Introduction to Time Series Analysis

Time series analysis is a crucial skill for data scientists and analysts working with sequential data. Whether you're predicting stock prices, analyzing weather patterns, or forecasting sales, understanding how to handle time-dependent data is essential. In this blog post, we'll explore how to perform time series analysis using Scikit-learn in Python.

Setting Up Your Environment

Before we begin, make sure you have the necessary libraries installed:

import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
import matplotlib.pyplot as plt

Loading and Preprocessing Time Series Data

Let's start by loading a sample time series dataset:

# Load data
data = pd.read_csv('time_series_data.csv')
data['Date'] = pd.to_datetime(data['Date'])
data.set_index('Date', inplace=True)

Next, we'll create features from the time series:

def create_features(df):
    df['dayofweek'] = df.index.dayofweek
    df['quarter'] = df.index.quarter
    df['month'] = df.index.month
    df['year'] = df.index.year
    df['dayofyear'] = df.index.dayofyear
    return df

data = create_features(data)

Splitting the Data

When working with time series, it's important to maintain the temporal order of the data:

train = data.loc[data.index < '2022-01-01']
test = data.loc[data.index >= '2022-01-01']

FEATURES = ['dayofweek', 'quarter', 'month', 'year', 'dayofyear']
TARGET = 'Sales'

X_train = train[FEATURES]
y_train = train[TARGET]

X_test = test[FEATURES]
y_test = test[TARGET]

Applying Linear Regression

Let's start with a simple linear regression model:

scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

model = LinearRegression()
model.fit(X_train_scaled, y_train)

train_predictions = model.predict(X_train_scaled)
test_predictions = model.predict(X_test_scaled)

train_mse = mean_squared_error(y_train, train_predictions)
test_mse = mean_squared_error(y_test, test_predictions)

print(f"Train MSE: {train_mse}")
print(f"Test MSE: {test_mse}")

Visualizing the Results

Let's plot our predictions against the actual values:

plt.figure(figsize=(12, 6))
plt.plot(train.index, y_train, label='Train Actual')
plt.plot(train.index, train_predictions, label='Train Predicted')
plt.plot(test.index, y_test, label='Test Actual')
plt.plot(test.index, test_predictions, label='Test Predicted')
plt.legend()
plt.title('Time Series Forecast')
plt.show()

Advanced Techniques

While linear regression provides a good baseline, more advanced techniques can improve our predictions:

Random Forest Regressor

from sklearn.ensemble import RandomForestRegressor

rf_model = RandomForestRegressor(n_estimators=100, random_state=42)
rf_model.fit(X_train_scaled, y_train)

rf_train_predictions = rf_model.predict(X_train_scaled)
rf_test_predictions = rf_model.predict(X_test_scaled)

rf_train_mse = mean_squared_error(y_train, rf_train_predictions)
rf_test_mse = mean_squared_error(y_test, rf_test_predictions)

print(f"Random Forest Train MSE: {rf_train_mse}")
print(f"Random Forest Test MSE: {rf_test_mse}")

ARIMA with Scikit-learn

While Scikit-learn doesn't have built-in ARIMA models, we can combine it with statsmodels:

from statsmodels.tsa.arima.model import ARIMA
from sklearn.base import BaseEstimator, RegressorMixin

class ARIMAWrapper(BaseEstimator, RegressorMixin):
    def __init__(self, order=(1,1,1)):
        self.order = order
        
    def fit(self, X, y):
        self.model = ARIMA(y, order=self.order)
        self.result = self.model.fit()
        return self
    
    def predict(self, X):
        return self.result.forecast(steps=len(X))

arima_model = ARIMAWrapper(order=(1,1,1))
arima_model.fit(X_train, y_train)

arima_predictions = arima_model.predict(X_test)

arima_mse = mean_squared_error(y_test, arima_predictions)
print(f"ARIMA Test MSE: {arima_mse}")

Feature Importance

Understanding which features contribute most to our predictions can provide valuable insights:

feature_importance = pd.DataFrame({'feature': FEATURES, 'importance': rf_model.feature_importances_})
feature_importance = feature_importance.sort_values('importance', ascending=False)

plt.figure(figsize=(10, 6))
plt.bar(feature_importance['feature'], feature_importance['importance'])
plt.title('Feature Importance')
plt.xlabel('Features')
plt.ylabel('Importance')
plt.xticks(rotation=45)
plt.show()

Cross-Validation for Time Series

Traditional cross-validation doesn't work well for time series due to temporal dependencies. Instead, we can use time series cross-validation:

from sklearn.model_selection import TimeSeriesSplit

tscv = TimeSeriesSplit(n_splits=5)

cv_scores = []
for train_index, val_index in tscv.split(X_train):
    X_train_cv, X_val_cv = X_train.iloc[train_index], X_train.iloc[val_index]
    y_train_cv, y_val_cv = y_train.iloc[train_index], y_train.iloc[val_index]
    
    model = RandomForestRegressor(n_estimators=100, random_state=42)
    model.fit(X_train_cv, y_train_cv)
    
    predictions = model.predict(X_val_cv)
    mse = mean_squared_error(y_val_cv, predictions)
    cv_scores.append(mse)

print(f"Cross-validation MSE scores: {cv_scores}")
print(f"Average MSE: {np.mean(cv_scores)}")

Conclusion

In this blog post, we've explored various techniques for time series analysis using Scikit-learn in Python. We've covered data preprocessing, feature engineering, model building, and evaluation. By leveraging these tools and techniques, you can build powerful time series models for a wide range of applications.

Remember, time series analysis is a vast field, and there's always more to learn. Experiment with different models, feature engineering techniques, and preprocessing steps to find what works best for your specific time series problem.