Introduction to Time Series and Forecasting.

Preface 1 INTRODUCTION 1. 1 Examples of Time Series 1. 2 Objectives of Time Series Analysis 1. 3 Some Simple Time Series Models 1. 3. 3 A General Approach to Time Series Modelling 1. 4 Stationary Models and the Autocorrelation Function 1. 4. 1 The Sample Autocorrelation Function 1. 4. 2 A Model for the Lake Huron Data 1. 5 Estimation and Elimination of Trend and Seasonal Components 1. 5. 1 Estimation and Elimination of Trend in the Absence of Seasonality 1. 5. 2 Estimation and Elimination of Both Trend and Seasonality 1. 6 Testing the Estimated Noise Sequence 1. 7 Problems 2 STATIONARY PROCESSES 2. 1 Basic Properties 2. 2 Linear Processes 2. 3 Introduction to ARMA Processes 2. 4 Properties of the Sample Mean and Autocorrelation Function 2. 4. 2 Estimation of () and () 2. 5 Forecasting Stationary Time Series 2. 5. 3 Prediction of a Stationary Process in Terms of Infinitely Many Past Values 2. 6 The Wold Decomposition 1. 7 Problems 3 ARMA MODELS 3. 1 ARMA (p, q) Processes 3. 2 The ACF and PACF of an ARMA (p, q) Process 3. 2. 1 Calculation of the ACVF 3. 2. 2 The Autocorrelation Function 3. 2. 3 The Partial Autocorrelation Function 3. 3 Forecasting ARMA Processes 1. 7 Problems 4 SPECTRAL ANALYSIS 4. 1 Spectral Densities 4. 2 The Periodogram 4. 3 Time-Invariant Linear Filters 4. 4 The Spectral Density of an ARMA Process 1. 7 Problems 5 MODELLING AND PREDICTION WITH ARMA PROCESSES 5. 1 Preliminary Estimation 5. 1. 1 Yule-Walker Estimation 5. 1. 3 The Innovations Algorithm 5. 1. 4 The Hannan-Rissanen Algorithm 5. 2 Maximum Likelihood Estimation 5. 3 Diagnostic Checking 5. 3. 1 The Graph of =1, , n 5. 3. 2 The Sample ACF of the Residuals