Prédiction du cours boursier

Objectif

• prédire le cours boursier à horizon 60 jours

• comparer les modèles

Modèles choisis

• ARMA

• SARIMA

• XGBoost

• Extra Trees (variante de Random Forest)

• Support Vector Machine (SVM)

• Prophet

Tableau. Modèles de prédiction

Modèle	Detrend	Saisonnalité	Type
ARMA	Moyenne mobile linéaire	Moyenne mobile linéaire	Série temporelle
SARIMA	Moyenne mobile linéaire	Moyenne mobile linéaire	Série temporelle
XGBoost	Régression linéaire	Mensuelle	Machine Learning
ExtraTrees	Régression linéaire	Mensuelle	Machine Learning
Support Vector Machine	Régression linéaire	Mensuelle	Machine Learning
Prophet	Pas de detrend	Automatique	Autre

Critères d’évaluation

• train / test split (test = 60 jours)

• AIC

• MSE

• graphiquement (la courbe ne doit pas faire “n’importe quoi”)

Imports

import matplotlib.dates as mdates
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import xgboost
from prophet import Prophet
from sklearn.ensemble import ExtraTreesRegressor
from sklearn.linear_model import LinearRegression
from sklearn.svm import SVR

from src.data.load_data import load_processed_data, load_stock_data
from src.regression.models.machine_learning_detrend import detrend_prediction
from src.regression.models.sarima import sarimax
from src.regression.plot import true_vs_prediction
from src.regression.training.metrics import compute_metrics
from src.utils.misc import init_notebook

init_notebook()

detrend_linear_ma_window100 = "detrend/LinearMADetrend/window-100"
stock_name = "AAPL"

df_detrend = load_processed_data(stock_name, detrend_linear_ma_window100)

df_detrend.head()

	Open	High	Low	Close	Adj Close	Volume
Date
2019-01-02	-2.636750	-1.646748	-2.801751	-1.879250	-3.465916	148158800
2019-01-03	-5.465638	-5.030637	-5.960637	-5.913137	-7.341764	365248800
2019-01-04	-5.434760	-4.429759	-5.617259	-4.502261	-5.991877	234428400
2019-01-07	-4.487831	-4.455330	-5.187832	-4.680332	-6.166622	219111200
2019-01-08	-4.372408	-3.807405	-4.632406	-4.074907	-5.589533	164101200

prediction_results_dict = {}

SARIMA

price_detrend = df_detrend["Close"]

Train test split

train_test_split_date = pd.Timestamp("2021-10-01")
train, test = (
    price_detrend[price_detrend.index <= train_test_split_date],
    price_detrend[price_detrend.index > train_test_split_date],
)

model = sarimax(train)
result = model.fit()

/home/runner/work/stock-analysis/stock-analysis/.venv/lib/python3.13/site-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
/home/runner/work/stock-analysis/stock-analysis/.venv/lib/python3.13/site-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)

/home/runner/work/stock-analysis/stock-analysis/.venv/lib/python3.13/site-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "

print(result.summary())

                               SARIMAX Results                                
==============================================================================
Dep. Variable:                  Close   No. Observations:                  694
Model:             SARIMAX(10, 0, 10)   Log Likelihood               -1419.635
Date:                Wed, 15 Oct 2025   AIC                           2881.270
Time:                        12:40:12   BIC                           2976.662
Sample:                             0   HQIC                          2918.160
                                - 694                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1          0.9860      0.112      8.769      0.000       0.766       1.206
ar.L2         -0.0215      0.091     -0.236      0.813      -0.200       0.157
ar.L3          0.0526      0.095      0.551      0.582      -0.134       0.240
ar.L4         -0.0071      0.093     -0.077      0.939      -0.189       0.174
ar.L5         -0.0374      0.081     -0.459      0.646      -0.197       0.122
ar.L6          0.0583      0.091      0.638      0.524      -0.121       0.237
ar.L7         -0.0317      0.091     -0.349      0.727      -0.210       0.146
ar.L8         -0.1617      0.083     -1.938      0.053      -0.325       0.002
ar.L9          0.9649      0.111      8.717      0.000       0.748       1.182
ar.L10        -0.8306      0.086     -9.655      0.000      -0.999      -0.662
ma.L1         -0.1299      0.119     -1.095      0.274      -0.362       0.103
ma.L2         -0.0127      0.093     -0.137      0.891      -0.195       0.169
ma.L3         -0.0716      0.090     -0.797      0.426      -0.248       0.105
ma.L4         -0.0788      0.104     -0.758      0.448      -0.283       0.125
ma.L5          0.0334      0.100      0.333      0.739      -0.163       0.230
ma.L6         -0.0906      0.091     -0.997      0.319      -0.269       0.088
ma.L7         -0.0072      0.106     -0.068      0.946      -0.215       0.201
ma.L8          0.1326      0.100      1.331      0.183      -0.063       0.328
ma.L9         -0.8112      0.103     -7.841      0.000      -1.014      -0.608
ma.L10         0.1090      0.043      2.560      0.010       0.026       0.192
sigma2         3.5329      0.138     25.571      0.000       3.262       3.804
===================================================================================
Ljung-Box (L1) (Q):                   0.00   Jarque-Bera (JB):               432.17
Prob(Q):                              0.95   Prob(JB):                         0.00
Heteroskedasticity (H):               6.79   Skew:                             0.01
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.87
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).

forecast_steps = len(test)
forecast = result.get_forecast(steps=forecast_steps)
predicted_values = forecast.predicted_mean

/home/runner/work/stock-analysis/stock-analysis/.venv/lib/python3.13/site-packages/statsmodels/tsa/base/tsa_model.py:837: ValueWarning: No supported index is available. Prediction results will be given with an integer index beginning at `start`.
  return get_prediction_index(
/home/runner/work/stock-analysis/stock-analysis/.venv/lib/python3.13/site-packages/statsmodels/tsa/base/tsa_model.py:837: FutureWarning: No supported index is available. In the next version, calling this method in a model without a supported index will result in an exception.
  return get_prediction_index(

plot_n_days_prior_pred = 2 * forecast_steps

plt.plot(train[-plot_n_days_prior_pred:], label="Original training price")
plt.plot(test, label="Original test price")
plt.plot(test.index, predicted_values, label="SARIMA predictions")
plt.title("SARIMA predictions for Apple stock price")
plt.legend()


# Display limited number of date index
plt.gca().xaxis.set_major_locator(mdates.MonthLocator(interval=3))
# Rotate x-axis labels
plt.gcf().autofmt_xdate()

plt.show()

Prédiction du prix d’Apple à 2 mois

Recomposons les prédictions du modèle SARIMA pour la stochasticité avec la tendance pour obtenir une prévision du cours d’Apple.

original_data = load_stock_data(stock_name)

# Get only close price
original_price = original_data["Close"]

# Train test split
original_data_train, original_data_test = (
    original_price[original_price.index <= train_test_split_date],
    original_price[original_price.index > train_test_split_date],
)

# Drop time index in order to vanish weekend days issues
original_data_train.reset_index(drop=True, inplace=True)
original_data_test.reset_index(drop=True, inplace=True)

Tendance

On reconstruit la tendance que l’on avait prédite par la méthode de la moyenne mobile.

for i in range(forecast_steps):
    rolling_mean = original_data_train.rolling(window=100, center=False).mean()
    pred_trend = rolling_mean.iloc[-1]
    pred_index = original_data_train.index[-1] + 1
    original_data_train = pd.concat(
        [original_data_train, pd.Series([pred_trend], index=[pred_index])]
    )

plt.plot(original_data_train.iloc[-300:-forecast_steps], label="Original price")
plt.plot(
    original_data_train.iloc[-forecast_steps:],
    label="Predicted trend price",
)
plt.legend()

<matplotlib.legend.Legend at 0x7f3a93385310>

Saisonnalité et stochasticité

# Make SARIMA predicted values begin at zero
predicted_values -= predicted_values.iloc[0]

# Calculate trend + ARIMA
add_components = original_data_train.iloc[-forecast_steps] + predicted_values

# Put predicted data in train series set
original_data_train.iloc[-forecast_steps:] = add_components

Evaluation de la prédiction

# Set index for test data i.e. actual data
original_data_test.index = original_data_train.index[-forecast_steps:]

plt.plot(
    original_data_train.iloc[-200:-forecast_steps], color="blue", label="Original price"
)
plt.plot(
    original_data_train.iloc[-forecast_steps:],
    color="red",
    label="Predicted price with trend + seasonality + stochasticity",
)
plt.plot(original_data_test, color="green", label="Actual price")
plt.legend()

<matplotlib.legend.Legend at 0x7f3a90169450>

y_true = original_data_test
y_pred = original_data_train[-forecast_steps:]

prediction_results_dict["SARIMA"] = compute_metrics(y_true, y_pred)
prediction_results_dict["SARIMA"]

(10.698355198814452, 13.862575751530015)

XGBoost

Traitement des données

type(original_data)

pandas.core.frame.DataFrame

train_start = pd.Timestamp("2019-01-01")
train_end = pd.Timestamp("2021-10-01")

df_train = original_data.loc[train_start:train_end].copy()
df_test = original_data.loc[train_end:].copy()

type(df_train)
df_train["time_dummy"] = np.arange(len(df_train))
df_train

	Open	High	Low	Close	Adj Close	Volume	time_dummy
Date
2019-01-02	38.722500	39.712502	38.557499	39.480000	37.943256	148158800	0
2019-01-03	35.994999	36.430000	35.500000	35.547501	34.163822	365248800	1
2019-01-04	36.132500	37.137501	35.950001	37.064999	35.622250	234428400	2
2019-01-07	37.174999	37.207500	36.474998	36.982498	35.542965	219111200	3
2019-01-08	37.389999	37.955002	37.130001	37.687500	36.220528	164101200	4
...	...	...	...	...	...	...	...
2021-09-27	145.470001	145.960007	143.820007	145.369995	143.707413	74150700	689
2021-09-28	143.250000	144.750000	141.690002	141.910004	140.286987	108972300	690
2021-09-29	142.470001	144.449997	142.029999	142.830002	141.196472	74602000	691
2021-09-30	143.660004	144.380005	141.279999	141.500000	139.881668	89056700	692
2021-10-01	141.899994	142.919998	139.110001	142.649994	141.018539	94639600	693

694 rows × 7 columns

df_train["time_dummy"] = np.arange(len(df_train))
df_test["time_dummy"] = np.arange(len(df_test)) + len(df_train)
df_train["day"] = df_train.index.day
df_test["day"] = df_test.index.day

df_train["time_dummy"].tail()

Date
2021-09-27    689
2021-09-28    690
2021-09-29    691
2021-09-30    692
2021-10-01    693
Name: time_dummy, dtype: int64

df_test["time_dummy"].head()

Date
2021-10-01    694
2021-10-04    695
2021-10-05    696
2021-10-06    697
2021-10-07    698
Name: time_dummy, dtype: int64

x_col = ["time_dummy", "day"]
y_col = ["Close"]

x_train = df_train[x_col]
y_train = df_train[y_col]

x_test = df_test[x_col]
y_test = df_test[y_col]

Apprentissage des modèles

lr = LinearRegression()
lr.fit(x_train, y_train)
y_residuals = y_train - lr.predict(x_train)

xgb = xgboost.XGBRegressor(random_state=0, n_jobs=-2, colsample_bytree=0.3, max_depth=3)
xgb.fit(x_train, y_residuals)

XGBRegressor(base_score=None, booster=None, callbacks=None,
             colsample_bylevel=None, colsample_bynode=None,
             colsample_bytree=0.3, device=None, early_stopping_rounds=None,
             enable_categorical=False, eval_metric=None, feature_types=None,
             feature_weights=None, gamma=None, grow_policy=None,
             importance_type=None, interaction_constraints=None,
             learning_rate=None, max_bin=None, max_cat_threshold=None,
             max_cat_to_onehot=None, max_delta_step=None, max_depth=3,
             max_leaves=None, min_child_weight=None, missing=nan,
             monotone_constraints=None, multi_strategy=None, n_estimators=None,
             n_jobs=-2, num_parallel_tree=None, ...)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

y_pred_train = detrend_prediction(xgb, lr, x_train)
y_pred_test = detrend_prediction(xgb, lr, x_test)
prediction_results_dict["XGBoost"] = compute_metrics(y_test, y_pred_test)
prediction_results_dict["XGBoost"]

(9.821550637003275, 13.252235166510234)

_ = true_vs_prediction(
    df_train["Close"],
    y_pred_train,
    true_label="Train set",
    prediction_label="XGBoost + Linear Regression",
)

_ = true_vs_prediction(
    df_test["Close"],
    y_pred_test,
    true_label="Test set",
    prediction_label="XGBoost + Linear Regression",
)

true_vs_prediction(
    df_test["Close"],
    y_pred_test,
    true_label="Test set",
    prediction_label="XGBoost + Linear Regression",
)
plt.plot(df_train["Close"], label="Train set")
plt.legend()

<matplotlib.legend.Legend at 0x7f3a900e6d50>

Extra Trees

Apprentissage des modèles

et = ExtraTreesRegressor(random_state=0, n_jobs=-2)
et.fit(x_train, y_residuals)

/home/runner/work/stock-analysis/stock-analysis/.venv/lib/python3.13/site-packages/sklearn/base.py:1365: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples,), for example using ravel().
  return fit_method(estimator, *args, **kwargs)

ExtraTreesRegressor(n_jobs=-2, random_state=0)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

y_pred_test = detrend_prediction(et, lr, x_test)
prediction_results_dict["ExtraTrees"] = compute_metrics(y_test, y_pred_test)
prediction_results_dict["ExtraTrees"]

(9.74557499696818, 13.20182282007082)

_ = true_vs_prediction(
    df_test["Close"],
    y_pred_test,
    true_label="Test set",
    prediction_label="ExtraTrees + Linear Regression",
)

SVM

Apprentissage des modèles

svr = SVR()
svr.fit(x_train, y_residuals)

/home/runner/work/stock-analysis/stock-analysis/.venv/lib/python3.13/site-packages/sklearn/utils/validation.py:1406: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  y = column_or_1d(y, warn=True)

SVR()

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

y_pred_test = detrend_prediction(svr, lr, x_test)
prediction_results_dict["Support Vector Machine"] = compute_metrics(y_test, y_pred_test)
prediction_results_dict["Support Vector Machine"]

(8.73950426028892, 10.297525832287155)

_ = true_vs_prediction(
    df_test["Close"],
    y_pred_test,
    true_label="Test set",
    prediction_label="Support Vector + Linear Regression",
)

Prophet

Pré-traitement pour Prophet

x_train_prophet = pd.DataFrame(
    {
        "ds": x_train.index,
        "y": df_train["Close"].values,
    }
)

x_test_prophet = pd.DataFrame(
    {
        "ds": x_test.index,
        "y": df_test["Close"].values,
    }
)

x_test_prophet.head()

	ds	y
0	2021-10-01	142.649994
1	2021-10-04	139.139999
2	2021-10-05	141.110001
3	2021-10-06	142.000000
4	2021-10-07	143.289993

Prédiction

Calcul de la prédiction

model = Prophet()
model.fit(x_train_prophet)

12:40:14 - cmdstanpy - INFO - Chain [1] start processing

12:40:14 - cmdstanpy - INFO - Chain [1] done processing

<prophet.forecaster.Prophet at 0x7f3a974db8c0>

forecast = model.predict(x_test_prophet)
forecast[["ds", "yhat", "yhat_lower", "yhat_upper"]].tail()

	ds	yhat	yhat_lower	yhat_upper
58	2021-12-23	163.485849	157.429297	169.888856
59	2021-12-27	164.851525	158.423615	171.336812
60	2021-12-28	165.169482	158.395403	171.728886
61	2021-12-29	165.506546	159.233661	171.649162
62	2021-12-30	165.524170	159.169593	172.744326

prediction_results_dict["Prophet"] = compute_metrics(
    x_test_prophet["y"], forecast["yhat"]
)
prediction_results_dict["Prophet"]

(7.378329691676633, 9.228347960218333)

Affichage de la prédiction

fig, ax1 = plt.subplots(figsize=(10, 10))
fig1 = model.plot(forecast, ax=ax1)
# plt.scatter(forecast["ds"],df_test["Close"], color="orange", s=10, label="Close")
df_test["Close"].plot(ax=ax1, color="orange")
plt.legend()

/home/runner/work/stock-analysis/stock-analysis/.venv/lib/python3.13/site-packages/pandas/plotting/_matplotlib/core.py:981: UserWarning: This axis already has a converter set and is updating to a potentially incompatible converter
  return ax.plot(*args, **kwds)

<matplotlib.legend.Legend at 0x7f3a97526d50>

Animation

# Tailwind CSS colors
sky600 = "#0084d1"
orange600 = "#f54900"

import matplotlib.animation as animation
import matplotlib.dates as mdates

x = np.array(range(len(forecast["ds"])))
y_pred = forecast["yhat"]
y_lower = forecast["yhat_lower"]
y_upper = forecast["yhat_upper"]
x_dates = forecast["ds"]
x = mdates.date2num(x_dates)

y_true = x_test_prophet["y"]

xmin, xmax, ymin, ymax = np.min(x), np.max(x), np.min(y_pred), np.max(y_pred)

import seaborn as sns

sns.set_theme(context="talk", style="ticks", rc={"axes.grid": True})

fig = plt.figure(figsize=(8, 6), dpi=75)

plt.title("Apple (AAPL) prediction with Prophet")
plt.xlabel("Date")
plt.ylabel("Stock close price (daily)")
plt.gca().xaxis.set_major_formatter(mdates.DateFormatter("%Y-%m-%d"))
plt.gcf().autofmt_xdate()

# initialise la figure
(line_pred,) = plt.plot(
    [],
    [],
    label="Prediction",
    marker="o",
    markersize=5,
)
(line_pred_upper,) = plt.plot(
    [], [], label="Prediction confidence interval", color="blue", alpha=0.2
)
(line_pred_lower,) = plt.plot([], [], color="blue", alpha=0.2)
(line_true,) = plt.plot(
    [],
    [],
    label="True value",
    ls="none",
    marker="+",
    markersize=10,
    color="gray",
    markeredgewidth=1.5,
)

(point_pred,) = plt.plot([], [], ls="none", marker="o", color=sky600)
(point_true,) = plt.plot([], [], ls="none", marker="+", markersize=10, color="gray")

plt.legend(loc="upper left", fontsize=12)

plt.xlim(xmin, xmax)
plt.ylim(ymin, ymax)

padding_x = 5
padding_y = 10


def animate(i: int):
    x_data = x[: i + 1]
    y_data = (y_pred[: i + 1], y_true[: i + 1], y_upper[: i + 1], y_lower[: i + 1])
    xmin, xmax, ymin, ymax = (
        np.min(x_data) - padding_x / 10,
        np.max(x_data) + padding_x,
        np.min(np.concatenate(y_data)) - padding_y,
        np.max(np.concatenate(y_data)) + padding_y,
    )
    plt.xlim(xmin, xmax)
    plt.ylim(ymin, ymax)

    point_pred.set_data(x[i - 1 : i], y_pred[i - 1 : i])
    line_pred.set_data(x[:i], y_pred[:i])
    line_pred_upper.set_data(x[:i], y_upper[:i])
    line_pred_lower.set_data(x[:i], y_lower[:i])

    point_true.set_data(x[i - 1 : i], y_true[i - 1 : i])
    line_true.set_data(x[:i], y_true[:i])

    return line_pred, line_true


ani = animation.FuncAnimation(
    fig, animate, frames=len(x), interval=1, blit=True, repeat=False
)
ani.save("assets/img/prophet-prediction.gif")

MovieWriter ffmpeg unavailable; using Pillow instead.

plt.rcParams["axes.prop_cycle"].by_key()["color"]

[(0.2980392156862745, 0.4470588235294118, 0.6901960784313725),
 (0.8666666666666667, 0.5176470588235295, 0.3215686274509804),
 (0.3333333333333333, 0.6588235294117647, 0.40784313725490196),
 (0.7686274509803922, 0.3058823529411765, 0.3215686274509804),
 (0.5058823529411764, 0.4470588235294118, 0.7019607843137254),
 (0.5764705882352941, 0.47058823529411764, 0.3764705882352941),
 (0.8549019607843137, 0.5450980392156862, 0.7647058823529411),
 (0.5490196078431373, 0.5490196078431373, 0.5490196078431373),
 (0.8, 0.7254901960784313, 0.4549019607843137),
 (0.39215686274509803, 0.7098039215686275, 0.803921568627451)]

Décomposition

fig2 = model.plot_components(forecast)

Comparaison des modèles

prediction_results_df = pd.DataFrame(prediction_results_dict).T
prediction_results_df.columns = ["RMSE", "MAE"]
# prediction_results_df

prediction_results_df.plot(kind="bar")
plt.title("Comparaison des modèles de prédiction")

plt.xticks(rotation=45, ha="right")

(array([0, 1, 2, 3, 4]),
 [Text(0, 0, 'SARIMA'),
  Text(1, 0, 'XGBoost'),
  Text(2, 0, 'ExtraTrees'),
  Text(3, 0, 'Support Vector Machine'),
  Text(4, 0, 'Prophet')])

# print(prediction_results_df.to_markdown())

Tableau. Comparaison des modèles de prédiction

	RMSE	MAE	Graphiquement
ARMA	17.3524	14.9797	✅
SARIMA	13.6817	11.6047	✅
XGBoost	13.2914	9.85264	✅
ExtraTrees	13.2018	9.74557	✅
Support Vector Machine	10.2975	8.7395	❌
Prophet	8.97155	7.26206	✅

Meilleur modèle : Prophet