!pip install statsmodels==0.12.2

import pandas as pd import numpy as np import matplotlib.pyplot as plt import os import math import numpy as np import pandas as pd import matplotlib.pyplot as plt import statsmodels.tsa.api as smt import statsmodels.api as sm import itertools import sys from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Dense, LSTM from sklearn.preprocessing import MinMaxScaler from sklearn.metrics import mean_squared_error df = pd.read_csv("IPC.csv", delimiter = ";") mois_str = df["Libellé"][2:] indices = df["Indice des prix à la consommation - Base 2015 - Ensemble des ménages - France - Ensemble"][2:] # mois_int permet de convertir les mois en entiers mois = [] cpt = 1 for i in mois_str: mois.append(cpt) cpt+=1 mois = np.array(mois) plt.figure(figsize=(13, 6)) plt.plot(indices, 'b--', linewidth=1) plt.title("Evolution mensuel de l'IPC") plt.xlabel('Mois', fontsize=18) plt.ylabel('Indice', fontsize=18) plt.grid(True) plt.show

import statistics import math moyenne = statistics.mean(indices) mediane = np.median(indices) q1 = np.quantile(indices, .25) q3 = np.quantile(indices, .75) var = np.var(indices) ectype = math.sqrt(var) CV = ectype/moyenne plt.figure(figsize=(13, 6)) plt.plot(indices, 'b--', linewidth=1) plt.axhline(y=moyenne, color = "red") plt.axhline(y=mediane, color = "purple") plt.axhline(y=q1, color = "green") plt.axhline(y=q3, color = "green") #plt.title("Evolution des ventes par jour") plt.xlabel('Mois', fontsize=18) plt.ylabel('Indice', fontsize=18) plt.grid(True) plt.legend(("Quantité", "Moyenne", "Médiane", "Quartiles")) plt.show print("moyenne = ", moyenne) print("médiane = ", mediane) print("Q1 = ", q1) print("Q3 = ", q3) print("variance = ", var) print("écart type = ", ectype) print("coefficient de variation = ", CV)

!pip install statsmodels==0.12.2

from statsmodels.tsa.tsatools import detrend from scipy import stats import matplotlib.pyplot as plt train_mois = mois[:300] train_indices = indices[:300] slope, intercept, r_value, p_value, std_error = stats.linregress(train_mois, train_indices) def predict(x): return slope * x + intercept lin_reg = predict(mois) fig_trend = plt.figure(figsize=(13, 6)) plt.plot(mois, indices, 'b--', linewidth=1) plt.plot(mois, lin_reg, 'g-', linewidth=1) plt.title("Tendance linéaire") plt.xlabel('Mois', fontsize=18) plt.ylabel('Incide', fontsize=18) plt.grid(True) plt.show print("y = ", slope,"x ", intercept)

detrend_indices = indices - lin_reg fig_trend = plt.figure(figsize=(13, 6)) plt.plot(mois, detrend_indices, 'b--', linewidth=1) plt.title("Série corrigée de sa tendance") plt.xlabel('Mois', fontsize=18) plt.ylabel('indice', fontsize=18) plt.grid(True) plt.show

indices_diff_seas = [a-b for a, b in zip(indices[11:], indices[:-11])] annee2 = np.mean(detrend_indices[16:27]) annee3 = np.mean(detrend_indices[28:39]) annee4 = np.mean(detrend_indices[40:51]) annee5 = np.mean(detrend_indices[52:63]) annee6 = np.mean(detrend_indices[64:75]) annee7 = np.mean(detrend_indices[76:87]) annee8 = np.mean(detrend_indices[88:99]) annee9 = np.mean(detrend_indices[100:111]) annee10 = np.mean(detrend_indices[112:123]) annee11 = np.mean(detrend_indices[124:135]) annee12 = np.mean(detrend_indices[136:147]) annee13 = np.mean(detrend_indices[148:159]) annee14 = np.mean(detrend_indices[160:171]) annee15 = np.mean(detrend_indices[172:183]) annee16 = np.mean(detrend_indices[184:195]) annee17 = np.mean(detrend_indices[196:207]) annee18 = np.mean(detrend_indices[208:219]) annee19 = np.mean(detrend_indices[220:231]) annee20 = np.mean(detrend_indices[232:243]) annee21 = np.mean(detrend_indices[244:255]) annee22 = np.mean(detrend_indices[256:267]) annee23 = np.mean(detrend_indices[268:279]) annee24 = np.mean(detrend_indices[280:291]) seas1 = np.mean([detrend_indices[16]-annee2, detrend_indices[28]-annee3, detrend_indices[40]-annee4, detrend_indices[52]-annee5, detrend_indices[64]-annee6, detrend_indices[76]-annee7, detrend_indices[88]-annee8, detrend_indices[100]-annee9, detrend_indices[112]-annee10, detrend_indices[124]-annee11, detrend_indices[136]-annee12, detrend_indices[148]-annee13, detrend_indices[160]-annee14, detrend_indices[172]-annee15, detrend_indices[184]-annee16, detrend_indices[196]-annee17, detrend_indices[208]-annee18, detrend_indices[220]-annee19, detrend_indices[232]-annee20, detrend_indices[244]-annee21, detrend_indices[256]-annee22, detrend_indices[268]-annee23, detrend_indices[280]-annee24]) seas2 = np.mean([detrend_indices[17]-annee2, detrend_indices[29]-annee3, detrend_indices[41]-annee4, detrend_indices[53]-annee5, detrend_indices[65]-annee6, detrend_indices[77]-annee7, detrend_indices[89]-annee8, detrend_indices[101]-annee9, detrend_indices[113]-annee10, detrend_indices[125]-annee11, detrend_indices[137]-annee12, detrend_indices[149]-annee13, detrend_indices[161]-annee14, detrend_indices[173]-annee15, detrend_indices[185]-annee16, detrend_indices[197]-annee17, detrend_indices[209]-annee18, detrend_indices[221]-annee19, detrend_indices[233]-annee20, detrend_indices[245]-annee21, detrend_indices[257]-annee22, detrend_indices[269]-annee23, detrend_indices[281]-annee24]) seas3 = np.mean([detrend_indices[18]-annee2, detrend_indices[30]-annee3, detrend_indices[42]-annee4, detrend_indices[54]-annee5, detrend_indices[66]-annee6, detrend_indices[78]-annee7, detrend_indices[90]-annee8, detrend_indices[102]-annee9, detrend_indices[114]-annee10, detrend_indices[126]-annee11, detrend_indices[138]-annee12, detrend_indices[150]-annee13, detrend_indices[162]-annee14, detrend_indices[174]-annee15, detrend_indices[186]-annee16, detrend_indices[198]-annee17, detrend_indices[210]-annee18, detrend_indices[222]-annee19, detrend_indices[234]-annee20, detrend_indices[246]-annee21, detrend_indices[258]-annee22, detrend_indices[270]-annee23, detrend_indices[282]-annee24]) seas4 = np.mean([detrend_indices[19]-annee2, detrend_indices[31]-annee3, detrend_indices[43]-annee4, detrend_indices[55]-annee5, detrend_indices[67]-annee6, detrend_indices[79]-annee7, detrend_indices[91]-annee8, detrend_indices[103]-annee9, detrend_indices[115]-annee10, detrend_indices[127]-annee11, detrend_indices[139]-annee12, detrend_indices[151]-annee13, detrend_indices[163]-annee14, detrend_indices[175]-annee15, detrend_indices[187]-annee16, detrend_indices[199]-annee17, detrend_indices[211]-annee18, detrend_indices[223]-annee19, detrend_indices[235]-annee20, detrend_indices[247]-annee21, detrend_indices[259]-annee22, detrend_indices[271]-annee23, detrend_indices[283]-annee24]) seas5 = np.mean([detrend_indices[20]-annee2, detrend_indices[32]-annee3, detrend_indices[44]-annee4, detrend_indices[56]-annee5, detrend_indices[68]-annee6, detrend_indices[80]-annee7, detrend_indices[92]-annee8, detrend_indices[104]-annee9, detrend_indices[116]-annee10, detrend_indices[128]-annee11, detrend_indices[140]-annee12, detrend_indices[152]-annee13, detrend_indices[164]-annee14, detrend_indices[176]-annee15, detrend_indices[188]-annee16, detrend_indices[200]-annee17, detrend_indices[212]-annee18, detrend_indices[224]-annee19, detrend_indices[236]-annee20, detrend_indices[248]-annee21, detrend_indices[260]-annee22, detrend_indices[272]-annee23, detrend_indices[284]-annee24]) seas6 = np.mean([detrend_indices[21]-annee2, detrend_indices[33]-annee3, detrend_indices[45]-annee4, detrend_indices[57]-annee5, detrend_indices[69]-annee6, detrend_indices[81]-annee7, detrend_indices[93]-annee8, detrend_indices[105]-annee9, detrend_indices[117]-annee10, detrend_indices[129]-annee11, detrend_indices[141]-annee12, detrend_indices[153]-annee13, detrend_indices[165]-annee14, detrend_indices[177]-annee15, detrend_indices[189]-annee16, detrend_indices[201]-annee17, detrend_indices[213]-annee18, detrend_indices[225]-annee19, detrend_indices[237]-annee20, detrend_indices[249]-annee21, detrend_indices[261]-annee22, detrend_indices[273]-annee23, detrend_indices[285]-annee24]) seas7 = np.mean([detrend_indices[22]-annee2, detrend_indices[34]-annee3, detrend_indices[46]-annee4, detrend_indices[58]-annee5, detrend_indices[70]-annee6, detrend_indices[82]-annee7, detrend_indices[94]-annee8, detrend_indices[106]-annee9, detrend_indices[118]-annee10, detrend_indices[130]-annee11, detrend_indices[142]-annee12, detrend_indices[154]-annee13, detrend_indices[166]-annee14, detrend_indices[178]-annee15, detrend_indices[190]-annee16, detrend_indices[202]-annee17, detrend_indices[214]-annee18, detrend_indices[226]-annee19, detrend_indices[238]-annee20, detrend_indices[250]-annee21, detrend_indices[262]-annee22, detrend_indices[274]-annee23, detrend_indices[286]-annee24]) seas8 = np.mean([detrend_indices[23]-annee2, detrend_indices[35]-annee3, detrend_indices[47]-annee4, detrend_indices[59]-annee5, detrend_indices[71]-annee6, detrend_indices[83]-annee7, detrend_indices[95]-annee8, detrend_indices[107]-annee9, detrend_indices[119]-annee10, detrend_indices[131]-annee11, detrend_indices[143]-annee12, detrend_indices[155]-annee13, detrend_indices[167]-annee14, detrend_indices[179]-annee15, detrend_indices[191]-annee16, detrend_indices[203]-annee17, detrend_indices[215]-annee18, detrend_indices[227]-annee19, detrend_indices[239]-annee20, detrend_indices[251]-annee21, detrend_indices[263]-annee22, detrend_indices[275]-annee23, detrend_indices[287]-annee24]) seas9 = np.mean([detrend_indices[24]-annee2, detrend_indices[36]-annee3, detrend_indices[48]-annee4, detrend_indices[60]-annee5, detrend_indices[72]-annee6, detrend_indices[84]-annee7, detrend_indices[96]-annee8, detrend_indices[108]-annee9, detrend_indices[120]-annee10, detrend_indices[132]-annee11, detrend_indices[144]-annee12, detrend_indices[156]-annee13, detrend_indices[168]-annee14, detrend_indices[180]-annee15, detrend_indices[192]-annee16, detrend_indices[204]-annee17, detrend_indices[216]-annee18, detrend_indices[228]-annee19, detrend_indices[240]-annee20, detrend_indices[252]-annee21, detrend_indices[264]-annee22, detrend_indices[276]-annee23, detrend_indices[288]-annee24]) seas10 = np.mean([detrend_indices[25]-annee2, detrend_indices[37]-annee3, detrend_indices[49]-annee4, detrend_indices[61]-annee5, detrend_indices[73]-annee6, detrend_indices[85]-annee7, detrend_indices[97]-annee8, detrend_indices[109]-annee9, detrend_indices[121]-annee10, detrend_indices[133]-annee11, detrend_indices[145]-annee12, detrend_indices[157]-annee13, detrend_indices[169]-annee14, detrend_indices[181]-annee15, detrend_indices[193]-annee16, detrend_indices[205]-annee17, detrend_indices[217]-annee18, detrend_indices[229]-annee19, detrend_indices[241]-annee20, detrend_indices[253]-annee21, detrend_indices[265]-annee22, detrend_indices[277]-annee23, detrend_indices[289]-annee24]) seas11 = np.mean([detrend_indices[26]-annee2, detrend_indices[38]-annee3, detrend_indices[50]-annee4, detrend_indices[62]-annee5, detrend_indices[74]-annee6, detrend_indices[86]-annee7, detrend_indices[98]-annee8, detrend_indices[110]-annee9, detrend_indices[122]-annee10, detrend_indices[134]-annee11, detrend_indices[146]-annee12, detrend_indices[158]-annee13, detrend_indices[170]-annee14, detrend_indices[182]-annee15, detrend_indices[194]-annee16, detrend_indices[206]-annee17, detrend_indices[219]-annee18, detrend_indices[230]-annee19, detrend_indices[242]-annee20, detrend_indices[254]-annee21, detrend_indices[266]-annee22, detrend_indices[278]-annee23, detrend_indices[290]-annee24]) seas12 = np.mean([detrend_indices[27]-annee2, detrend_indices[39]-annee3, detrend_indices[51]-annee4, detrend_indices[63]-annee5, detrend_indices[75]-annee6, detrend_indices[87]-annee7, detrend_indices[99]-annee8, detrend_indices[111]-annee9, detrend_indices[123]-annee10, detrend_indices[135]-annee11, detrend_indices[147]-annee12, detrend_indices[159]-annee13, detrend_indices[171]-annee14, detrend_indices[183]-annee15, detrend_indices[195]-annee16, detrend_indices[207]-annee17, detrend_indices[220]-annee18, detrend_indices[231]-annee19, detrend_indices[243]-annee20, detrend_indices[255]-annee21, detrend_indices[267]-annee22, detrend_indices[279]-annee23, detrend_indices[291]-annee24]) seas = [seas8, seas9, seas10, seas11, seas12, seas1, seas2, seas3, seas4, seas5, seas6, seas7, seas8, seas9, seas10, seas11, seas12, seas1, seas2, seas3, seas4, seas5, seas6, seas7, seas8, seas9, seas10, seas11, seas12, seas1, seas2, seas3, seas4, seas5, seas6, seas7, seas8, seas9, seas10, seas11, seas12, seas1, seas2, seas3, seas4, seas5, seas6, seas7, seas8, seas9, seas10, seas11, seas12, seas1, seas2, seas3, seas4, seas5, seas6, seas7, seas8] print(seas) fig = plt.figure(figsize=(13, 6)) #plt.plot(mois, indices, 'b-', linewidth=1) plt.plot(mois[11:], indices_diff_seas, 'g-', linewidth=2) plt.title("Série IPC corrigée de sa tendance désaisonnalisée par différenciation") plt.xlabel('Mois', fontsize=18) plt.ylabel('indice', fontsize=18) plt.grid(True)

prev_t = [a * slope + intercept for a in mois[300:]] prev_ts = [prev_t[i] + seas[i] for i in range(61)] fig_trend = plt.figure(figsize=(13, 6)) plt.plot(mois[300:], indices[300:], 'b--', linewidth=1) plt.plot(mois[300:], prev_ts, 'g-', linewidth=1) plt.title("Prévisions du modèle crée") plt.xlabel('Mois', fontsize=18) plt.ylabel('Incide', fontsize=18) plt.grid(True) plt.show erreur = np.mean([np.sqrt((a-b)**2) for a in prev_ts[:] for b in indices[300:]]) print("Racine de l'erreur au carré :", erreur)

import statsmodels.api as sm model = sm.tsa.statespace.SARIMAX(indices, order=(2,1,1),seasonnal_order=(0,0,0,12), trend=('ct')) res=model.fit() pred = res.get_prediction(start = 350, end = 362, dynamic = False, full_results=True) mois_prev = mois mois_prev=[a for a in range(363)] plt.figure(figsize=(13, 6)) plt.plot(mois[349:], indices[349:], 'b--', linewidth=2) plt.plot(mois_prev[350:],pred.predicted_mean[:], 'g-', linewidth=3) plt.title("Prévisions ARIMA (2,1,1)") plt.xlabel('Mois', fontsize=18) plt.ylabel('Indice', fontsize=18) plt.grid(True) plt.show erreur = np.mean([np.sqrt((a-b)**2) for a in pred.predicted_mean[:-1] for b in indices[349:]]) print("Racine de l'erreur au carré :", erreur)

train = indices[0:350] test = indices[350:] def preparation_data(data, lags=1): X, y = [], [] for row in range(len(data) - lags - 1): a = data[row:(row + lags)] X.append(a) y.append(data[row + lags]) return np.array(X), np.array(y) np.random.seed(1) scaler = MinMaxScaler(feature_range=(0, 1)) dataset = scaler.fit_transform(pd.DataFrame(indices)) train = dataset[0:300,] test = dataset[300:,] lags = 1 X_train, y_train = preparation_data(train, lags) X_test, y_test = preparation_data(test, lags) X_train = np.reshape(X_train, (X_train.shape[0], 1, X_train.shape[1])) X_test = np.reshape(X_test, (X_test.shape[0], 1, X_test.shape[1])) mdl = Sequential() mdl.add(Dense(12, input_shape=(1, lags), activation='relu')) mdl.add(LSTM(8, activation='relu')) mdl.add(Dense(1, activation='relu')) mdl.compile(loss='mean_squared_error', optimizer='adam') mdl.fit(X_train, y_train, epochs=100, batch_size=1, verbose=2) train_predict = mdl.predict(X_train) test_predict = mdl.predict(X_test) train_predict = scaler.inverse_transform(train_predict) y_train = scaler.inverse_transform(y_train) test_predict = scaler.inverse_transform(test_predict) y_test = scaler.inverse_transform(y_test) test_score = math.sqrt(mean_squared_error(y_test[:,0], test_predict[:,0])) print('Test Score: {:.2f} RMSE'.format(test_score))

predictions = [] for i in range(len(test_predict)): predictions.append(test_predict[i][0]) plt.figure(figsize=(13, 6)) plt.plot(mois[301:-1], test_predict, 'g-', linewidth=3) plt.plot(mois[250:-1], indices[250:-1], 'b--', linewidth=2) plt.title("Prévision IPC par LSTM à t+1") plt.xlabel('Mois', fontsize=18) plt.ylabel('Indice', fontsize=18) plt.grid(True) plt.show erreur = np.mean([np.sqrt((a-b)**2) for a in test_predict for b in indices[301:-1]]) print("Racine de l'erreur au carré :", erreur)

np.random.seed(1) scaler = MinMaxScaler(feature_range=(0, 1)) dataset = scaler.fit_transform(pd.DataFrame(indices)) train = dataset[0:300,] test = dataset[300:,] lags = 12 X_train, y_train = preparation_data(train, lags) X_test, y_test = preparation_data(test, lags) X_train = np.reshape(X_train, (X_train.shape[0], 1, X_train.shape[1])) X_test = np.reshape(X_test, (X_test.shape[0], 1, X_test.shape[1])) mdl = Sequential() mdl.add(Dense(12, input_shape=(1, lags), activation='relu')) mdl.add(LSTM(8, activation='relu')) mdl.add(Dense(1, activation='relu')) mdl.compile(loss='mean_squared_error', optimizer='adam') mdl.fit(X_train, y_train, epochs=100, batch_size=1, verbose=2) train_predict = mdl.predict(X_train) test_predict = mdl.predict(X_test) train_predict = scaler.inverse_transform(train_predict) y_train = scaler.inverse_transform(y_train) test_predict = scaler.inverse_transform(test_predict) y_test = scaler.inverse_transform(y_test) test_score = math.sqrt(mean_squared_error(y_test[:,0], test_predict[:,0])) print('Test Score: {:.2f} RMSE'.format(test_score))

predictions = [] for i in range(len(test_predict)): predictions.append(test_predict[i][0]) plt.figure(figsize=(13, 6)) plt.plot(mois[312:-1], test_predict, 'g-', linewidth=3) plt.plot(mois[250:-1], indices[250:-1], 'b--', linewidth=2) plt.title("Prévision IPC par LSTM à t+12") plt.xlabel('Mois', fontsize=18) plt.ylabel('Indice', fontsize=18) plt.grid(True) plt.show erreur = np.mean([np.sqrt((a-b)**2) for a in test_predict for b in indices[312:-1]]) print("Racine de l'erreur au carré : ", erreur)