It is the aim of this time series textbook repository to cover the 50 areas listed below. I started building this repository on 30 August 2023; it is a work in progress.
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Introduction to Time Series
- Definition and examples
- Components of time series: trend, seasonality, cyclical, and noise
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Time Series Visualization
- Time plots
- Seasonal decomposition
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Stationarity
- Definition and importance
- Dickey-Fuller test
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Autocorrelation and Partial Autocorrelation
- ACF and PACF plots
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Lag Operators
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Moving Averages
- Simple, weighted, and exponential
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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)
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Seasonal Models
- SARIMA (Seasonal ARIMA)
- 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)
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Cointegration and Error Correction Models
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State Space Models and the Kalman Filter
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ARCH and GARCH Models
- For modeling volatility
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Non-Linear Time Series Models
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Long Memory Models
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Intervention Analysis
- Identifying and modeling outliers
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Transfer Function Models
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Time Series Regression with ARIMA Errors
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Explanatory Variables in Time Series
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Spectral Analysis
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Wavelet Analysis
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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)
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Forecast Combination
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Hierarchical and Group Forecasting
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Ensemble Methods in Forecasting
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Real-time Forecasting
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High-frequency Data Analysis
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Bayesian Time Series Analysis
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Anomalies and Break Detection
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Functional Data Analysis
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Time Series Clustering and Classification
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Event Study Analysis
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Multiresolution Analysis
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Handling Missing Data in Time Series
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Time Series Cross-validation
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Stochastic Processes
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Markov Chains and Time Series
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Time Series Simulation
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Bootstrap Methods in Time Series
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Time Series in the Frequency Domain
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Panel Data Analysis
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Applications
- Finance (stock prices, exchange rates)
- Economics (GDP, inflation)
- Environment (temperature, precipitation)
- Medicine (disease incidence, vital signs)