Overview

Reading and exercises in Time Series Analysis - spring 2024

The book is available here Time Series Analysis.

For each week the chapters or sections to be read is listed below.

Sample solutions are available here: Solutions. They are from the book website, but some been corrected a bit.

Week 1 - Introduction

• Chapter 1: Introduction
• Chapter 2 (not 2.8): Multivariate random variables
• Exercises
  • 2.1, 2.2, 2.3

Week 2 - Regression based methods, 1st part

• 3.1: Introduction
• 3.2: The General Linear Model, including OLS-, WLS-, and ML-estimates
• 3.3: Prediction in the General Linear Model
• Exercises
  • 3.1 (maybe try solve it by hand as in the book and then check result with a computer)
  • 3.4

Week 3 - Regression based methods, 2nd part

• 3.4 (not Example 3.6): Global and local trend models
• 3.5: Read cursory
• Exercises
  • 3.2 (Skip Q3): Note that $x_t$ is a scalar - define $X_t = [x_1 x_2 \ldots]^T$ as a vector. Also note that the covariance structure for X is the same for all questions.
  • 3.6: In this exercise it should read “90% prediction interval” instead of “90% confidence interval”.
  • 3.3 (if time allows)

Week 4 - Introduction to Stochastic Processes, Operators and Linear Systems

• 4.5: Shift operators (for understanding 5.3)
• 5.1 and 5.2: Stochastic processes in general
• 5.3 (only slightly touch 5.3.2): Linear processes
• Exercises
  • 5.1 (for c != 0) (Q2: see page 117 for MA(1) process)
  • 5.4
  • 5.7

Week 5 - AR, MA and ARMA processes

• 5.5 (disregard ‘spectra’ like (5.67), (5.72), (5.85), (5.86), (5.112)): MA, AR, and ARMA-processes
• 5.3.2: Cursory material
• 5.6: Non-stationary models
• 5.7: Optimal Prediction
• 6.4: Estimation of parameters in ARMA models
• Exercises
  • Identification game
  • 5.5
  • 5.6 (Assume that the process is stationary and invertible.)
  • 5.10 (if time allows. In Question 2 you are expected to find a recursion for gamma(k) for k>2. Skip Question 3.),

Week 6 - ACF and PACF with a focus on model order selection

Identification of univariate time series models, 1st part:

• 6.1 (with intro): Introduction
• 6.2.1 (and the introduction to 6.2 (Sec. 6.2.1 (a))): Estimation of auto-covariance and -correlation
• 6.3 (not 6.3.3): Using the SACF and SPACF for model order selection
• 6.5: Model order selection
• 6.6: Model validation
• Exercises
  • ARIMA model identification
  • 6.1
  • 6.6
  • Carry on with Assignment 2

Week 7 - Linear systems

• 4.1 (with intro): Linear Systems
• 4.4: You should disregard Theorem 4.10 and the following example. Furthermore, we shall not discuss Theorem 4.12 until we start to look at the multivariate time series.
• 6.2.2: Cross-correlation functions
• Chapter 8: Linear systems and stochastic processes
• Exercises
  • Using Linear Regression with ARMA-noise
  • 4.1 (Q. 1-2)
  • 8.2
  • 6.6

Week 8 - Multivariate time series

• Chapter 9
• Exercises
  • 9.1
  • 9.3 (Note that there is a typo in the table. It is the cross-correlations that are given (although it reads $\hat \gamma_{\alpha \beta}(k)$

Week 9 - MARIMA

Spliids method for parameter estimation in multi-variable ARMAX models.

• Have a look at the original paper (don’t go too much into details, it’s too cumbersome): Marima_paper
• Have a look at the marima R package vignette (again, don’t go into details): Marima_vignette

Exercises Work on Assignment3.

Week 10 - State space models 1st part

• 10.1: The Linear Stochastic State Space Model, Sec. 10.1
• 10.3: The Kalman filter
• Exercises
  • 10.1
  • Kalman filter

Week 11 - State space models 2nd part

• 10.4 (not 10.4.1): ARMA-models on state space form
• 10.6: ML-estimates of state space models
• Exercises
  • Follow up on ‘Kalman Filter’ exercise from last week (estimate the gravity in the “throw” model)
  • Estimation in state-space model
  • 10.2
  • 10.3

Week 12 - Recursive and adaptive estimation

• Chapter 11: Recursive and adaptive estimation

Execises:

• 10.4
• Get help on Assignment4

Week 13 - Final lecture

During the final lecture we will consider a number of real world problems and discuss what tools from the course can be used to solve them.

• Exercises
  • Get help on Assignment4