Predicción 1 paso adelante usando 12 retardos

Vamos a importar la bases de datos y a convertirlas en objetos de series de Tiempo. \(\{X_t\}\)

Code 
# get working directory
import os
os.getcwd()
'C:\\Users\\dofca\\Desktop\\series'
Code 
# librerias
import pandas as pd
import numpy as np
import matplotlib.pylab as plt
import sklearn
import openpyxl
from skforecast.ForecasterAutoreg import ForecasterAutoreg
import warnings
print(f"Matplotlib Version: {plt.__version__}")
print(f"Pandas Version: {pd.__version__}")
print(f"Numpy Version: {np.__version__}")
print(f"Sklearn: {sklearn.__version__}")
Matplotlib Version: 1.25.2
Pandas Version: 2.0.3
Numpy Version: 1.25.2
Sklearn: 1.3.1
Code 
# Lectura de la serie
data = pd.read_excel("datos/Exportaciones.xlsx",
                   header = 0, usecols = ['Mes','Total']).iloc[96:].reset_index(drop = True).round()
data['Total'] = data['Total'].astype(int) 
data
Mes Total
0 2000-01-01 1011676
1 2000-02-01 1054098
2 2000-03-01 1053546
3 2000-04-01 886359
4 2000-05-01 1146258
... ... ...
277 2023-02-01 4202234
278 2023-03-01 4431911
279 2023-04-01 3739214
280 2023-05-01 4497862
281 2023-06-01 3985981

282 rows × 2 columns

Code 
# tipo de datos
print(data.info())
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 282 entries, 0 to 281
Data columns (total 2 columns):
 #   Column  Non-Null Count  Dtype         
---  ------  --------------  -----         
 0   Mes     282 non-null    datetime64[ns]
 1   Total   282 non-null    int32         
dtypes: datetime64[ns](1), int32(1)
memory usage: 3.4 KB
None
Code 
#mirando los datos
#objeto ts
exportaciones = data['Total']
print(type(exportaciones))
plt.plot(exportaciones)
<class 'pandas.core.series.Series'>

Code 
print(f'Numero de filas con valores faltantes: {data.isnull().any(axis=1).mean()}')
Numero de filas con valores faltantes: 0.0
Code 
data.shape
(282, 2)

1 Árboles de decisión

1.0.1 Creación de los rezagos

Debido al análisis previo tomaremos los rezagos de 3 días atrás para poder predecir un paso adelante.

Code 
from pandas import DataFrame
# reframe as supervised learning
# lag observation (t-1) is the input variable and t is the output variable.
df1 = DataFrame() # original
print(df1)
df2 = DataFrame() #diferenciada
print(df2)
Empty DataFrame
Columns: []
Index: []
Empty DataFrame
Columns: []
Index: []
Code 
# arreglo de datos para el arreglo de rezagos Serie Original
indice = pd.date_range(start='1/1/2000', periods=282, freq='M')
print(indice)
originalDatadf = pd.DataFrame(data['Total'].values,index=indice)
print(originalDatadf)
DatetimeIndex(['2000-01-31', '2000-02-29', '2000-03-31', '2000-04-30',
               '2000-05-31', '2000-06-30', '2000-07-31', '2000-08-31',
               '2000-09-30', '2000-10-31',
               ...
               '2022-09-30', '2022-10-31', '2022-11-30', '2022-12-31',
               '2023-01-31', '2023-02-28', '2023-03-31', '2023-04-30',
               '2023-05-31', '2023-06-30'],
              dtype='datetime64[ns]', length=282, freq='M')
                  0
2000-01-31  1011676
2000-02-29  1054098
2000-03-31  1053546
2000-04-30   886359
2000-05-31  1146258
...             ...
2023-02-28  4202234
2023-03-31  4431911
2023-04-30  3739214
2023-05-31  4497862
2023-06-30  3985981

[282 rows x 1 columns]
Code 
# Rezagos original
for i in range(12,0,-1):
    df1[['t-'+str(i)]] = originalDatadf.shift(i)
print(df1)
                 t-12       t-11       t-10        t-9        t-8        t-7  \
2000-01-31        NaN        NaN        NaN        NaN        NaN        NaN   
2000-02-29        NaN        NaN        NaN        NaN        NaN        NaN   
2000-03-31        NaN        NaN        NaN        NaN        NaN        NaN   
2000-04-30        NaN        NaN        NaN        NaN        NaN        NaN   
2000-05-31        NaN        NaN        NaN        NaN        NaN        NaN   
...               ...        ...        ...        ...        ...        ...   
2023-02-28  4209198.0  4780210.0  5460531.0  4662521.0  5497617.0  5913682.0   
2023-03-31  4780210.0  5460531.0  4662521.0  5497617.0  5913682.0  4388737.0   
2023-04-30  5460531.0  4662521.0  5497617.0  5913682.0  4388737.0  4778520.0   
2023-05-31  4662521.0  5497617.0  5913682.0  4388737.0  4778520.0  4213182.0   
2023-06-30  5497617.0  5913682.0  4388737.0  4778520.0  4213182.0  4562248.0   

                  t-6        t-5        t-4        t-3        t-2        t-1  
2000-01-31        NaN        NaN        NaN        NaN        NaN        NaN  
2000-02-29        NaN        NaN        NaN        NaN        NaN  1011676.0  
2000-03-31        NaN        NaN        NaN        NaN  1011676.0  1054098.0  
2000-04-30        NaN        NaN        NaN  1011676.0  1054098.0  1053546.0  
2000-05-31        NaN        NaN  1011676.0  1054098.0  1053546.0   886359.0  
...               ...        ...        ...        ...        ...        ...  
2023-02-28  4388737.0  4778520.0  4213182.0  4562248.0  4642084.0  3696188.0  
2023-03-31  4778520.0  4213182.0  4562248.0  4642084.0  3696188.0  4202234.0  
2023-04-30  4213182.0  4562248.0  4642084.0  3696188.0  4202234.0  4431911.0  
2023-05-31  4562248.0  4642084.0  3696188.0  4202234.0  4431911.0  3739214.0  
2023-06-30  4642084.0  3696188.0  4202234.0  4431911.0  3739214.0  4497862.0  

[282 rows x 12 columns]
Code 
# Create column t original
df1['t'] = originalDatadf.values
print(df1.head(14))
                 t-12       t-11       t-10        t-9        t-8        t-7  \
2000-01-31        NaN        NaN        NaN        NaN        NaN        NaN   
2000-02-29        NaN        NaN        NaN        NaN        NaN        NaN   
2000-03-31        NaN        NaN        NaN        NaN        NaN        NaN   
2000-04-30        NaN        NaN        NaN        NaN        NaN        NaN   
2000-05-31        NaN        NaN        NaN        NaN        NaN        NaN   
2000-06-30        NaN        NaN        NaN        NaN        NaN        NaN   
2000-07-31        NaN        NaN        NaN        NaN        NaN        NaN   
2000-08-31        NaN        NaN        NaN        NaN        NaN  1011676.0   
2000-09-30        NaN        NaN        NaN        NaN  1011676.0  1054098.0   
2000-10-31        NaN        NaN        NaN  1011676.0  1054098.0  1053546.0   
2000-11-30        NaN        NaN  1011676.0  1054098.0  1053546.0   886359.0   
2000-12-31        NaN  1011676.0  1054098.0  1053546.0   886359.0  1146258.0   
2001-01-31  1011676.0  1054098.0  1053546.0   886359.0  1146258.0  1153956.0   
2001-02-28  1054098.0  1053546.0   886359.0  1146258.0  1153956.0  1104408.0   

                  t-6        t-5        t-4        t-3        t-2        t-1  \
2000-01-31        NaN        NaN        NaN        NaN        NaN        NaN   
2000-02-29        NaN        NaN        NaN        NaN        NaN  1011676.0   
2000-03-31        NaN        NaN        NaN        NaN  1011676.0  1054098.0   
2000-04-30        NaN        NaN        NaN  1011676.0  1054098.0  1053546.0   
2000-05-31        NaN        NaN  1011676.0  1054098.0  1053546.0   886359.0   
2000-06-30        NaN  1011676.0  1054098.0  1053546.0   886359.0  1146258.0   
2000-07-31  1011676.0  1054098.0  1053546.0   886359.0  1146258.0  1153956.0   
2000-08-31  1054098.0  1053546.0   886359.0  1146258.0  1153956.0  1104408.0   
2000-09-30  1053546.0   886359.0  1146258.0  1153956.0  1104408.0  1242391.0   
2000-10-31   886359.0  1146258.0  1153956.0  1104408.0  1242391.0  1102913.0   
2000-11-30  1146258.0  1153956.0  1104408.0  1242391.0  1102913.0   981716.0   
2000-12-31  1153956.0  1104408.0  1242391.0  1102913.0   981716.0  1192681.0   
2001-01-31  1104408.0  1242391.0  1102913.0   981716.0  1192681.0  1228398.0   
2001-02-28  1242391.0  1102913.0   981716.0  1192681.0  1228398.0  1017195.0   

                  t  
2000-01-31  1011676  
2000-02-29  1054098  
2000-03-31  1053546  
2000-04-30   886359  
2000-05-31  1146258  
2000-06-30  1153956  
2000-07-31  1104408  
2000-08-31  1242391  
2000-09-30  1102913  
2000-10-31   981716  
2000-11-30  1192681  
2000-12-31  1228398  
2001-01-31  1017195  
2001-02-28   964437
Code 
# Create a new subsetted dataframe, removing Nans from first 3 rows original
df1_Ori = df1[12:]
print(df1_Ori)
df1_Ori.size
                 t-12       t-11       t-10        t-9        t-8        t-7  \
2001-01-31  1011676.0  1054098.0  1053546.0   886359.0  1146258.0  1153956.0   
2001-02-28  1054098.0  1053546.0   886359.0  1146258.0  1153956.0  1104408.0   
2001-03-31  1053546.0   886359.0  1146258.0  1153956.0  1104408.0  1242391.0   
2001-04-30   886359.0  1146258.0  1153956.0  1104408.0  1242391.0  1102913.0   
2001-05-31  1146258.0  1153956.0  1104408.0  1242391.0  1102913.0   981716.0   
...               ...        ...        ...        ...        ...        ...   
2023-02-28  4209198.0  4780210.0  5460531.0  4662521.0  5497617.0  5913682.0   
2023-03-31  4780210.0  5460531.0  4662521.0  5497617.0  5913682.0  4388737.0   
2023-04-30  5460531.0  4662521.0  5497617.0  5913682.0  4388737.0  4778520.0   
2023-05-31  4662521.0  5497617.0  5913682.0  4388737.0  4778520.0  4213182.0   
2023-06-30  5497617.0  5913682.0  4388737.0  4778520.0  4213182.0  4562248.0   

                  t-6        t-5        t-4        t-3        t-2        t-1  \
2001-01-31  1104408.0  1242391.0  1102913.0   981716.0  1192681.0  1228398.0   
2001-02-28  1242391.0  1102913.0   981716.0  1192681.0  1228398.0  1017195.0   
2001-03-31  1102913.0   981716.0  1192681.0  1228398.0  1017195.0   964437.0   
2001-04-30   981716.0  1192681.0  1228398.0  1017195.0   964437.0  1002450.0   
2001-05-31  1192681.0  1228398.0  1017195.0   964437.0  1002450.0  1058457.0   
...               ...        ...        ...        ...        ...        ...   
2023-02-28  4388737.0  4778520.0  4213182.0  4562248.0  4642084.0  3696188.0   
2023-03-31  4778520.0  4213182.0  4562248.0  4642084.0  3696188.0  4202234.0   
2023-04-30  4213182.0  4562248.0  4642084.0  3696188.0  4202234.0  4431911.0   
2023-05-31  4562248.0  4642084.0  3696188.0  4202234.0  4431911.0  3739214.0   
2023-06-30  4642084.0  3696188.0  4202234.0  4431911.0  3739214.0  4497862.0   

                  t  
2001-01-31  1017195  
2001-02-28   964437  
2001-03-31  1002450  
2001-04-30  1058457  
2001-05-31  1068023  
...             ...  
2023-02-28  4202234  
2023-03-31  4431911  
2023-04-30  3739214  
2023-05-31  4497862  
2023-06-30  3985981  

[270 rows x 13 columns]
3510
Code 
# Split data Serie Original
Orig_Split = df1_Ori.values
# split into lagged variables and original time series
X1 = Orig_Split[:, 0:-1]  # slice all rows and start with column 0 and go up to but not including the last column
y1 = Orig_Split[:,-1]  # slice all rows and last column, essentially separating out 't' column
print(X1)
print('Respuestas \n',y1)
[[1011676. 1054098. 1053546. ...  981716. 1192681. 1228398.]
 [1054098. 1053546.  886359. ... 1192681. 1228398. 1017195.]
 [1053546.  886359. 1146258. ... 1228398. 1017195.  964437.]
 ...
 [5460531. 4662521. 5497617. ... 3696188. 4202234. 4431911.]
 [4662521. 5497617. 5913682. ... 4202234. 4431911. 3739214.]
 [5497617. 5913682. 4388737. ... 4431911. 3739214. 4497862.]]
Respuestas 
 [1017195.  964437. 1002450. 1058457. 1068023.  996736. 1005867. 1189605.
 1078781. 1013772.  965973.  968599.  943702.  945935.  859303. 1123902.
 1076509.  921463. 1040876.  915457. 1055414. 1070342.  966897. 1055590.
  923427. 1033043. 1034233. 1101056. 1181888.  995297. 1267598. 1092850.
 1079472. 1169195. 1082836. 1167628. 1183399. 1031826. 1206657. 1271618.
 1335727. 1433647. 1541103. 1516523. 1519458. 1529291. 1585709. 1633370.
 1378980. 1529265. 1722081. 1682450. 1737198. 2097853. 1653833. 1882740.
 1908016. 1788905. 1826199. 1938567. 1668171. 1862024. 1929864. 1872161.
 2211681. 2039364. 2141958. 2129881. 2104243. 2271572. 2146547. 2134504.
 1843668. 1914770. 2384657. 2497750. 2727980. 2114259. 2648147. 2621002.
 2523170. 2623649. 3152653. 3227536. 2842306. 2822470. 3007288. 3365420.
 3392615. 3675654. 3801685. 3294187. 3133994. 2981105. 2245379. 2224271.
 2525698. 2340118. 2711332. 2427571. 2742519. 2738083. 2898600. 2673470.
 2795983. 2948687. 2861294. 3182972. 2913433. 2869156. 3337903. 3490978.
 3513331. 3060628. 3157626. 3291236. 3271661. 3535759. 3426095. 3845531.
 3760176. 3958572. 4893312. 4823094. 5153710. 4708737. 4866229. 4941645.
 4582401. 4772996. 5147330. 5306738. 4785773. 4999318. 5712355. 5010929.
 5403375. 4563431. 4976905. 4570780. 4910403. 5432930. 4807338. 4951628.
 4849196. 4667767. 4617842. 4949487. 5332470. 4870839. 4652297. 4977706.
 4849996. 4837983. 4948665. 5272122. 4808832. 4271442. 4408181. 4316676.
 5495867. 4704814. 5048930. 4813091. 5077247. 4322278. 3794686. 3794711.
 2916976. 3160957. 3461944. 3219706. 3381084. 3217408. 3043778. 2868451.
 2898168. 2815522. 2444535. 2588994. 1919053. 2328723. 2334998. 2463793.
 2751470. 2780512. 2266997. 3044377. 2797686. 2770014. 2833622. 3477094.
 2785044. 2716024. 3300421. 2697992. 3505436. 2895612. 3125483. 3191598.
 3389679. 3277516. 3122237. 4014818. 3324889. 3027603. 3365116. 3786537.
 3719410. 3331933. 3632055. 3684399. 3512842. 3768666. 3343509. 3407819.
 3066110. 3183071. 3344850. 3862819. 3748342. 3096363. 3255830. 3264261.
 3067349. 3326497. 2943625. 3330051. 3419466. 2943626. 2439036. 1864239.
 2221172. 2289482. 2551988. 2584767. 2544874. 2644954. 2523372. 3028837.
 2610936. 2938994. 3383554. 2976372. 3096913. 3182216. 3444158. 3465143.
 3792236. 3799111. 4155805. 4544551. 3801609. 4209198. 4780210. 5460531.
 4662521. 5497617. 5913682. 4388737. 4778520. 4213182. 4562248. 4642084.
 3696188. 4202234. 4431911. 3739214. 4497862. 3985981.]

2 Árbol para Serie Original

2.0.0.1 Entrenamiento, Validación y prueba

Code 
Y1 = y1
print('Complete Observations for Target after Supervised configuration: %d' %len(Y1))
traintarget_size = int(len(Y1) * 0.70) 
valtarget_size = int(len(Y1) * 0.10)+1# Set split
testtarget_size = int(len(Y1) * 0.20)# Set split
print(traintarget_size,valtarget_size,testtarget_size)
print('Train + Validation + Test: %d' %(traintarget_size+valtarget_size+testtarget_size))
Complete Observations for Target after Supervised configuration: 270
189 28 54
Train + Validation + Test: 271
Code 
# Target Train-Validation-Test split(70-10-20)
train_target, val_target,test_target = Y1[0:traintarget_size], Y1[(traintarget_size):(traintarget_size+valtarget_size)],Y1[(traintarget_size+valtarget_size):len(Y1)]

print('Observations for Target: %d' % (len(Y1)))
print('Training Observations for Target: %d' % (len(train_target)))
print('Validation Observations for Target: %d' % (len(val_target)))
print('Test Observations for Target: %d' % (len(test_target)))
Observations for Target: 270
Training Observations for Target: 189
Validation Observations for Target: 28
Test Observations for Target: 53
Code 
# Features Train--Val-Test split

trainfeature_size = int(len(X1) * 0.70)
valfeature_size = int(len(X1) * 0.10)+1# Set split
testfeature_size = int(len(X1) * 0.20)# Set split
train_feature, val_feature,test_feature = X1[0:traintarget_size],X1[(traintarget_size):(traintarget_size+valtarget_size)] ,X1[(traintarget_size+valtarget_size):len(Y1)]

print('Observations for Feature: %d' % (len(X1)))
print('Training Observations for Feature: %d' % (len(train_feature)))
print('Validation Observations for Feature: %d' % (len(val_feature)))
print('Test Observations for Feature: %d' % (len(test_feature)))
Observations for Feature: 270
Training Observations for Feature: 189
Validation Observations for Feature: 28
Test Observations for Feature: 53

2.0.1 Árbol

Code 
# Decision Tree Regresion Model
from sklearn.tree import DecisionTreeRegressor
# Create a decision tree regression model with default arguments
decision_tree_Orig = DecisionTreeRegressor()  # max-depth not set
# The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
# Fit the model to the training features(covariables) and targets(respuestas)
decision_tree_Orig.fit(train_feature, train_target)
# Check the score on train and test
print("Coeficiente R2 sobre el conjunto de entrenamiento:",decision_tree_Orig.score(train_feature, train_target))
print("Coeficiente R2 sobre el conjunto de Validación:",decision_tree_Orig.score(val_feature,val_target))  # predictions are horrible if negative value, no relationship if 0
print("el RECM sobre validación es:",(((decision_tree_Orig.predict(val_feature)-val_target)**2).mean()) )
Coeficiente R2 sobre el conjunto de entrenamiento: 1.0
Coeficiente R2 sobre el conjunto de Validación: -1.7548809186918701
el RECM sobre validación es: 332309503244.0

Vemos que el R2 para los datos de validación es bueno así sin ningún ajuste, Se relizara un ajuste de la profundidad como hiperparametro para ver si mejora dicho valor

Code 
# Find the best Max Depth

# Loop through a few different max depths and check the performance
# Try different max depths. We want to optimize our ML models to make the best predictions possible.
# For regular decision trees, max_depth, which is a hyperparameter, limits the number of splits in a tree.
# You can find the best value of max_depth based on the R-squared score of the model on the test set.

for d in [2, 3, 4, 5,6,7,8,9,10,11,12,13,14,15]:
    # Create the tree and fit it
    decision_tree_Orig = DecisionTreeRegressor(max_depth=d)
    decision_tree_Orig.fit(train_feature, train_target)
    
    # Print out the scores on train and test
    print('max_depth=', str(d))
    print("Coeficiente R2 sobre el conjunto de entrenamiento:",decision_tree_Orig.score(train_feature, train_target))
    print("Coeficiente R2 sobre el conjunto de validación:",decision_tree_Orig.score(val_feature, val_target), '\n')  # You want the test score to be positive and high
    print("el RECM sobre el conjunto de validación es:",sklearn.metrics.mean_squared_error(decision_tree_Orig.predict(val_feature),val_target, squared=False))
max_depth= 2
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9380991089808784
Coeficiente R2 sobre el conjunto de validación: -2.051209928658386 

el RECM sobre el conjunto de validación es: 606674.875354811
max_depth= 3
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9664178293704504
Coeficiente R2 sobre el conjunto de validación: -1.7135186026890032 

el RECM sobre el conjunto de validación es: 572118.9945819594
max_depth= 4
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9768825370828798
Coeficiente R2 sobre el conjunto de validación: -1.7037887014868796 

el RECM sobre el conjunto de validación es: 571092.3459406185
max_depth= 5
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9851230357060198
Coeficiente R2 sobre el conjunto de validación: -1.832333851372148 

el RECM sobre el conjunto de validación es: 584510.3243444414
max_depth= 6
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9925782041053538
Coeficiente R2 sobre el conjunto de validación: -2.2041965658843563 

el RECM sobre el conjunto de validación es: 621698.1004856585
max_depth= 7
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9978144610458868
Coeficiente R2 sobre el conjunto de validación: -2.3497128586740375 

el RECM sobre el conjunto de validación es: 635658.3486494402
max_depth= 8
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9994408733552114
Coeficiente R2 sobre el conjunto de validación: -2.811262198389598 

el RECM sobre el conjunto de validación es: 678038.5380785092
max_depth= 9
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9998981374422563
Coeficiente R2 sobre el conjunto de validación: -2.0147327960575905 

el RECM sobre el conjunto de validación es: 603037.5808233338
max_depth= 10
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9999911411632353
Coeficiente R2 sobre el conjunto de validación: -2.1214885273158406 

el RECM sobre el conjunto de validación es: 613621.8796439593
max_depth= 11
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9999995801959258
Coeficiente R2 sobre el conjunto de validación: -2.1521096826836246 

el RECM sobre el conjunto de validación es: 616624.2860853936
max_depth= 12
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9999999961093721
Coeficiente R2 sobre el conjunto de validación: -2.5439260490331046 

el RECM sobre el conjunto de validación es: 653826.1563723243
max_depth= 13
Coeficiente R2 sobre el conjunto de entrenamiento: 1.0
Coeficiente R2 sobre el conjunto de validación: -2.7126672435521564 

el RECM sobre el conjunto de validación es: 669210.8571930343
max_depth= 14
Coeficiente R2 sobre el conjunto de entrenamiento: 1.0
Coeficiente R2 sobre el conjunto de validación: -1.9050269567306248 

el RECM sobre el conjunto de validación es: 591963.6624602235
max_depth= 15
Coeficiente R2 sobre el conjunto de entrenamiento: 1.0
Coeficiente R2 sobre el conjunto de validación: -2.3128435879041693 

el RECM sobre el conjunto de validación es: 632150.42019757

Note que los scores para el conjunto de validación son negativos para todas las profundidades evaluadas. Ahora uniremos validacion y entrenamiento para re para reestimar los parametros

Code 
print(type(train_feature))
print(type(val_feature))
#######
print(type(train_target))
print(type(val_target))
####
print(train_feature.shape)
print(val_feature.shape)
#####
####
print(train_target.shape)
print(val_target.shape)
###Concatenate Validation and test
train_val_feature=np.concatenate((train_feature,val_feature),axis=0)
train_val_target=np.concatenate((train_target,val_target),axis=0)
print(train_val_feature.shape)
print(train_val_target.shape)
<class 'numpy.ndarray'>
<class 'numpy.ndarray'>
<class 'numpy.ndarray'>
<class 'numpy.ndarray'>
(189, 12)
(28, 12)
(189,)
(28,)
(217, 12)
(217,)
Code 
# Use the best max_depth 
decision_tree_Orig = DecisionTreeRegressor(max_depth=4)  # fill in best max depth here
decision_tree_Orig.fit(train_val_feature, train_val_target)

# Predict values for train and test
train_val_prediction = decision_tree_Orig.predict(train_val_feature)
test_prediction = decision_tree_Orig.predict(test_feature)

# Scatter the predictions vs actual values
plt.scatter(train_val_prediction, train_val_target, label='train')  # blue
plt.scatter(test_prediction, test_target, label='test')  # orange
# Agrega títulos a los ejes
plt.xlabel('Valores Predichos')  # Título para el eje x
plt.ylabel('Valores Objetivo')  # Título para el eje y
# Muestra una leyenda
plt.legend()
plt.show()
print("Raíz de la Pérdida cuadrática Entrenamiento:",sklearn.metrics.mean_squared_error( train_val_prediction, train_val_target,squared=False))

print("Raíz de la Pérdida cuadrática Prueba:",sklearn.metrics.mean_squared_error(test_prediction, test_target,squared=False))

Raíz de la Pérdida cuadrática Entrenamiento: 237470.97155102508
Raíz de la Pérdida cuadrática Prueba: 512170.57525904087
Code 
from sklearn import tree

listacaract=list(df1_Ori.columns.values)
respuesta=listacaract.pop()
text_representation = tree.export_text(decision_tree_Orig)
print(text_representation)
|--- feature_11 <= 2818996.00
|   |--- feature_0 <= 1406313.50
|   |   |--- feature_11 <= 1269608.00
|   |   |   |--- feature_7 <= 944818.50
|   |   |   |   |--- value: [944508.20]
|   |   |   |--- feature_7 >  944818.50
|   |   |   |   |--- value: [1068707.63]
|   |   |--- feature_11 >  1269608.00
|   |   |   |--- feature_7 <= 1524374.50
|   |   |   |   |--- value: [1485522.56]
|   |   |   |--- feature_7 >  1524374.50
|   |   |   |   |--- value: [1688654.00]
|   |--- feature_0 >  1406313.50
|   |   |--- feature_0 <= 2101048.00
|   |   |   |--- feature_0 <= 1729639.50
|   |   |   |   |--- value: [1895482.33]
|   |   |   |--- feature_0 >  1729639.50
|   |   |   |   |--- value: [2177202.55]
|   |   |--- feature_0 >  2101048.00
|   |   |   |--- feature_6 <= 2851036.50
|   |   |   |   |--- value: [2806855.75]
|   |   |   |--- feature_6 >  2851036.50
|   |   |   |   |--- value: [2414665.18]
|--- feature_11 >  2818996.00
|   |--- feature_11 <= 3902051.50
|   |   |--- feature_11 <= 3328411.00
|   |   |   |--- feature_5 <= 3491265.00
|   |   |   |   |--- value: [3049887.90]
|   |   |   |--- feature_5 >  3491265.00
|   |   |   |   |--- value: [3412516.20]
|   |   |--- feature_11 >  3328411.00
|   |   |   |--- feature_8 <= 2810078.00
|   |   |   |   |--- value: [2840328.00]
|   |   |   |--- feature_8 >  2810078.00
|   |   |   |   |--- value: [3496117.27]
|   |--- feature_11 >  3902051.50
|   |   |--- feature_7 <= 3308846.50
|   |   |   |--- value: [3324889.00]
|   |   |--- feature_7 >  3308846.50
|   |   |   |--- feature_5 <= 5150520.00
|   |   |   |   |--- value: [4812843.37]
|   |   |   |--- feature_5 >  5150520.00
|   |   |   |   |--- value: [5188817.57]
Code 
fig = plt.figure(figsize=(25,20))
_ = tree.plot_tree(decision_tree_Orig, 
                   feature_names=listacaract,  
                   class_names=[respuesta],
                   filled=True)

Ahora miraremos las predicciones comparadas con los valores verdaderos, para ver más claro lo anterior.

Code 
print(train_val_prediction.size)
print(train_val_target.size)

print(test_prediction.size)
print(test_target.size)
217
217
53
53
Code 
indicetrian_val_test=df1_Ori.index
print(indicetrian_val_test.size)  ###Tamaño del índice
indicetrain_val=indicetrian_val_test[0:225]
indicetest=indicetrian_val_test[225:280]
270
Code 
print(indicetrain_val.size)
print(indicetest.size)
225
45
Code 
targetjoint=np.concatenate((train_val_target,test_target))
predictionjoint=np.concatenate((train_val_prediction,test_prediction))
print(targetjoint.size)
print(predictionjoint.size)
270
270
Code 
d = {'observado': targetjoint, 'Predicción': predictionjoint}
ObsvsPred1=pd.DataFrame(data=d,index=indicetrian_val_test)
ObsvsPred1.head(10)
observado Predicción
2001-01-31 1017195.0 1.068708e+06
2001-02-28 964437.0 1.068708e+06
2001-03-31 1002450.0 1.068708e+06
2001-04-30 1058457.0 1.068708e+06
2001-05-31 1068023.0 1.068708e+06
2001-06-30 996736.0 1.068708e+06
2001-07-31 1005867.0 1.068708e+06
2001-08-31 1189605.0 1.068708e+06
2001-09-30 1078781.0 1.068708e+06
2001-10-31 1013772.0 1.068708e+06
Code 
#gráfico
ax = ObsvsPred1['observado'].plot(marker="o", figsize=(10, 6), linewidth=1, markersize=4)  # Ajusta el grosor de las líneas y puntos
ObsvsPred1['Predicción'].plot(marker="o", linewidth=1, markersize=2, ax=ax)  # Ajusta el grosor de las líneas y puntos
# Agrega una línea vertical roja
ax.axvline(x=indicetrian_val_test[223].date(), color='red', linewidth=0.5)  # Ajusta el grosor de la línea vertical
# Muestra una leyenda
plt.legend()
plt.show()

3 Serie de Exportaciones sin Tendencia

Implementaremos ahora el modelo de árboles sobre la serie sin tendencia, eliminada usando la estimación dada por medio del filtro de promedios móviles. Vamos a importar la bases de datos y a convertirlas en objetos de series de Tiempo. \(\{X_t\}\)

Code 
# Lectura de la serie
data2 = pd.read_excel("ExportacionesSinTendencia.xlsx",
                   header = 0, usecols = ['Fecha','ExportacionesSinTend']).reset_index(drop = True).round()
data2['ExportacionesSinTend'] = data2['ExportacionesSinTend'].astype(int) 
data2
Fecha ExportacionesSinTend
0 2000-07-01 5
1 2000-08-01 70
2 2000-09-01 9
3 2000-10-01 -53
4 2000-11-01 46
... ... ...
265 2022-08-01 -71
266 2022-09-01 17
267 2022-10-01 -88
268 2022-11-01 7
269 2022-12-01 39

270 rows × 2 columns

Code 
# tipo de datos
print(data2.info())
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 270 entries, 0 to 269
Data columns (total 2 columns):
 #   Column                Non-Null Count  Dtype         
---  ------                --------------  -----         
 0   Fecha                 270 non-null    datetime64[ns]
 1   ExportacionesSinTend  270 non-null    int32         
dtypes: datetime64[ns](1), int32(1)
memory usage: 3.3 KB
None
Code 
#mirando los datos
#objeto ts
exportaciones = data2['ExportacionesSinTend']
print(type(exportaciones))
plt.plot(exportaciones)
<class 'pandas.core.series.Series'>

Code 
print(f'Numero de filas con valores faltantes: {data2.isnull().any(axis=1).mean()}')
Numero de filas con valores faltantes: 0.0
Code 
data2.shape
(270, 2)

4 Árboles de decisión

4.0.1 Creación de los rezagos

Tomaremos los rezagos de 12 meses atrás para poder predecir un paso adelante.

Code 
from pandas import DataFrame
# reframe as supervised learning
# lag observation (t-1) is the input variable and t is the output variable.
df1 = DataFrame() # original
print(df1)
df2 = DataFrame() #diferenciada
print(df2)
Empty DataFrame
Columns: []
Index: []
Empty DataFrame
Columns: []
Index: []
Code 
# arreglo de datos para el arreglo de rezagos Serie Original
indice = pd.date_range(start='1/7/2000', periods=270, freq='M')
print(indice)
originalDatadf = pd.DataFrame(data2['ExportacionesSinTend'].values,index=indice)
print(originalDatadf)
DatetimeIndex(['2000-01-31', '2000-02-29', '2000-03-31', '2000-04-30',
               '2000-05-31', '2000-06-30', '2000-07-31', '2000-08-31',
               '2000-09-30', '2000-10-31',
               ...
               '2021-09-30', '2021-10-31', '2021-11-30', '2021-12-31',
               '2022-01-31', '2022-02-28', '2022-03-31', '2022-04-30',
               '2022-05-31', '2022-06-30'],
              dtype='datetime64[ns]', length=270, freq='M')
             0
2000-01-31   5
2000-02-29  70
2000-03-31   9
2000-04-30 -53
2000-05-31  46
...         ..
2022-02-28 -71
2022-03-31  17
2022-04-30 -88
2022-05-31   7
2022-06-30  39

[270 rows x 1 columns]
Code 
# Rezagos original
for i in range(12,0,-1):
    df1[['t-'+str(i)]] = originalDatadf.shift(i)
print(df1)
            t-12   t-11   t-10    t-9    t-8    t-7    t-6    t-5    t-4  \
2000-01-31   NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN   
2000-02-29   NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN   
2000-03-31   NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN   
2000-04-30   NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN   
2000-05-31   NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    5.0   
...          ...    ...    ...    ...    ...    ...    ...    ...    ...   
2022-02-28 -30.0   24.0  -12.0   33.0   82.0 -132.0  -68.0   39.0  164.0   
2022-03-31  24.0  -12.0   33.0   82.0 -132.0  -68.0   39.0  164.0   -7.0   
2022-04-30 -12.0   33.0   82.0 -132.0  -68.0   39.0  164.0   -7.0  159.0   
2022-05-31  33.0   82.0 -132.0  -68.0   39.0  164.0   -7.0  159.0  239.0   
2022-06-30  82.0 -132.0  -68.0   39.0  164.0   -7.0  159.0  239.0  -71.0   

              t-3    t-2    t-1  
2000-01-31    NaN    NaN    NaN  
2000-02-29    NaN    NaN    5.0  
2000-03-31    NaN    5.0   70.0  
2000-04-30    5.0   70.0    9.0  
2000-05-31   70.0    9.0  -53.0  
...           ...    ...    ...  
2022-02-28   -7.0  159.0  239.0  
2022-03-31  159.0  239.0  -71.0  
2022-04-30  239.0  -71.0   17.0  
2022-05-31  -71.0   17.0  -88.0  
2022-06-30   17.0  -88.0    7.0  

[270 rows x 12 columns]
Code 
# Create column t original
df1['t'] = originalDatadf.values
print(df1.head(14))
            t-12  t-11  t-10   t-9   t-8   t-7   t-6   t-5   t-4   t-3   t-2  \
2000-01-31   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   
2000-02-29   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   
2000-03-31   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   5.0   
2000-04-30   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   5.0  70.0   
2000-05-31   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   5.0  70.0   9.0   
2000-06-30   NaN   NaN   NaN   NaN   NaN   NaN   NaN   5.0  70.0   9.0 -53.0   
2000-07-31   NaN   NaN   NaN   NaN   NaN   NaN   5.0  70.0   9.0 -53.0  46.0   
2000-08-31   NaN   NaN   NaN   NaN   NaN   5.0  70.0   9.0 -53.0  46.0  67.0   
2000-09-30   NaN   NaN   NaN   NaN   5.0  70.0   9.0 -53.0  46.0  67.0 -28.0   
2000-10-31   NaN   NaN   NaN   5.0  70.0   9.0 -53.0  46.0  67.0 -28.0 -51.0   
2000-11-30   NaN   NaN   5.0  70.0   9.0 -53.0  46.0  67.0 -28.0 -51.0 -31.0   
2000-12-31   NaN   5.0  70.0   9.0 -53.0  46.0  67.0 -28.0 -51.0 -31.0  -3.0   
2001-01-31   5.0  70.0   9.0 -53.0  46.0  67.0 -28.0 -51.0 -31.0  -3.0   5.0   
2001-02-28  70.0   9.0 -53.0  46.0  67.0 -28.0 -51.0 -31.0  -3.0   5.0 -20.0   

             t-1   t  
2000-01-31   NaN   5  
2000-02-29   5.0  70  
2000-03-31  70.0   9  
2000-04-30   9.0 -53  
2000-05-31 -53.0  46  
2000-06-30  46.0  67  
2000-07-31  67.0 -28  
2000-08-31 -28.0 -51  
2000-09-30 -51.0 -31  
2000-10-31 -31.0  -3  
2000-11-30  -3.0   5  
2000-12-31   5.0 -20  
2001-01-31 -20.0  -9  
2001-02-28  -9.0  81
Code 
# Create a new subsetted dataframe, removing Nans from first 3 rows original
df1_Ori = df1[12:]
print(df1_Ori)
df1_Ori.size
            t-12   t-11   t-10    t-9    t-8    t-7    t-6    t-5    t-4  \
2001-01-31   5.0   70.0    9.0  -53.0   46.0   67.0  -28.0  -51.0  -31.0   
2001-02-28  70.0    9.0  -53.0   46.0   67.0  -28.0  -51.0  -31.0   -3.0   
2001-03-31   9.0  -53.0   46.0   67.0  -28.0  -51.0  -31.0   -3.0    5.0   
2001-04-30 -53.0   46.0   67.0  -28.0  -51.0  -31.0   -3.0    5.0  -20.0   
2001-05-31  46.0   67.0  -28.0  -51.0  -31.0   -3.0    5.0  -20.0   -9.0   
...          ...    ...    ...    ...    ...    ...    ...    ...    ...   
2022-02-28 -30.0   24.0  -12.0   33.0   82.0 -132.0  -68.0   39.0  164.0   
2022-03-31  24.0  -12.0   33.0   82.0 -132.0  -68.0   39.0  164.0   -7.0   
2022-04-30 -12.0   33.0   82.0 -132.0  -68.0   39.0  164.0   -7.0  159.0   
2022-05-31  33.0   82.0 -132.0  -68.0   39.0  164.0   -7.0  159.0  239.0   
2022-06-30  82.0 -132.0  -68.0   39.0  164.0   -7.0  159.0  239.0  -71.0   

              t-3    t-2    t-1   t  
2001-01-31   -3.0    5.0  -20.0  -9  
2001-02-28    5.0  -20.0   -9.0  81  
2001-03-31  -20.0   -9.0   81.0  32  
2001-04-30   -9.0   81.0   32.0   2  
2001-05-31   81.0   32.0    2.0 -23  
...           ...    ...    ...  ..  
2022-02-28   -7.0  159.0  239.0 -71  
2022-03-31  159.0  239.0  -71.0  17  
2022-04-30  239.0  -71.0   17.0 -88  
2022-05-31  -71.0   17.0  -88.0   7  
2022-06-30   17.0  -88.0    7.0  39  

[258 rows x 13 columns]
3354
Code 
# Split data Serie Original
Orig_Split = df1_Ori.values
# split into lagged variables and original time series
X1 = Orig_Split[:, 0:-1]  # slice all rows and start with column 0 and go up to but not including the last column
y1 = Orig_Split[:,-1]  # slice all rows and last column, essentially separating out 't' column
print(X1)
print('Respuestas \n',y1)
[[   5.   70.    9. ...   -3.    5.  -20.]
 [  70.    9.  -53. ...    5.  -20.   -9.]
 [   9.  -53.   46. ...  -20.   -9.   81.]
 ...
 [ -12.   33.   82. ...  239.  -71.   17.]
 [  33.   82. -132. ...  -71.   17.  -88.]
 [  82. -132.  -68. ...   17.  -88.    7.]]
Respuestas 
 [  -9.   81.   32.    2.  -23.  -20.  -32.  -26.  -66.   67.   43.  -37.
   23.  -42.   23.   27.  -26.   14.  -58.  -11.  -14.   15.   49.  -45.
   75.  -10.  -20.   16.  -31.   -2.   -8.  -92.  -26.  -11.    1.   25.
   57.   34.   18.    6.   15.   16.  -98.  -44.   18.   -7.    6.  124.
  -43.   31.   31.  -17.  -14.   20.  -84.  -24.   -6.  -36.   67.    3.
   32.   24.    9.   49.   -7.  -19. -126. -114.   29.   54.  105. -110.
   30.   -3.  -52.  -40.   91.   85.  -51.  -77.  -41.   43.   56.  150.
  197.   80.   47.   20. -180. -169.  -55.  -95.   28.  -52.   34.   13.
   43.  -33.  -11.   12.  -33.   42.  -38.  -60.   54.   81.   74.  -57.
  -47.  -33.  -65.  -25.  -81.   -9.  -63.  -48.  130.   90.  131.    9.
   19.   16.  -77.  -45.   29.   61.  -46.    1.  143.   -5.   72.  -97.
   -6.  -90.   -6.  110.  -16.   12.   -9.  -49.  -63.   13.   95.   -3.
  -52.   21.   -1.    5.   32.   98.    1. -118.  -88. -106.  156.   18.
  123.  104.  180.   38.  -53.  -19. -211. -106.   13.  -12.   61.   47.
   27.    1.   33.   31.  -62.   -6. -207.  -64.  -63.  -21.   60.   53.
 -123.   89.    4.  -18.  -11.  151.  -47.  -78.   73. -104.  104.  -66.
  -15.   -7.   40.   -1.  -56.  159.  -20. -110.  -27.   71.   47.  -46.
   39.   53.    9.   71.  -36.  -17. -100.  -61.   -9.  129.  110.  -51.
  -12.  -11.  -50.   53.   -8.  123.  164.   54.  -79. -254. -121.  -90.
    3.   22.   -1.    4.  -58.   66.  -74.    0.   94.  -41.  -38.  -48.
   -9.  -30.   24.  -12.   33.   82. -132.  -68.   39.  164.   -7.  159.
  239.  -71.   17.  -88.    7.   39.]

5 Árbol para Serie Sin Tendencia

5.0.0.1 Entrenamiento, Validación y prueba

Code 
Y1 = y1
print('Complete Observations for Target after Supervised configuration: %d' %len(Y1))
traintarget_size = int(len(Y1) * 0.70) 
valtarget_size = int(len(Y1) * 0.10)+1# Set split
testtarget_size = int(len(Y1) * 0.20)# Set split
print(traintarget_size,valtarget_size,testtarget_size)
print('Train + Validation + Test: %d' %(traintarget_size+valtarget_size+testtarget_size))
Complete Observations for Target after Supervised configuration: 258
180 26 51
Train + Validation + Test: 257
Code 
# Target Train-Validation-Test split(70-10-20)
train_target, val_target,test_target = Y1[0:traintarget_size], Y1[(traintarget_size):(traintarget_size+valtarget_size)],Y1[(traintarget_size+valtarget_size):len(Y1)]

print('Observations for Target: %d' % (len(Y1)))
print('Training Observations for Target: %d' % (len(train_target)))
print('Validation Observations for Target: %d' % (len(val_target)))
print('Test Observations for Target: %d' % (len(test_target)))
Observations for Target: 258
Training Observations for Target: 180
Validation Observations for Target: 26
Test Observations for Target: 52
Code 
# Features Train--Val-Test split

trainfeature_size = int(len(X1) * 0.70)
valfeature_size = int(len(X1) * 0.10)+1# Set split
testfeature_size = int(len(X1) * 0.20)# Set split
train_feature, val_feature,test_feature = X1[0:traintarget_size],X1[(traintarget_size):(traintarget_size+valtarget_size)] ,X1[(traintarget_size+valtarget_size):len(Y1)]

print('Observations for Feature: %d' % (len(X1)))
print('Training Observations for Feature: %d' % (len(train_feature)))
print('Validation Observations for Feature: %d' % (len(val_feature)))
print('Test Observations for Feature: %d' % (len(test_feature)))
Observations for Feature: 258
Training Observations for Feature: 180
Validation Observations for Feature: 26
Test Observations for Feature: 52

5.0.1 Árbol

Code 
# Decision Tree Regresion Model
from sklearn.tree import DecisionTreeRegressor
# Create a decision tree regression model with default arguments
decision_tree_Orig = DecisionTreeRegressor()  # max-depth not set
# The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
# Fit the model to the training features(covariables) and targets(respuestas)
decision_tree_Orig.fit(train_feature, train_target)
# Check the score on train and test
print("Coeficiente R2 sobre el conjunto de entrenamiento:",decision_tree_Orig.score(train_feature, train_target))
print("Coeficiente R2 sobre el conjunto de Validación:",decision_tree_Orig.score(val_feature,val_target))  # predictions are horrible if negative value, no relationship if 0
print("el RECM sobre validación es:",(((decision_tree_Orig.predict(val_feature)-val_target)**2).mean()) )
Coeficiente R2 sobre el conjunto de entrenamiento: 1.0
Coeficiente R2 sobre el conjunto de Validación: -0.36155906119852443
el RECM sobre validación es: 7475.307692307692

Vemos que el R2 para los datos de validación es malo pues es negativo, Se relizará un ajuste de la profundidad como hiperparametro para ver si mejora dicho valor

Code 
# Find the best Max Depth

# Loop through a few different max depths and check the performance
# Try different max depths. We want to optimize our ML models to make the best predictions possible.
# For regular decision trees, max_depth, which is a hyperparameter, limits the number of splits in a tree.
# You can find the best value of max_depth based on the R-squared score of the model on the test set.

for d in [2, 3, 4, 5,6,7,8,9,10,11,12,13,14,15]:
    # Create the tree and fit it
    decision_tree_Orig = DecisionTreeRegressor(max_depth=d)
    decision_tree_Orig.fit(train_feature, train_target)
    
    # Print out the scores on train and test
    print('max_depth=', str(d))
    print("Coeficiente R2 sobre el conjunto de entrenamiento:",decision_tree_Orig.score(train_feature, train_target))
    print("Coeficiente R2 sobre el conjunto de validación:",decision_tree_Orig.score(val_feature, val_target), '\n')  # You want the test score to be positive and high
    print("el RECM sobre el conjunto de validación es:",sklearn.metrics.mean_squared_error(decision_tree_Orig.predict(val_feature),val_target, squared=False), '\n')
max_depth= 2
Coeficiente R2 sobre el conjunto de entrenamiento: 0.25686511970310677
Coeficiente R2 sobre el conjunto de validación: -0.2651415670711108 

el RECM sobre el conjunto de validación es: 83.3423720244207 

max_depth= 3
Coeficiente R2 sobre el conjunto de entrenamiento: 0.4245443431150394
Coeficiente R2 sobre el conjunto de validación: -0.25312344192618963 

el RECM sobre el conjunto de validación es: 82.94557487875332 

max_depth= 4
Coeficiente R2 sobre el conjunto de entrenamiento: 0.570233841687424
Coeficiente R2 sobre el conjunto de validación: -0.3946378641992552 

el RECM sobre el conjunto de validación es: 87.50382155206147 

max_depth= 5
Coeficiente R2 sobre el conjunto de entrenamiento: 0.7247525080241783
Coeficiente R2 sobre el conjunto de validación: -0.19662975618360146 

el RECM sobre el conjunto de validación es: 81.05432498970345 

max_depth= 6
Coeficiente R2 sobre el conjunto de entrenamiento: 0.8709713841871555
Coeficiente R2 sobre el conjunto de validación: -0.35559462890663207 

el RECM sobre el conjunto de validación es: 86.27028128286491 

max_depth= 7
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9433510456062553
Coeficiente R2 sobre el conjunto de validación: -0.709072303001282 

el RECM sobre el conjunto de validación es: 96.86714780774055 

max_depth= 8
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9726668839828992
Coeficiente R2 sobre el conjunto de validación: -0.6473773745003699 

el RECM sobre el conjunto de validación es: 95.10269911072858 

max_depth= 9
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9865860401853749
Coeficiente R2 sobre el conjunto de validación: -0.39089588349704174 

el RECM sobre el conjunto de validación es: 87.38635107682887 

max_depth= 10
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9941479557500952
Coeficiente R2 sobre el conjunto de validación: -0.48267762709243045 

el RECM sobre el conjunto de validación es: 90.2234981331616 

max_depth= 11
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9978703406029361
Coeficiente R2 sobre el conjunto de validación: -0.8745405463882787 

el RECM sobre el conjunto de validación es: 101.44805235569653 

max_depth= 12
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9990766376693829
Coeficiente R2 sobre el conjunto de validación: -0.4727281499619058 

el RECM sobre el conjunto de validación es: 89.92026712424794 

max_depth= 13
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9995620305866239
Coeficiente R2 sobre el conjunto de validación: -0.24182245414347547 

el RECM sobre el conjunto de validación es: 82.57071561348538 

max_depth= 14
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9999093006589739
Coeficiente R2 sobre el conjunto de validación: -0.5578788994919184 

el RECM sobre el conjunto de validación es: 92.48326251897608 

max_depth= 15
Coeficiente R2 sobre el conjunto de entrenamiento: 0.9999917449841307
Coeficiente R2 sobre el conjunto de validación: -0.7418972235102907 

el RECM sobre el conjunto de validación es: 97.79295239669135

Note que los scores para el conjunto de validación son negativos para todas las profundidades evaluadas. Tomaremos el más cercano a cero que el el de la profundidad 6. Ahora uniremos validacion y entrenamiento para re para reestimar los parametros

Code 
print(type(train_feature))
print(type(val_feature))
#######
print(type(train_target))
print(type(val_target))
####
print(train_feature.shape)
print(val_feature.shape)
#####
####
print(train_target.shape)
print(val_target.shape)
###Concatenate Validation and test
train_val_feature=np.concatenate((train_feature,val_feature),axis=0)
train_val_target=np.concatenate((train_target,val_target),axis=0)
print(train_val_feature.shape)
print(train_val_target.shape)
<class 'numpy.ndarray'>
<class 'numpy.ndarray'>
<class 'numpy.ndarray'>
<class 'numpy.ndarray'>
(180, 12)
(26, 12)
(180,)
(26,)
(206, 12)
(206,)
Code 
# Use the best max_depth 
decision_tree_Orig = DecisionTreeRegressor(max_depth=6)  # fill in best max depth here
decision_tree_Orig.fit(train_val_feature, train_val_target)

# Predict values for train and test
train_val_prediction = decision_tree_Orig.predict(train_val_feature)
test_prediction = decision_tree_Orig.predict(test_feature)

# Scatter the predictions vs actual values
plt.scatter(train_val_prediction, train_val_target, label='train')  # blue
plt.scatter(test_prediction, test_target, label='test')  # orange
# Agrega títulos a los ejes
plt.xlabel('Valores Predichos')  # Título para el eje x
plt.ylabel('Valores Objetivo')  # Título para el eje y
# Muestra una leyenda
plt.legend()
plt.show()
print("Raíz de la Pérdida cuadrática Entrenamiento:",sklearn.metrics.mean_squared_error( train_val_prediction, train_val_target,squared=False))

print("Raíz de la Pérdida cuadrática Prueba:",sklearn.metrics.mean_squared_error(test_prediction, test_target,squared=False))

Raíz de la Pérdida cuadrática Entrenamiento: 34.410731597123124
Raíz de la Pérdida cuadrática Prueba: 102.6782863348308
Code 
from sklearn import tree

listacaract=list(df1_Ori.columns.values)
respuesta=listacaract.pop()
text_representation = tree.export_text(decision_tree_Orig)
print(text_representation)
|--- feature_6 <= 18.50
|   |--- feature_5 <= 80.00
|   |   |--- feature_0 <= -10.50
|   |   |   |--- feature_9 <= -42.50
|   |   |   |   |--- feature_9 <= -62.50
|   |   |   |   |   |--- feature_4 <= 18.00
|   |   |   |   |   |   |--- value: [-42.50]
|   |   |   |   |   |--- feature_4 >  18.00
|   |   |   |   |   |   |--- value: [-5.00]
|   |   |   |   |--- feature_9 >  -62.50
|   |   |   |   |   |--- feature_9 <= -59.00
|   |   |   |   |   |   |--- value: [-64.00]
|   |   |   |   |   |--- feature_9 >  -59.00
|   |   |   |   |   |   |--- value: [-107.00]
|   |   |   |--- feature_9 >  -42.50
|   |   |   |   |--- feature_1 <= 30.00
|   |   |   |   |   |--- feature_9 <= -16.50
|   |   |   |   |   |   |--- value: [-54.60]
|   |   |   |   |   |--- feature_9 >  -16.50
|   |   |   |   |   |   |--- value: [-3.48]
|   |   |   |   |--- feature_1 >  30.00
|   |   |   |   |   |--- feature_10 <= -35.50
|   |   |   |   |   |   |--- value: [76.00]
|   |   |   |   |   |--- feature_10 >  -35.50
|   |   |   |   |   |   |--- value: [15.00]
|   |   |--- feature_0 >  -10.50
|   |   |   |--- feature_10 <= 116.50
|   |   |   |   |--- feature_8 <= 48.00
|   |   |   |   |   |--- feature_1 <= -71.50
|   |   |   |   |   |   |--- value: [-37.25]
|   |   |   |   |   |--- feature_1 >  -71.50
|   |   |   |   |   |   |--- value: [29.84]
|   |   |   |   |--- feature_8 >  48.00
|   |   |   |   |   |--- feature_5 <= -15.50
|   |   |   |   |   |   |--- value: [7.30]
|   |   |   |   |   |--- feature_5 >  -15.50
|   |   |   |   |   |   |--- value: [-38.25]
|   |   |   |--- feature_10 >  116.50
|   |   |   |   |--- feature_4 <= 8.50
|   |   |   |   |   |--- feature_3 <= 32.50
|   |   |   |   |   |   |--- value: [131.00]
|   |   |   |   |   |--- feature_3 >  32.50
|   |   |   |   |   |   |--- value: [180.00]
|   |   |   |   |--- feature_4 >  8.50
|   |   |   |   |   |--- feature_4 <= 50.50
|   |   |   |   |   |   |--- value: [31.00]
|   |   |   |   |   |--- feature_4 >  50.50
|   |   |   |   |   |   |--- value: [80.00]
|   |--- feature_5 >  80.00
|   |   |--- feature_8 <= 26.00
|   |   |   |--- feature_11 <= 120.50
|   |   |   |   |--- feature_0 <= 111.50
|   |   |   |   |   |--- feature_1 <= 7.00
|   |   |   |   |   |   |--- value: [75.17]
|   |   |   |   |   |--- feature_1 >  7.00
|   |   |   |   |   |   |--- value: [116.50]
|   |   |   |   |--- feature_0 >  111.50
|   |   |   |   |   |--- value: [159.00]
|   |   |   |--- feature_11 >  120.50
|   |   |   |   |--- value: [197.00]
|   |   |--- feature_8 >  26.00
|   |   |   |--- feature_10 <= 12.00
|   |   |   |   |--- value: [-84.00]
|   |   |   |--- feature_10 >  12.00
|   |   |   |   |--- feature_7 <= 22.50
|   |   |   |   |   |--- value: [-15.00]
|   |   |   |   |--- feature_7 >  22.50
|   |   |   |   |   |--- value: [-19.00]
|--- feature_6 >  18.50
|   |--- feature_9 <= 25.50
|   |   |--- feature_0 <= -7.50
|   |   |   |--- feature_8 <= -18.50
|   |   |   |   |--- feature_4 <= -24.50
|   |   |   |   |   |--- feature_10 <= 21.00
|   |   |   |   |   |   |--- value: [32.00]
|   |   |   |   |   |--- feature_10 >  21.00
|   |   |   |   |   |   |--- value: [150.00]
|   |   |   |   |--- feature_4 >  -24.50
|   |   |   |   |   |--- feature_9 <= -85.50
|   |   |   |   |   |   |--- value: [23.33]
|   |   |   |   |   |--- feature_9 >  -85.50
|   |   |   |   |   |   |--- value: [-37.38]
|   |   |   |--- feature_8 >  -18.50
|   |   |   |   |--- feature_7 <= 33.00
|   |   |   |   |   |--- feature_11 <= -112.00
|   |   |   |   |   |   |--- value: [-114.00]
|   |   |   |   |   |--- feature_11 >  -112.00
|   |   |   |   |   |   |--- value: [-27.77]
|   |   |   |   |--- feature_7 >  33.00
|   |   |   |   |   |--- feature_1 <= -84.50
|   |   |   |   |   |   |--- value: [-102.00]
|   |   |   |   |   |--- feature_1 >  -84.50
|   |   |   |   |   |   |--- value: [-66.50]
|   |   |--- feature_0 >  -7.50
|   |   |   |--- feature_0 <= -5.50
|   |   |   |   |--- feature_6 <= 79.00
|   |   |   |   |   |--- value: [151.00]
|   |   |   |   |--- feature_6 >  79.00
|   |   |   |   |   |--- value: [91.00]
|   |   |   |--- feature_0 >  -5.50
|   |   |   |   |--- feature_11 <= -85.50
|   |   |   |   |   |--- value: [156.00]
|   |   |   |   |--- feature_11 >  -85.50
|   |   |   |   |   |--- feature_2 <= 36.50
|   |   |   |   |   |   |--- value: [13.46]
|   |   |   |   |   |--- feature_2 >  36.50
|   |   |   |   |   |   |--- value: [-46.67]
|   |--- feature_9 >  25.50
|   |   |--- feature_4 <= 27.50
|   |   |   |--- feature_8 <= 173.50
|   |   |   |   |--- feature_2 <= -38.50
|   |   |   |   |   |--- feature_0 <= -1.50
|   |   |   |   |   |   |--- value: [-8.50]
|   |   |   |   |   |--- feature_0 >  -1.50
|   |   |   |   |   |   |--- value: [20.00]
|   |   |   |   |--- feature_2 >  -38.50
|   |   |   |   |   |--- feature_9 <= 151.00
|   |   |   |   |   |   |--- value: [-71.83]
|   |   |   |   |   |--- feature_9 >  151.00
|   |   |   |   |   |   |--- value: [-3.50]
|   |   |   |--- feature_8 >  173.50
|   |   |   |   |--- value: [-180.00]
|   |   |--- feature_4 >  27.50
|   |   |   |--- feature_1 <= -38.50
|   |   |   |   |--- feature_11 <= -99.50
|   |   |   |   |   |--- value: [-169.00]
|   |   |   |   |--- feature_11 >  -99.50
|   |   |   |   |   |--- feature_11 <= -12.50
|   |   |   |   |   |   |--- value: [-211.00]
|   |   |   |   |   |--- feature_11 >  -12.50
|   |   |   |   |   |   |--- value: [-207.00]
|   |   |   |--- feature_1 >  -38.50
|   |   |   |   |--- feature_1 <= -25.00
|   |   |   |   |   |--- value: [-58.00]
|   |   |   |   |--- feature_1 >  -25.00
|   |   |   |   |   |--- value: [-126.00]
Code 
fig = plt.figure(figsize=(25,20))
_ = tree.plot_tree(decision_tree_Orig, 
                   feature_names=listacaract,  
                   class_names=[respuesta],
                   filled=True)

Ahora miraremos las predicciones comparadas con los valores verdaderos, para ver más claro lo anterior.

Code 
print(train_val_prediction.size)
print(train_val_target.size)

print(test_prediction.size)
print(test_target.size)
206
206
52
52
Code 
indicetrian_val_test=df1_Ori.index
print(indicetrian_val_test.size)  ###Tamaño del índice
indicetrain_val=indicetrian_val_test[0:206]
indicetest=indicetrian_val_test[206:258]
258
Code 
print(indicetrain_val.size)
print(indicetest.size)
206
52
Code 
targetjoint=np.concatenate((train_val_target,test_target))
predictionjoint=np.concatenate((train_val_prediction,test_prediction))
print(targetjoint.size)
print(predictionjoint.size)
258
258
Code 
d = {'observado': targetjoint, 'Predicción': predictionjoint}
ObsvsPred1=pd.DataFrame(data=d,index=indicetrian_val_test)
ObsvsPred1.tail(52)
observado Predicción
2018-03-31 9.0 29.842105
2018-04-30 71.0 -71.833333
2018-05-31 -36.0 -71.833333
2018-06-30 -17.0 -38.250000
2018-07-31 -100.0 -211.000000
2018-08-31 -61.0 -27.769231
2018-09-30 -9.0 76.000000
2018-10-31 129.0 13.461538
2018-11-30 110.0 29.842105
2018-12-31 -51.0 15.000000
2019-01-31 -12.0 29.842105
2019-02-28 -11.0 7.300000
2019-03-31 -50.0 7.300000
2019-04-30 53.0 13.461538
2019-05-31 -8.0 -27.769231
2019-06-30 123.0 75.166667
2019-07-31 164.0 -3.476190
2019-08-31 54.0 -3.476190
2019-09-30 -79.0 131.000000
2019-10-31 -254.0 20.000000
2019-11-30 -121.0 -38.250000
2019-12-31 -90.0 -66.500000
2020-01-31 3.0 23.333333
2020-02-29 22.0 23.333333
2020-03-31 -1.0 -5.000000
2020-04-30 4.0 29.842105
2020-05-31 -58.0 29.842105
2020-06-30 66.0 29.842105
2020-07-31 -74.0 29.842105
2020-08-31 0.0 13.461538
2020-09-30 94.0 -3.476190
2020-10-31 -41.0 -5.000000
2020-11-30 -38.0 -3.476190
2020-12-31 -48.0 -71.833333
2021-01-31 -9.0 -38.250000
2021-02-28 -30.0 29.842105
2021-03-31 24.0 13.461538
2021-04-30 -12.0 75.166667
2021-05-31 33.0 15.000000
2021-06-30 82.0 -37.250000
2021-07-31 -132.0 -3.476190
2021-08-31 -68.0 29.842105
2021-09-30 39.0 -71.833333
2021-10-31 164.0 -42.500000
2021-11-30 -7.0 -37.375000
2021-12-31 159.0 -71.833333
2022-01-31 239.0 -84.000000
2022-02-28 -71.0 -3.476190
2022-03-31 17.0 -3.500000
2022-04-30 -88.0 -3.500000
2022-05-31 7.0 -19.000000
2022-06-30 39.0 13.461538
Code 
#gráfico
ax = ObsvsPred1['observado'].plot(marker="o", figsize=(10, 6), linewidth=1, markersize=4)  # Ajusta el grosor de las líneas y puntos
ObsvsPred1['Predicción'].plot(marker="o", linewidth=1, markersize=2, ax=ax)  # Ajusta el grosor de las líneas y puntos
# Agrega una línea vertical roja
ax.axvline(x=indicetrian_val_test[223].date(), color='red', linewidth=0.5)  # Ajusta el grosor de la línea vertical
# Muestra una leyenda
plt.legend()
plt.show()

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