Description
A time series is a set of numerical observations, each one being recorded at a specific time. Such data arise everywhere. This course aims to teach you how to analyze time series data (we will focus mostly on univariate time series data). There exist two main approaches to time series analysis: the Time Domain approach and the Frequency Domain approach. Approximately, about 70% of the course will be on time domain methods and 30% on frequency domain methods.
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Download full Syllabus from button above.
General Information
Lecture Topics and Readings in Shumway and Stoffer
Lecture 1 (8/24): Overview (Chapter 1.1--1.4)
Lecture 2 (8/29): Dependence, Noise Models, Correlogram (ACF). Parametric Detrending. (Chapter 1, Chapter 2.2)
Lecture 3 (8/31): Smoothing and Differencing. Additional EDA. (Chapter 2.3, 2.4).
Lecture 4 (9/5): Differencing and Seasonality. EDA wrapup. (Chapter 2.3).
Lecture 5 (9/7): Stationarity. (Chapter 1.5).
Lecture 6 (9/12): MA(\infty) and AR(1). (Chapter 3.2, from Example 3.1 through Definition 3.4; pp 86-90).
Lecture 7 (9/14): ARMA processes and polynomials. (Chapter 3.2, pp 92-100).
Lecture 8 (9/19): Polynomial roots and solutions. (Same reading as last).
Lecture 9 (9/21): Some review + difference equations. (Chapter 3.4 thru Example 3.13).
Lecture 10 (9/26): Examples
Lecture 11 (9/28): Sample ACF, Prediction (Appendix A, Theorem A.7)
Lecture 12 (10/3): Linear Prediction, PACF (Section 3.4, 3.5)
Lecture 13 (10/5): PACF + Estimation (Section 3.5, 3.6)
Lecture 14 (10/10): Estimation Wrapup
Class 15 (10/12): Midterm 1
Lecture 15 (10/17): Estimation Uncertainty in AR Models (Example 3.34)
Lecture 16 (10/19): ARMA Estimation + Inference (Section 3.6)
Lecture 17 (10/24): ARIMA, Forecasting, Diagnostics (Section 3.5, Section 3.7)
Lecture 18 (10/26): Analysis Examples + Seasonal ARIMA (Section 3.8, 3.9)
Lecture 20 (11/2): Frequency Domain Overview + DFT (Sections 4.1, 4.2, 4.4)
Lecture 21 (11/7): DFT + Periodogram (Section 4.2, 4.4)
Lecture 22 (11/9): DFT & ACVF + Process Representation (Section 4.2, 4.4)
Lectuer 23 (11/14): The Spectral Density (Section 4.3)
Lecture 2 (8/29): Dependence, Noise Models, Correlogram (ACF). Parametric Detrending. (Chapter 1, Chapter 2.2)
Lecture 3 (8/31): Smoothing and Differencing. Additional EDA. (Chapter 2.3, 2.4).
Lecture 4 (9/5): Differencing and Seasonality. EDA wrapup. (Chapter 2.3).
Lecture 5 (9/7): Stationarity. (Chapter 1.5).
Lecture 6 (9/12): MA(\infty) and AR(1). (Chapter 3.2, from Example 3.1 through Definition 3.4; pp 86-90).
Lecture 7 (9/14): ARMA processes and polynomials. (Chapter 3.2, pp 92-100).
Lecture 8 (9/19): Polynomial roots and solutions. (Same reading as last).
Lecture 9 (9/21): Some review + difference equations. (Chapter 3.4 thru Example 3.13).
Lecture 10 (9/26): Examples
Lecture 11 (9/28): Sample ACF, Prediction (Appendix A, Theorem A.7)
Lecture 12 (10/3): Linear Prediction, PACF (Section 3.4, 3.5)
Lecture 13 (10/5): PACF + Estimation (Section 3.5, 3.6)
Lecture 14 (10/10): Estimation Wrapup
Class 15 (10/12): Midterm 1
Lecture 15 (10/17): Estimation Uncertainty in AR Models (Example 3.34)
Lecture 16 (10/19): ARMA Estimation + Inference (Section 3.6)
Lecture 17 (10/24): ARIMA, Forecasting, Diagnostics (Section 3.5, Section 3.7)
Lecture 18 (10/26): Analysis Examples + Seasonal ARIMA (Section 3.8, 3.9)
Lecture 20 (11/2): Frequency Domain Overview + DFT (Sections 4.1, 4.2, 4.4)
Lecture 21 (11/7): DFT + Periodogram (Section 4.2, 4.4)
Lecture 22 (11/9): DFT & ACVF + Process Representation (Section 4.2, 4.4)
Lectuer 23 (11/14): The Spectral Density (Section 4.3)
| Name | Office Hours | |
|---|---|---|
Yannik Pitcan | When? Where? | |
Chelsea Zhang | When? Where? | |
Alexander D'Amour | When? Where? |