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Time Series

8.1 Time Series and Key Concepts

Time series analysis is a technique for analyzing and forecasting data collected sequentially over time.

Key Concepts:

  • Trend: Long-term movement in data.
  • Seasonality: Regular patterns at fixed intervals.
  • Cyclic Patterns: Long-term fluctuations without fixed periodicity.
  • Stationarity: Constant mean and variance over time.
  • Autocorrelation: Correlation of data points with past values.
  • Noise: Random variations.

8.2 ARIMA, SARIMA, and Seasonal Decomposition

ARIMA (AutoRegressive Integrated Moving Average)

ARIMA consists of three components:

  • AR: Uses past values.
  • I: Differencing to remove trends.
  • MA: Uses past errors.
SARIMA (Seasonal ARIMA)

Handles seasonality with additional parameters (P, D, Q, m).

Seasonal Decomposition
  • Trend: Long-term direction.
  • Seasonal: Recurring patterns.
  • Residual: Irregular fluctuations.

8.3 Forecasting Models and Applications in Business

Forecasting Methods:
  • Naïve Method: Uses the last observed value.
  • Moving Average: Averages past 'n' values.
  • Exponential Smoothing: Assigns more weight to recent values.
  • ARIMA & SARIMA: Statistical models.
  • LSTM: Deep learning model.
Business Applications:
  • Retail Sales Forecasting
  • Stock Market Predictions
  • Demand Forecasting
  • Energy Consumption Forecasting

8.4 Evaluating Time Series Models

Evaluation Metrics:
  • Mean Absolute Error (MAE)
  • Mean Squared Error (MSE)
  • Root Mean Squared Error (RMSE)
  • Mean Absolute Percentage Error (MAPE)
  • AIC & BIC: Model selection criteria.
Residual Analysis:
  • Should be normally distributed.
  • Should have no autocorrelation.
  • Should have constant variance.

Interactive Features: Real-World Time Series Modeling

Example Datasets:
  • Stock Market Data
  • Retail Sales Data
  • Airline Passenger Data
  • Plot and decompose time series data.
  • Train ARIMA/SARIMA models.
  • Forecast future values.
  • Evaluate models using metrics.

Conclusion

Time series analysis is essential for forecasting in finance, business, and technology. Using ARIMA, SARIMA, and deep learning, we can make data-driven decisions.