Time Series Analysis

This course shall introduce data manipulation, numerical processing, data visualization, working with time-series data, analysis of time series data, forecasting and understanding ARIMA for forecasting. Topics include building, classifying, testing, and analyzing stochastic models for time series and describes their application in forecasting.

1 Introduction

1.1 Taxonomy of 5 Types of Time Series Forecasting Problems

1.2 Stochastic and Deterministic Dynamic Mathematical Models

1.3 Preparing Time Series Data for Supervised Learning

1.3 Basic Ideas in Model Building

1.4 Deep Learning Methods for Time Series Forecasting

PART ONE STOCHASTIC MODELS AND THEIR FORECASTING

2 Autocorrelation Function and Spectrum of Stationary Processes

2.1 Autocorrelation Properties of Stationary Models

2.2 Spectral Properties of Stationary Models

3 Linear Stationary Models

3.1 General Linear Process

3.2 Autoregressive Processes

3.3 Moving Average Processes

3.4 Mixed Autoregressive--Moving Average Processes

4 Linear Nonstationary Models

4.1 Autoregressive Integrated Moving Average Processes

4.2 Three Explicit Forms for the ARIMA Model

4.3 Integrated Moving Average Processes

5 Forecasting

5.1 Minimum Mean Square Error Forecasts and Their Properties

5.2 Calculating Forecasts and Probability Limits

5.3 Forecast Function and Forecast Weights

5.4 Examples of Forecast Functions and Their Updating

5.5 Use of State-Space Model Formulation for Exact Forecasting

5.6 Applications of Deep Learning Methods to Different Types of Time Series Forecasting Problems

PART TWO STOCHASTIC MODEL BUILDING

6 Model Identification

6.1 Objectives of Identification

6.2 Identification Techniques

6.3 Initial Estimates for the Parameters

6.4 Model Multiplicity

7 Parameter Estimation

7.1 Study of the Likelihood and Sum-of-Squares Functions

7.2 Nonlinear Estimation

7.3 Some Estimation Results for Specific Models

7.4 Likelihood Function Based on the State-Space Model

7.5 Estimation Using Bayes’ Theorem

7.6 Grid Search for Deep Learning Model Hyperparameters

8 Model Diagnostic Checking

8.1 Checking the Stochastic Model

8.2 Diagnostic Checks Applied to Residuals

8.3 Use of Residuals to Modify the Model

9 Analysis of Seasonal Time Series

9.1 Parsimonious Models for Seasonal Time Series

9.2 Representation of the Airline Data by a Multiplicative (0 1 1) × (0 1 1)12 Model

9.3 Some Aspects of More General Seasonal ARIMA Models

9.4 Structural Component Models and Deterministic Seasonal Components

9.5 Regression Models with Time Series Error Terms

• George E. P. Box, , Gwilym M. Jenkins, Gregory C. Reinsel, Greta M. Ljung. [2015]. Time Series Analysis: Forecasting and Control, 5th edition, Wiley Series in Probability and Statistics, Kindle Edition.

• Aileen Nielsen. [2019]. Practical Time Series Analysis: Prediction with Statistics and Machine Learning, 1st Edition, O’Reilly, Kindle Edition.

Ts. Dr. Yasmin Mohd Yacob