1 Introduction

2 Stationarity
2.1 Stationary Stochastic Process
2.2 How to Test for Stationarity?

3 Time Series Decomposition
3.1 Objectives of Time Series Decomposition
3.2 Additive Decomposition - Non-Stationary Mean
3.3 Multiplicative Decomposition - Non-Stationary Variance
3.4 Mixed Decomposition - Non-Stationary Mean and Variance
3.5 Recapitulation for Time Series Decomposition Models
3.6 Time Series Decomposition and Prediction

4 Linear Time Series Models
4.1 Linear Autoregressive Model - AR(p)
4.2 Moving Average Model - MA(q)
4.3 Autoregressive Moving Average Model - ARMA(p, q)
4.4 Autoregressive Moving Average-based Models

5 Nonlinear Time Series Models
5.1 Polynomial Autoregressive Model - PAR(q, p)
5.2 Functional-Coefficient Autoregressive Model - FAR(p, k)
5.3 Markov Switching Autoregressive Model - MSAR(q, p)
5.4 Smooth Transition Autoregressive Model - STAR(p)
5.5 Autoregressive Conditional Heteroscedasticity - ARCH(p)

6 Deep Learning
6.1 Multilayer Perceptrons
6.2 Recurrent Neural Networks
6.3 Long Short-Term Memory Networks
6.4 Convolutional Neural Networks
6.5 Transformers

7 Time Series Model Evaluation
7.1 Model Diagnosis - Goodness-of-Fit
7.2 Out-of-Sample Forecast Performance

8 Available Implementations

9 Future Directions of Research
9.1 Conventional Models versus Deep Neural Models
9.2 Multivariate Framework
9.3 General Machine Learning Techniques to Enhance Conventional Methods
9.4 Beyond Time Series: Bivariate Processes
9.5 Dealing with Data Obsolescence

10 Glossary