• Assignment 1 

• Assignment 2 

• Assignment 3 

• Assignment 4 

Quiz 1 will be in class on February 5th (1 hour and 20 minutes). Please bring your student ID to the exam. The quiz will test all of the material up to and including Section 4 in the course notes. It will consist of long answer questions. You will be allowed one double-sided sheet of notes in the exam.

Practice problems for the quiz can be found here. Solutions to the practice problems will not be provided; please come talk with me in office hours if you want to work through any of the problems.

I recommend that you do the practice problems, review the homework questions, relevant sections in the textbook, and your notes in preparation for the quiz. 

Quiz 2 will be in class on March 12th (1 hour and 20 minutes). Please bring your student ID to the exam. The quiz will test all of the material up to and including the start of Section 10 in the course notes. The only material in Section 10 that is covered is the Yule Walker estimation procedure. The focus of the quiz material will be the material covered after quiz 1. The quiz will consist of long answer questions. You will be allowed one double-sided sheet of notes in the exam.

Practice problems for the quiz can be found here. Some problems appearing on the quiz will be similar, but not identical to, these practice problems. Solutions to the practice problems will not be provided; please come talk with me in office hours if you want to work through any of the problems.

I recommend that you do the practice problems, review the homework questions, relevant sections in the textbook, and your notes in preparation for the quiz. 

• Week 1:  Stochastic processes, time series, classical decomposition into trend + seasonal + noise components, strict and weak stationarity, autocovariance and autocorrelation functions and their properties, white noise, random walks.  

• Week 2: Computing the ACVF for an MA(q) and the AR(1) process, bias and variance of the sample mean, sample autocovariance function, asymptotic distribution of the sample autocorrelation of white noise, beginning of discussion on OLS regression for a mean function with trends or periodicity. 

• Week 3: More on OLS and GLS regression, smoothing time series via a window smoother and kernel smoothers, the backshift operator, differencing, seasonal differencing,  revisiting the MA(q) process in terms of backshifts, discussion on the identifiability of MA processes.  

• Week 4: Inverting the AR(p) polynomial, convergence of linear filters applied to stationary processes, existence of stationary AR(p) solutions, roots of the AR(p) polynomial. 

• Week 5: Finding stationary solutions to the ARMA equations. Causality of ARMA processes and how it is related to the roots of the AR polynomial.

• Week 6: Computation of the ACVF for ARMA processes by solving a linear system of equations via multiplying the ARMA equation by X_{t-k}. An introduction to finding the best predictors and the best linear predictors of a random variable given a random vector.

• Week 7: Reading week

• Week 8: Examples of finding the BLPs for AR and MA processes. Prediction intervals under Gaussianity. Backcasting and the fact that the backcasting regression coefficients equal the forecasting regression coefficients in a reversed order. Partial autocorrelation and its interpretation as correlation in a conditional distribution under Gaussianity. The PACF function and its behavior for AR, MA and ARMA processes.

• Week 9: The sample PACF. Theory on the asymptotic distribution of the sample ACF (Bartlett's formula) and on the asymptotic distribution of the sample PACF for MA and AR processes respectively. The Durbin-Levinson algorithm and how it speeds up predictions. The definition of innovations and a brief discussion of the innovations algorithm. Predictions using the infinite past and the resulting prediction error. Yule-Walker equations and estimates for AR(p) processes. The asymptotic distribution of the Yule-Walker estimates and forming asymptotic confidence intervals for the AR parameters using this asymptotic distribution. The similarities between the Yule-Walker estimates and the coefficients appearing in a best linear predictor.  

• Week 10: (Quiz 2) Closed-form solutions via least squares for maximum likelihood estimates using the conditional likelihood for AR(p) processes. The challenge of obtaining closed-form solutions for general ARMA processes. A brief discussion on the Newton-Raphson method for optimization.  The asymptotic distribution of the ARMA MLEs. 

• Week 12: 

• Week 13: 

• Week 14:   

• Introduction R Code  

• Smoothing and Differencing R Code 

• Simulating AR and MA R Code 

• Simulating ARMA Models and Making Predictions 

• The Frequency Domain: Estimating and Examining Periodograms and Spectral Densities 

Course Description: Stationary series, spectral analysis, models in time series: autoregressive, moving average, ARMA and ARIMA. Smoothing series, computational techniques and computer packages for time series.

Prerequisites: STAT 372 and 378. 

Grading:

Grade breakdown

• 5 assignments for 35% of the total grade. The lowest assignment grade is dropped.

• 2 quizzes, each worth 15%.

• The final exam is worth 35%.

Assignments: All assignments are to be submitted on Canvas. You may scan handwritten solutions or write up solutions in LaTeX (preferred). If you choose to write up your solutions by hand please make sure that they are legible. For coding questions please submit relevant code chunks and output as part of your solution, while also including your raw code in a separate file. Assignments are meant to be completed individually without the assistance from your peers or generative AI models.

Late policy: 25% is subtracted from the grade of a given assignment for every day that this assignment is late. Assignments are due at 11:59 PM MST on the day indicated in the syllabus. 

Resources:

Textbooks:

There is no required textbook for this course. However, we will loosely be following 

Time Series Analysis and its Applications by Shumway and Stoffer (2009). This book can be downloaded here.

Two other books that may be useful are:

Introduction to Time Series and Forecasting by Brockwell and Davis (2016). This book can be downloaded here.

Time Series: Theory and Methods by Brockwell and Davis (1991). This book can be downloaded here. 

The former book is another introductory book on time series. The latter book is more advanced, but is a classic.

Software: We will be using R throughout this course. Coding portions of assignments should be done in R. 

Other resources: Professor Adam Kashlak taught a previous version of this course. His lecture recordings and course notes are bound to be helpful and can be found here and here respectively. The material covered in this version of the course will be similar, but not identical, to the material covered by Professor Kashlak. 

Class Time, Office Hours, and Contact Information:

Class time: Tuesdays and Thursdays, 9:30-10:50 AM, GSB 8-59.

Office hours: Tuesdays and Thursdays, 10:50-11:50 AM, CAB 475. 

My email is: mccorma2[AT]ualberta[DOT]ca