1. What is a Time Series?

  • A time series = sequence of data points collected over time at regular intervals.
    • Examples: stock prices, weather data, energy demand, website traffic.
  • Goal: understand past patterns and predict future values.

2. Time Series Forecasting

  • Forecasting = using historical data to predict future observations.
  • Different from regular regression:
    • Observations are ordered in time.
    • Values are often correlated with past values (autocorrelation).
    • Seasonality and trends must be considered.

3. Components of a Time Series

  1. Trend – long-term increase/decrease in data.
  2. Seasonality – repeating patterns (e.g., daily, weekly, yearly).
  3. Cyclic patterns – irregular cycles (business cycles).
  4. Noise – random variation not explained by the above.

A forecasting model tries to separate these components.

4. Methods for Forecasting

A. Statistical Models

  • ARIMA (AutoRegressive Integrated Moving Average)
    • Captures autoregression (past values), differencing (trend removal), moving average (error terms).
  • SARIMA – ARIMA + seasonality.
  • Exponential Smoothing (ETS, Holt-Winters)
    • Weights recent observations more strongly.
  • State Space Models (Kalman filters).

B. Machine Learning Models

  • Regression-based: Use lagged variables as features.
  • Tree models: Random Forests, XGBoost (need feature engineering).
  • Support Vector Regression (SVR).

C. Deep Learning Models

  • RNNs (Recurrent Neural Networks): Good for sequential data.
  • LSTMs/GRUs: Handle long-term dependencies.
  • Temporal CNNs.
  • Transformers (e.g., Informer, TFT): State-of-the-art for large-scale forecasting.

5. Forecasting Process

  1. Exploratory Data Analysis (EDA): plot, check stationarity, autocorrelation (ACF/PACF).
  2. Preprocessing:
    • Handle missing values.
    • Normalize or scale data.
    • Transform if needed (log to stabilize variance).
  3. Model Selection: choose ARIMA, LSTM, etc.
  4. Training: fit model on historical data.
  5. Validation: use rolling window or walk-forward validation (not random split).
  6. Forecasting: predict next kkk steps (point forecasts or intervals).

6. Example (Simple)

Suppose monthly sales:
[120, 135, 150, 160, 145, 170, …]

  • Trend: upward.
  • Seasonality: higher sales in holiday months.
  • Forecast: next month ~ 180 (based on model).

7. Applications

  • Finance: stock, currency prediction.
  • Energy: electricity load forecasting.
  • Retail: demand forecasting.
  • Healthcare: patient flow, disease outbreaks.
  • Web: server load, traffic prediction.

8. Challenges

  • Non-stationarity: mean/variance changes over time.
  • Noise and anomalies: unpredictable shocks (COVID-19, market crashes).
  • Multiple series: need hierarchical or multivariate forecasting.
  • Accuracy vs Interpretability: deep learning may be accurate but hard to explain.

Summary:
Time series forecasting = predicting future values based on past data. Traditional methods (ARIMA, ETS) handle trend/seasonality well, while machine learning and deep learning (LSTM, Transformers) are powerful for complex patterns. Core challenges include non-stationarity, noise, and choosing the right validation scheme.