Time Series Forecasting

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.

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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.

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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.

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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.

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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).

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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).

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7. Applications

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

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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.

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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.