11
p = 0.3880813876059074
pendiente no significativa
R^2 0.0018723188046217538
y = f(x) = -9.851452950958728e-10 x + 1.4372871687382767e-06
error 2.0422528814979408e-10
p = 2.004159852045715e-06
pendiente significativa
R^2 0.05484537751521497
y = f(x) = -4.5977874526241305e-09 x + 2.970356116391645e-06
error 1.2200834000344058e-10
p = 5.731116914266081e-137
pendiente significativa
R^2 0.7713322815069262
y = f(x) = -3.141197049928086e-08 x + 0.00011159382796415527
error 1.555599789385595e-08
p = 0.04432369209037648
pendiente significativa
R^2 0.013065683803978847
y = f(x) = -1.0673850709576887e-11 x + 4.355250762325799e-09
error 3.1880871555405942e-12
p = 0.0008764994132686745
pendiente significativa
R^2 0.02236467960180641
y = f(x) = -1.1834633525276088e-09 x + 7.100912129285122e-07
error 9.393463801467669e-11
p = 1.2559331815198554e-31
pendiente significativa
R^2 0.24928894104283042
y = f(x) = -2.6544241562890327e-10 x + 3.2049521522763566e-07
error 3.7319118941308474e-11
p = 4.610321182741757e-12
pendiente significativa
R^2 0.10270484494415096
y = f(x) = -4.556172046800565e-10 x + 3.7500114147077754e-07
error 3.423510008372152e-11
p = 1.8548314561638924e-34
pendiente significativa
R^2 0.27626166419878756
y = f(x) = -6.932314608726674e-06 x + 0.008805967823835786
error 6.162044690299544e-07
p = 7.503334430143699e-26
pendiente significativa
R^2 0.23113873276962404
y = f(x) = -4.3876585629436324e-08 x + 5.08928603405923e-05
error 4.181979380800392e-09
p = 2.3727736779313174e-23
pendiente significativa
R^2 0.1846709286259034
y = f(x) = 3.0607452607643954e-14 x + 8.632235917582137e-10
error 1.081125720208934e-12
p = 0.977427221531179
pendiente no significativa
R^2 1.8298987789071008e-06
y = f(x) = -7.142618310354189e-10 x + 1.178302593061399e-06
error 1.457944295445013e-10
p = 1.332329783777257e-06
pendiente significativa
R^2 0.04918267323938655
y = f(x) = -1.3158987800860395e-08 x + 1.643445025799908e-05
error 1.6084785128648306e-09
p = 1.0885896084621633e-14
pendiente significativa
R^2 0.19747207526346663
y = f(x) = -5.001283641779608e-08 x + 8.79623291848092e-05
error 5.714736801137942e-09
p = 3.9731738436330694e-17
pendiente significativa
R^2 0.14220420601744926
y = f(x) = -8.130421944150189e-10 x + 1.4827816461880552e-06
error 5.134961166576471e-10
p = 0.11399979312553642
pendiente no significativa
R^2 0.005185003922499099
y = f(x) = -2.3438815029578847e-11 x + 1.5962437413039917e-07
error 5.628337741371575e-11
p = 0.6772793134611802
pendiente no significativa
R^2 0.00037523732655554817
y = f(x) = -5.193298199318447e-08 x + 4.533358442590547e-05
error 1.6692637054937939e-09
p = 1.6078008523125964e-114
pendiente significativa
R^2 0.6811910446622308
y = f(x) = -9.132331371853938e-10 x + 1.3202325787207294e-06
error 1.431149104840528e-10
p = 4.359158383428425e-10
pendiente significativa
R^2 0.08264080526994147
y = f(x) = 3.638834463785146e-10 x + 1.1174278631513553e-06
error 1.1201987356227443e-10
p = 0.001257639893824037
pendiente significativa
R^2 0.025453964627936122
for name, group in cieG:
# https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.detrend.html
detrended = signal.detrend(group.casos)
a, b, r, p, e = stats.linregress(group['sem'], group.casos)
print("y = f(x) = {} x + {}".format(a, b))
print("error", e)
print("p = ", p)
print("pendiente {:s}significativa".format("no " if p >= 0.05 else ""))
print("R^2", r**2)
plt.figure(figsize=(12, 2))
plt.plot(group['sem'], group.casos)
plt.plot(group['sem'], detrended, c='black')
plt.plot(group['sem'], (a * group['sem'] + b), label = 'y = {:.1f}x + {:.0f}'.format(a, b), color = 'red', linewidth = 3)
plt.title(name)
plt.xlabel("Semana")
plt.ylabel("Casos normalizados")
plt.show()
# https://stackoverflow.com/questions/48497756/time-series-distance-metric
plt.figure(figsize=(12, 2))
# https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.cumsum.html
plt.plot(group['sem'], group.casos.cumsum(), c='green')
plt.title(name)
plt.xlabel("Semana")
plt.ylabel("Acumulado de Casos normalizados")
plt.show()
plt.figure()
# https://machinelearningmastery.com/gentle-introduction-autocorrelation-partial-autocorrelation/
plot_acf(detrended, lags=52)
# https://www.statsmodels.org/dev/generated/statsmodels.tsa.stattools.acf.html
plt.title(name)
plt.xlabel("Retraso en semanas")
plt.ylabel('Correlación')
plt.show()y = f(x) = -2.3224356070873255e-07 x + 0.00018642953885186607
error 2.458069138569354e-08
p = 4.2189376399252386e-21
pendiente significativa
R^2 0.008834750473414046
<Figure size 432x288 with 0 Axes>
y = f(x) = -1.9503026794867653e-08 x + 2.1003475197080275e-05
error 2.9914826904487065e-09
p = 7.747452841909533e-11
pendiente significativa
R^2 0.008415817644051377
<Figure size 432x288 with 0 Axes>
y = f(x) = -7.687412126573934e-08 x + 6.301895314999713e-05
error 1.1457310486128478e-07
p = 0.5026730466383222
pendiente no significativa
R^2 0.0012420716051614582
<Figure size 432x288 with 0 Axes>
y = f(x) = 4.324626671299835e-10 x + 2.04941342972253e-07
error 7.239655510808932e-11
p = 4.1887790791163235e-09
pendiente significativa
R^2 0.06134442012808605
<Figure size 432x288 with 0 Axes>
y = f(x) = 6.114012516943938e-08 x + -9.37021948204884e-06
error 5.454249521195378e-09
p = 7.943541732517958e-27
pendiente significativa
R^2 0.1593291079485521
<Figure size 432x288 with 0 Axes>
y = f(x) = -5.4762876304630354e-06 x + 0.004047543918036931
error 6.313606290646645e-07
p = 1.2891385768087959e-17
pendiente significativa
R^2 0.057202405083796086
<Figure size 432x288 with 0 Axes>
y = f(x) = 3.0607452607643954e-14 x + 8.632235917582137e-10
error 1.081125720208934e-12
p = 0.977427221531179
pendiente no significativa
R^2 1.8298987789071008e-06
<Figure size 432x288 with 0 Axes>
y = f(x) = -4.552145867367468e-08 x + 4.150055938885172e-05
error 5.28039387715845e-09
p = 1.7027198403366345e-17
pendiente significativa
R^2 0.04850098103773122
<Figure size 432x288 with 0 Axes>
y = f(x) = -5.496981234999186e-10 x + 8.572895488021172e-07
error 2.657552949170129e-10
p = 0.038856309457124164
pendiente significativa
R^2 0.004272969521096534
<Figure size 432x288 with 0 Axes>
y = f(x) = -3.11383856620073e-08 x + 3.0350821580836582e-05
error 3.4613396780786333e-09
p = 2.313921331364859e-18
pendiente significativa
R^2 0.10649538120403663
<Figure size 432x288 with 0 Axes>
y = f(x) = -9.132331371853938e-10 x + 1.3202325787207294e-06
error 1.431149104840528e-10
p = 4.359158383428425e-10
pendiente significativa
R^2 0.08264080526994147
<Figure size 432x288 with 0 Axes>
y = f(x) = 3.638834463785146e-10 x + 1.1174278631513553e-06
error 1.1201987356227443e-10
p = 0.001257639893824037
pendiente significativa
R^2 0.025453964627936122
<Figure size 432x288 with 0 Axes>
Se extraen las características de cada CIE en tanto serie de tiempo. A saber, su pendiente, ordenada en el origen y las autocorrelaciones con retraso de 1 a 52 semanas (eliminando el retraso de 0 semanas)
ciesF = pd.DataFrame(ciesF)
# https://stackoverflow.com/a/11346337
colNames = ['m', 'b']
for i in range (53):
colNames.append('ac' + str(i))
colNames.append('cie')
ciesF.columns = colNames
ciesF = ciesF.drop(['ac0'], axis=1)
ciesF.sort_values(by=['m'], ascending=False)
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| m | b | ac1 | ac2 | ac3 | ac4 | ac5 | ac6 | ac7 | ac8 | ... | ac44 | ac45 | ac46 | ac47 | ac48 | ac49 | ac50 | ac51 | ac52 | cie | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 38 | 3.638834e-10 | 1.117428e-06 | 0.497210 | 0.371337 | 0.338770 | 0.295026 | 0.246889 | 0.170797 | 0.177532 | 0.174927 | ... | 0.095734 | 0.079953 | 0.094433 | 0.045073 | 0.020609 | 0.002565 | -0.025604 | 0.001100 | 0.014393 | z21 |
| 11 | 2.725401e-10 | 1.947195e-08 | 0.089659 | -0.019229 | -0.025867 | -0.002608 | -0.028985 | -0.001130 | -0.058919 | -0.019433 | ... | -0.034949 | -0.062431 | -0.002219 | 0.029734 | 0.005434 | -0.050439 | 0.078625 | 0.029168 | -0.002898 | a37 |
| 20 | 4.306189e-11 | 4.531178e-07 | 0.299805 | 0.225857 | 0.068495 | 0.057942 | 0.001655 | 0.017533 | 0.033656 | 0.100137 | ... | 0.050684 | 0.016318 | 0.061034 | 0.053793 | 0.021663 | 0.059753 | -0.005982 | 0.033164 | -0.047455 | b17.1 |
| 0 | 4.268750e-11 | -5.612765e-09 | 0.393749 | 0.122484 | 0.010328 | 0.026661 | 0.015698 | 0.021141 | -0.002905 | -0.010120 | ... | -0.017536 | -0.017607 | -0.017679 | -0.017751 | -0.017822 | -0.017893 | -0.017965 | -0.018036 | -0.018107 | a00 |
| 8 | 3.893878e-11 | 4.432440e-08 | 0.393243 | 0.260146 | 0.044702 | 0.032172 | 0.012605 | 0.025166 | 0.014480 | 0.009281 | ... | -0.017366 | 0.067969 | 0.005142 | 0.003701 | -0.020010 | 0.007456 | 0.042142 | 0.077540 | 0.090818 | a27 |
| 9 | 2.343471e-13 | -3.600315e-11 | -0.007522 | -0.007561 | -0.007600 | -0.007639 | -0.007678 | -0.007717 | -0.007756 | -0.007795 | ... | -0.000592 | -0.000605 | -0.000618 | -0.000631 | -0.000644 | -0.000657 | -0.000670 | -0.000683 | -0.000696 | a33 |
| 30 | 3.060745e-14 | 8.632236e-10 | 0.055952 | 0.062823 | 0.076371 | 0.006623 | 0.030863 | -0.037294 | -0.060305 | 0.059805 | ... | -0.057127 | -0.057262 | -0.035717 | -0.035852 | -0.057666 | -0.057801 | -0.057936 | -0.058070 | -0.058205 | p35.0 |
| 24 | -1.067385e-11 | 4.355251e-09 | 0.077117 | 0.322187 | 0.046591 | 0.036037 | -0.023600 | 0.020128 | -0.018800 | -0.026529 | ... | -0.023442 | 0.017590 | -0.018073 | -0.018183 | -0.023882 | 0.032515 | -0.001876 | 0.011733 | 0.004771 | b50 |
| 6 | -1.462773e-11 | 4.515318e-08 | 0.085993 | 0.048897 | 0.064574 | 0.118768 | -0.023565 | -0.026439 | 0.023959 | -0.036252 | ... | 0.064103 | 0.019108 | -0.021642 | -0.019077 | 0.015544 | 0.031099 | -0.056185 | -0.073401 | -0.004459 | a17.0 |
| 35 | -2.343882e-11 | 1.596244e-07 | 0.550097 | 0.512561 | 0.454005 | 0.411662 | 0.363330 | 0.254477 | 0.225435 | 0.181761 | ... | -0.032387 | -0.007867 | 0.004137 | -0.020714 | 0.015187 | -0.003246 | 0.008389 | 0.020997 | 0.018492 | u98 |
| 10 | -3.423410e-11 | 1.862211e-08 | -0.081445 | 0.057375 | -0.049496 | 0.012841 | 0.056102 | -0.020204 | -0.009801 | -0.032175 | ... | -0.005745 | 0.005151 | -0.043027 | 0.056617 | -0.031916 | 0.114628 | -0.035333 | 0.052850 | -0.016788 | a34 |
| 14 | -4.514430e-11 | 5.003110e-08 | 0.076912 | 0.149122 | 0.088945 | 0.072881 | 0.114257 | 0.074084 | 0.108017 | 0.108573 | ... | 0.036326 | 0.015114 | 0.051616 | 0.032731 | -0.039804 | 0.002215 | 0.025619 | 0.016111 | -0.024214 | a50 |
| 13 | -1.074456e-10 | 5.326971e-08 | 0.003941 | -0.012528 | -0.008077 | -0.013007 | -0.007537 | -0.016467 | 0.003030 | -0.001938 | ... | -0.011364 | -0.003043 | -0.003882 | 0.012084 | 0.000458 | -0.001701 | 0.007212 | -0.004964 | -0.004440 | a39.0 |
| 19 | -1.241134e-10 | 2.116017e-07 | 0.289203 | 0.226359 | 0.276856 | 0.274657 | 0.253692 | 0.247411 | 0.247509 | 0.206441 | ... | 0.021663 | 0.093129 | 0.023837 | 0.146601 | 0.018644 | 0.036760 | 0.043459 | -0.015475 | -0.004356 | b16 |
| 7 | -1.764268e-10 | 6.894953e-07 | 0.522652 | 0.363609 | 0.361372 | 0.385651 | 0.326709 | 0.325553 | 0.318398 | 0.252245 | ... | 0.196099 | 0.182101 | 0.163183 | 0.167669 | 0.235813 | 0.206676 | 0.215066 | 0.167751 | 0.183912 | a23 |
| 26 | -2.654424e-10 | 3.204952e-07 | 0.110847 | 0.069672 | 0.107836 | 0.080559 | 0.128797 | -0.027006 | 0.042914 | -0.009807 | ... | 0.029668 | 0.076565 | 0.089312 | 0.024519 | 0.008848 | 0.059614 | 0.099755 | 0.046717 | -0.020862 | g00-g03 |
| 17 | -2.722126e-10 | 1.262294e-07 | 0.488103 | 0.474707 | 0.426456 | 0.414057 | 0.317635 | 0.304248 | 0.261418 | 0.248762 | ... | 0.072010 | 0.087184 | 0.117220 | 0.163608 | 0.087383 | 0.129308 | 0.128205 | 0.131949 | 0.139945 | b06 |
| 27 | -4.556172e-10 | 3.750011e-07 | 0.232941 | 0.165279 | 0.155966 | 0.155952 | 0.159776 | 0.110074 | 0.261158 | 0.168664 | ... | 0.016427 | 0.004149 | -0.044051 | 0.007307 | -0.018886 | -0.029089 | 0.021237 | 0.039481 | 0.027578 | i00-i02 |
| 31 | -7.142618e-10 | 1.178303e-06 | 0.791010 | 0.750958 | 0.691090 | 0.610929 | 0.512450 | 0.434146 | 0.366592 | 0.258712 | ... | 0.341533 | 0.408299 | 0.435233 | 0.469282 | 0.511489 | 0.522807 | 0.498786 | 0.480615 | 0.470837 | t60 |
| 34 | -8.130422e-10 | 1.482782e-06 | 0.026306 | 0.067629 | 0.068971 | 0.106583 | 0.028512 | 0.007521 | 0.073457 | -0.032228 | ... | 0.055582 | 0.128333 | 0.022517 | 0.066484 | 0.006181 | 0.028253 | 0.168174 | 0.105951 | 0.083272 | u97 |
| 37 | -9.132331e-10 | 1.320233e-06 | 0.826727 | 0.781848 | 0.727522 | 0.675235 | 0.624828 | 0.550919 | 0.484088 | 0.401629 | ... | 0.459125 | 0.506974 | 0.547571 | 0.601010 | 0.631255 | 0.670476 | 0.649844 | 0.640989 | 0.621946 | x20 |
| 21 | -9.851453e-10 | 1.437287e-06 | 0.149215 | 0.272471 | 0.152501 | 0.089044 | 0.100963 | 0.106820 | 0.087191 | -0.016662 | ... | 0.075923 | 0.128809 | 0.068058 | 0.029803 | 0.013137 | -0.020469 | -0.029275 | -0.055377 | -0.035842 | b20-b24 |
| 25 | -1.183463e-09 | 7.100912e-07 | 0.388003 | 0.416624 | 0.313638 | 0.387392 | 0.284052 | 0.250379 | 0.164883 | 0.231499 | ... | 0.188028 | 0.150510 | 0.140413 | 0.147020 | 0.207482 | 0.171138 | 0.209809 | 0.209396 | 0.200214 | b51 |
| 15 | -2.875762e-09 | 8.658057e-06 | 0.895262 | 0.842421 | 0.792705 | 0.707147 | 0.622664 | 0.527720 | 0.432752 | 0.356828 | ... | 0.243528 | 0.298282 | 0.370211 | 0.423460 | 0.466082 | 0.511227 | 0.539638 | 0.552434 | 0.540235 | a90 |
| 2 | -3.075234e-09 | 1.290497e-05 | 0.667701 | 0.505751 | 0.436771 | 0.352219 | 0.289719 | 0.228429 | 0.172198 | 0.107678 | ... | 0.223528 | 0.189754 | 0.185963 | 0.183744 | 0.179380 | 0.151920 | 0.143924 | 0.134758 | 0.057089 | a01.0 |
| 5 | -3.831012e-09 | 4.559111e-06 | 0.380632 | 0.195406 | 0.107774 | 0.091505 | 0.073293 | 0.073178 | 0.027202 | 0.086867 | ... | 0.121356 | 0.134870 | 0.096912 | 0.037600 | 0.126218 | 0.126044 | 0.177925 | 0.161334 | 0.038959 | a15-a16 |
| 12 | -4.255464e-09 | 2.747090e-06 | 0.140500 | 0.121196 | 0.127669 | 0.099854 | 0.073198 | 0.027292 | -0.002968 | -0.016134 | ... | 0.035622 | 0.029450 | 0.045802 | 0.047865 | 0.060802 | 0.095082 | 0.062623 | 0.058167 | 0.053912 | a38 |
| 22 | -4.597787e-09 | 2.970356e-06 | 0.564047 | 0.398251 | 0.335638 | 0.284887 | 0.179178 | 0.078869 | 0.009511 | -0.045524 | ... | 0.070795 | 0.069166 | 0.100421 | 0.164831 | 0.185766 | 0.150027 | 0.154843 | 0.220636 | 0.151552 | b26 |
| 18 | -7.433435e-09 | 6.901512e-06 | 0.765747 | 0.587239 | 0.516973 | 0.418962 | 0.348350 | 0.239331 | 0.135074 | 0.112791 | ... | 0.326428 | 0.312633 | 0.307638 | 0.296214 | 0.237261 | 0.190637 | 0.124537 | 0.059086 | 0.007564 | b15 |
| 4 | -9.213574e-09 | 1.295795e-05 | 0.605797 | 0.479571 | 0.410353 | 0.367218 | 0.341321 | 0.311389 | 0.234742 | 0.219977 | ... | 0.255961 | 0.229158 | 0.221748 | 0.178246 | 0.191535 | 0.225850 | 0.294085 | 0.313643 | 0.295370 | a05 |
| 3 | -1.078567e-08 | 6.155839e-06 | 0.620012 | 0.595386 | 0.535631 | 0.462663 | 0.438088 | 0.373148 | 0.289653 | 0.300332 | ... | 0.178095 | 0.234208 | 0.255625 | 0.278374 | 0.284554 | 0.274991 | 0.301086 | 0.266200 | 0.231869 | a03 |
| 32 | -1.315899e-08 | 1.643445e-05 | 0.903920 | 0.826842 | 0.732156 | 0.614444 | 0.497397 | 0.376862 | 0.268490 | 0.160477 | ... | 0.183030 | 0.131180 | 0.085666 | 0.037463 | -0.008971 | -0.066770 | -0.114970 | -0.152466 | -0.191697 | t63 excepto t63.2 |
| 23 | -3.141197e-08 | 1.115938e-04 | 0.767118 | 0.547797 | 0.395471 | 0.291686 | 0.210417 | 0.128438 | 0.081658 | 0.051735 | ... | -0.017768 | -0.024711 | -0.028894 | -0.060319 | -0.058954 | -0.048837 | -0.020363 | -0.004847 | -0.005577 | b30 |
| 29 | -4.387659e-08 | 5.089286e-05 | 0.927733 | 0.858740 | 0.790416 | 0.727838 | 0.637424 | 0.545003 | 0.449916 | 0.365855 | ... | 0.569450 | 0.607758 | 0.624284 | 0.633800 | 0.647336 | 0.649295 | 0.625177 | 0.589587 | 0.547403 | j12 |
| 33 | -5.001284e-08 | 8.796233e-05 | 0.881185 | 0.793629 | 0.694008 | 0.596382 | 0.456681 | 0.319222 | 0.189304 | 0.062305 | ... | 0.314212 | 0.388623 | 0.451051 | 0.497185 | 0.527848 | 0.531338 | 0.510950 | 0.475725 | 0.426713 | t63.2 |
| 36 | -5.193298e-08 | 4.533358e-05 | 0.844756 | 0.768593 | 0.723830 | 0.666654 | 0.614451 | 0.564508 | 0.510689 | 0.441227 | ... | 0.355990 | 0.405624 | 0.456501 | 0.503929 | 0.521726 | 0.555444 | 0.542070 | 0.525043 | 0.500933 | w54 |
| 16 | -1.464468e-07 | 1.121105e-04 | 0.946239 | 0.892301 | 0.837622 | 0.778140 | 0.711102 | 0.629254 | 0.536098 | 0.431731 | ... | 0.530872 | 0.565769 | 0.593141 | 0.613168 | 0.623759 | 0.618582 | 0.598455 | 0.570398 | 0.530427 | b01 |
| 1 | -1.765308e-06 | 1.975491e-03 | 0.831565 | 0.690654 | 0.594390 | 0.516446 | 0.437316 | 0.326857 | 0.221760 | 0.104962 | ... | 0.289442 | 0.214354 | 0.137897 | 0.059001 | -0.016753 | -0.061065 | -0.108941 | -0.158795 | -0.225823 | a01-a03 |
| 28 | -6.932315e-06 | 8.805968e-03 | 0.853479 | 0.727355 | 0.620092 | 0.535945 | 0.445607 | 0.349639 | 0.267460 | 0.175938 | ... | 0.200076 | 0.214129 | 0.232129 | 0.213833 | 0.204222 | 0.194258 | 0.186803 | 0.151652 | 0.122209 | j00-j06 |
39 rows × 55 columns
Se agrupan las CIEs por casos dados en una semana, como series de tiempo.
ciesTS = pd.DataFrame(ciesTSt)
t = list(cie.groups.keys())
t.remove('a92.3')
ciesTS['cie'] = t
ciesTS.sample(3)
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| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... | 499 | 500 | 501 | 502 | 503 | 504 | 505 | 506 | 507 | cie | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 12 | 3.413076e-06 | 2.295700e-06 | 2.031593e-06 | 2.620755e-06 | 3.331812e-06 | 3.372444e-06 | 3.331812e-06 | 4.347608e-06 | 3.392760e-06 | 3.453708e-06 | ... | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | a38 |
| 20 | 4.875822e-07 | 5.078982e-07 | 4.063185e-07 | 4.266345e-07 | 4.266345e-07 | 6.297937e-07 | 4.875822e-07 | 6.501096e-07 | 3.656867e-07 | 3.453708e-07 | ... | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | b17.1 |
| 25 | 7.110574e-07 | 7.110574e-07 | 1.015796e-07 | 9.548485e-07 | 1.422115e-07 | 3.047389e-07 | 2.031593e-07 | 2.641070e-07 | 5.891619e-07 | 1.828433e-07 | ... | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | b51 |
3 rows × 509 columns
Una vez eliminada la tendencia se puede comprobar que las series de tiempo para cada enfermedad son estacionales
from statsmodels.tsa.stattools import adfuller
def test_stationarity(timeseries, w, name):
#Determing rolling statistics
rolmean = timeseries.rolling(w).mean()
rolstd = timeseries.rolling(w).std()
#Plot rolling statistics:
orig = plt.plot(timeseries,label='Original')
mean = plt.plot(rolmean, color='red', label='Rolling Mean')
std = plt.plot(rolstd, color='black', label = 'Rolling Std')
plt.legend(loc='best')
plt.title(name)
plt.show(block=False)
#Perform Dickey-Fuller test:
print('Results of Dickey-Fuller Test:')
dftest = adfuller(timeseries, autolag='AIC')
dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])
for key,value in dftest[4].items():
dfoutput['Critical Value (%s)'%key] = value
print(dfoutput)
for i in range(len(ciesTS)):
temp = ciesTS.iloc[i, : 508]
temp.dropna(inplace=True)
test_stationarity(temp, 52, ciesTS.iloc[i, -1])
Results of Dickey-Fuller Test:
Test Statistic -1.356054e+01
p-value 2.314720e-25
#Lags Used 0.000000e+00
Number of Observations Used 4.300000e+02
Critical Value (1%) -3.445649e+00
Critical Value (5%) -2.868285e+00
Critical Value (10%) -2.570363e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -3.424746
p-value 0.010144
#Lags Used 2.000000
Number of Observations Used 348.000000
Critical Value (1%) -3.449282
Critical Value (5%) -2.869881
Critical Value (10%) -2.571214
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -5.719534e+00
p-value 6.993272e-07
#Lags Used 2.000000e+00
Number of Observations Used 4.150000e+02
Critical Value (1%) -3.446206e+00
Critical Value (5%) -2.868530e+00
Critical Value (10%) -2.570493e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -2.106851
p-value 0.241769
#Lags Used 7.000000
Number of Observations Used 461.000000
Critical Value (1%) -3.444615
Critical Value (5%) -2.867830
Critical Value (10%) -2.570120
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -3.760647
p-value 0.003337
#Lags Used 4.000000
Number of Observations Used 476.000000
Critical Value (1%) -3.444163
Critical Value (5%) -2.867631
Critical Value (10%) -2.570014
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -2.133072
p-value 0.231426
#Lags Used 10.000000
Number of Observations Used 461.000000
Critical Value (1%) -3.444615
Critical Value (5%) -2.867830
Critical Value (10%) -2.570120
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -8.720275e+00
p-value 3.400303e-14
#Lags Used 3.000000e+00
Number of Observations Used 4.700000e+02
Critical Value (1%) -3.444340e+00
Critical Value (5%) -2.867709e+00
Critical Value (10%) -2.570056e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -4.078834
p-value 0.001050
#Lags Used 5.000000
Number of Observations Used 435.000000
Critical Value (1%) -3.445473
Critical Value (5%) -2.868207
Critical Value (10%) -2.570321
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -1.063365e+01
p-value 5.137862e-19
#Lags Used 2.000000e+00
Number of Observations Used 4.810000e+02
Critical Value (1%) -3.444018e+00
Critical Value (5%) -2.867568e+00
Critical Value (10%) -2.569980e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -21.517435
p-value 0.000000
#Lags Used 0.000000
Number of Observations Used 463.000000
Critical Value (1%) -3.444553
Critical Value (5%) -2.867803
Critical Value (10%) -2.570106
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -1.468685e+01
p-value 3.093388e-27
#Lags Used 1.000000e+00
Number of Observations Used 5.060000e+02
Critical Value (1%) -3.443340e+00
Critical Value (5%) -2.867269e+00
Critical Value (10%) -2.569821e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -3.809081
p-value 0.002816
#Lags Used 11.000000
Number of Observations Used 445.000000
Critical Value (1%) -3.445131
Critical Value (5%) -2.868057
Critical Value (10%) -2.570241
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -5.053787
p-value 0.000017
#Lags Used 4.000000
Number of Observations Used 468.000000
Critical Value (1%) -3.444400
Critical Value (5%) -2.867736
Critical Value (10%) -2.570070
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -20.908062
p-value 0.000000
#Lags Used 0.000000
Number of Observations Used 449.000000
Critical Value (1%) -3.444998
Critical Value (5%) -2.867999
Critical Value (10%) -2.570210
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -2.973026
p-value 0.037491
#Lags Used 11.000000
Number of Observations Used 447.000000
Critical Value (1%) -3.445064
Critical Value (5%) -2.868028
Critical Value (10%) -2.570226
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -5.304842
p-value 0.000005
#Lags Used 12.000000
Number of Observations Used 488.000000
Critical Value (1%) -3.443821
Critical Value (5%) -2.867481
Critical Value (10%) -2.569934
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -6.501620e+00
p-value 1.158034e-08
#Lags Used 9.000000e+00
Number of Observations Used 4.630000e+02
Critical Value (1%) -3.444553e+00
Critical Value (5%) -2.867803e+00
Critical Value (10%) -2.570106e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -1.996208
p-value 0.288238
#Lags Used 11.000000
Number of Observations Used 433.000000
Critical Value (1%) -3.445543
Critical Value (5%) -2.868238
Critical Value (10%) -2.570338
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -3.403355
p-value 0.010845
#Lags Used 8.000000
Number of Observations Used 376.000000
Critical Value (1%) -3.447862
Critical Value (5%) -2.869258
Critical Value (10%) -2.570881
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -3.818212
p-value 0.002726
#Lags Used 6.000000
Number of Observations Used 433.000000
Critical Value (1%) -3.445543
Critical Value (5%) -2.868238
Critical Value (10%) -2.570338
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -9.927614e+00
p-value 2.878961e-17
#Lags Used 1.000000e+00
Number of Observations Used 3.980000e+02
Critical Value (1%) -3.446888e+00
Critical Value (5%) -2.868829e+00
Critical Value (10%) -2.570653e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -7.628780e+00
p-value 2.034981e-11
#Lags Used 2.000000e+00
Number of Observations Used 4.000000e+02
Critical Value (1%) -3.446804e+00
Critical Value (5%) -2.868793e+00
Critical Value (10%) -2.570634e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -1.383949
p-value 0.589947
#Lags Used 14.000000
Number of Observations Used 408.000000
Critical Value (1%) -3.446480
Critical Value (5%) -2.868650
Critical Value (10%) -2.570557
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -6.469065e+00
p-value 1.381678e-08
#Lags Used 1.000000e+00
Number of Observations Used 3.080000e+02
Critical Value (1%) -3.451761e+00
Critical Value (5%) -2.870970e+00
Critical Value (10%) -2.571794e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -1.049502e+01
p-value 1.121338e-18
#Lags Used 1.000000e+00
Number of Observations Used 4.900000e+02
Critical Value (1%) -3.443766e+00
Critical Value (5%) -2.867457e+00
Critical Value (10%) -2.569921e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -3.050080
p-value 0.030475
#Lags Used 8.000000
Number of Observations Used 471.000000
Critical Value (1%) -3.444310
Critical Value (5%) -2.867696
Critical Value (10%) -2.570049
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -4.194474
p-value 0.000673
#Lags Used 8.000000
Number of Observations Used 435.000000
Critical Value (1%) -3.445473
Critical Value (5%) -2.868207
Critical Value (10%) -2.570321
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -5.300617
p-value 0.000005
#Lags Used 17.000000
Number of Observations Used 448.000000
Critical Value (1%) -3.445031
Critical Value (5%) -2.868013
Critical Value (10%) -2.570218
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -5.196448
p-value 0.000009
#Lags Used 0.000000
Number of Observations Used 422.000000
Critical Value (1%) -3.445941
Critical Value (5%) -2.868413
Critical Value (10%) -2.570431
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -6.052569e+00
p-value 1.267267e-07
#Lags Used 1.300000e+01
Number of Observations Used 4.740000e+02
Critical Value (1%) -3.444221e+00
Critical Value (5%) -2.867657e+00
Critical Value (10%) -2.570028e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -1.053776e+01
p-value 8.810400e-19
#Lags Used 2.000000e+00
Number of Observations Used 4.370000e+02
Critical Value (1%) -3.445403e+00
Critical Value (5%) -2.868177e+00
Critical Value (10%) -2.570305e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -5.316712
p-value 0.000005
#Lags Used 14.000000
Number of Observations Used 451.000000
Critical Value (1%) -3.444933
Critical Value (5%) -2.867970
Critical Value (10%) -2.570195
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -4.113528
p-value 0.000920
#Lags Used 4.000000
Number of Observations Used 269.000000
Critical Value (1%) -3.454896
Critical Value (5%) -2.872345
Critical Value (10%) -2.572528
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -4.874372
p-value 0.000039
#Lags Used 11.000000
Number of Observations Used 452.000000
Critical Value (1%) -3.444900
Critical Value (5%) -2.867956
Critical Value (10%) -2.570187
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -5.375052
p-value 0.000004
#Lags Used 8.000000
Number of Observations Used 474.000000
Critical Value (1%) -3.444221
Critical Value (5%) -2.867657
Critical Value (10%) -2.570028
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -5.342202
p-value 0.000004
#Lags Used 5.000000
Number of Observations Used 458.000000
Critical Value (1%) -3.444709
Critical Value (5%) -2.867871
Critical Value (10%) -2.570142
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -1.813468
p-value 0.373796
#Lags Used 2.000000
Number of Observations Used 452.000000
Critical Value (1%) -3.444900
Critical Value (5%) -2.867956
Critical Value (10%) -2.570187
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -6.673468e+00
p-value 4.526341e-09
#Lags Used 1.100000e+01
Number of Observations Used 4.420000e+02
Critical Value (1%) -3.445232e+00
Critical Value (5%) -2.868101e+00
Critical Value (10%) -2.570265e+00
dtype: float64
Results of Dickey-Fuller Test:
Test Statistic -6.644475e+00
p-value 5.308127e-09
#Lags Used 2.000000e+00
Number of Observations Used 4.030000e+02
Critical Value (1%) -3.446681e+00
Critical Value (5%) -2.868739e+00
Critical Value (10%) -2.570605e+00
dtype: float64
Por ello es posible pronosticarlas con el método de Holt-Winter
# https://www.analyticsvidhya.com/blog/2018/02/time-series-forecasting-methods/
# https://machinelearningmastery.com/time-series-forecasting-methods-in-python-cheat-sheet/
# https://towardsdatascience.com/time-series-in-python-exponential-smoothing-and-arima-processes-2c67f2a52788
from statsmodels.tsa.api import Holt, SimpleExpSmoothing, ExponentialSmoothing
pronosticos = []
real = []
for i in range(len(ciesTS)):
temp = ciesTS.iloc[i, : 508]
temp.dropna(inplace=True)
# https://medium.com/datadriveninvestor/how-to-build-exponential-smoothing-models-using-python-simple-exponential-smoothing-holt-and-da371189e1a1
# Train = 0.7
train = round(0.7 * len(temp))
f = ExponentialSmoothing(np.asarray(temp.iloc[0:train])).fit(smoothing_level = 0.1)
# https://stackoverflow.com/a/50786171
pred = f.predict(start=train + 1, end=len(temp))
fcast = f.forecast(len(temp) - train)
plt.figure(figsize=(12, 4))
plt.plot(temp)
plt.plot(f.fittedvalues, c='black')
plt.plot(range(train, len(temp)), fcast, c='red')
#plt.plot(range(train, len(temp)), pred, c='red')
plt.title(ciesTS.iloc[i, 508])
plt.legend(["Serie de tiempo", "Ajuste de Holt-Winter", "Pronóstico de Holt-Winter"])
plt.show()
# https://stackoverflow.com/a/15863028
real.append(temp.iloc[-1])
pronosticos.append(fcast[0])
Que presenta muy buen ajuste respecto a los datos reales
a, b, r, p, e = stats.linregress(real, pronosticos)
print("y = f(x) = {:.4f} x + {:.4f}".format(a, b))
print("error", e)
print("p = ", p)
print("pendiente {:s}significativa".format("no " if p >= 0.05 else ""))
print("R^2", r**2)
plt.title('Logaritmo del pronóstico', fontsize = 20)
plt.xlabel('Logaritmo del último caso normalizado')
plt.ylabel('Pronóstico')
plt.scatter(real, pronosticos)
plt.show()y = f(x) = 1.1122 x + 0.0000
error 0.019116083562680818
p = 5.559074078899032e-38
pendiente significativa
R^2 0.9891871972161727
Lo que se evidencia claramente al utilizar escala logarítmica en los datos
plt.title('Logaritmo del pronóstico', fontsize = 20)
plt.xlabel('Logaritmo del último caso normalizado')
plt.ylabel('Pronóstico')
plt.scatter(np.log(real), np.log(pronosticos))
plt.show()C:\Users\bena8\AppData\Local\Programs\Python\Python37-32\lib\site-packages\ipykernel_launcher.py:4: RuntimeWarning: divide by zero encountered in log
after removing the cwd from sys.path.
# https://machinelearningmastery.com/time-series-forecast-uncertainty-using-confidence-intervals-python/
# https://machinelearningmastery.com/make-sample-forecasts-arima-python/
from statsmodels.tsa.arima_model import ARIMA
def difference(dataset, interval=1):
diff = list()
for i in range(interval, len(dataset)):
value = dataset[i] - dataset[i - interval]
diff.append(value)
return pd.Series(diff)
for i in range(len(ciesTS)):
temp = ciesTS.iloc[i, : 508]
temp.dropna(inplace=True)
train = round(0.9 * len(temp))
ts = difference(np.asarray(temp), interval=len(temp) - train - 1)
m = ARIMA(ts, order=(3, 1, 0))
f = m.fit(trend = 'nc', disp = 0)
pred = f.predict(start=train + 1, end=len(temp))
tempDiff = temp - temp.shift()
plt.figure(figsize=(16, 4))
plt.plot(tempDiff)
plt.plot(f.fittedvalues, color='red')
plt.plot(range(train, len(temp)), pred, c='black')
plt.legend(['Diferencia', 'Valores ajustados de ARIMA', 'Pronóstico de ARIMA'])
plt.show()
