This time series textbook repository aims to cover the 20 areas listed below. I started building this repository on 30 August 2023; it is a work in progress.
-
Introduction to Time Series
- Definition and examples
- Components of time series: trend, seasonality, cyclical, and noise
-
Time Series Visualization
- Time plots
- Seasonal decomposition
-
Stationarity
- Definition and importance
- Dickey-Fuller test
-
Autocorrelation and Partial Autocorrelation
- ACF and PACF plots
-
Moving Averages
- Simple, weighted, and exponential
-
Smoothing Techniques
- Holt-Winters
- Exponential smoothing
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Decomposition Methods
- Additive and multiplicative models
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Linear Time Series Models
- AR (AutoRegressive)
- MA (Moving Average)
- ARMA (AutoRegressive Moving Average)
- ARIMA (AutoRegressive Integrated Moving Average)
-
Seasonal Models
- SARIMA (Seasonal ARIMA)
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Model Identification
- Selecting the order of differencing
- Identifying the order of AR or MA terms
- Model Estimation
- Maximum likelihood estimation
- Method of moments
- Model Diagnostic Checking
- Residual analysis
- Ljung-Box test
- Forecasting
- Point forecasts
- Interval forecasts
- Forecast Error Measures
- Mean Absolute Error (MAE)
- Mean Squared Error (MSE)
- Root Mean Squared Error (RMSE)
- Model Selection
- Information Criteria: AIC, BIC
- Multivariate Time Series
- Vector autoregressive models (VAR)
- ARCH and GARCH Models
- For modeling volatility
- Intervention Analysis
- Identifying and modeling outliers
- Machine Learning for Time Series
- Regression trees and Random Forest
- Neural networks
- Support vector machines
- Deep Learning for Time Series
- LSTM (Long Short-Term Memory)
- GRU (Gated Recurrent Units)
- Economics (GDP, inflation)
- Environment (temperature, precipitation)
- Medicine (disease incidence, vital signs)