The main objective of this course is to develop the skills needed to do work in the industry or empirical research in fields operating with time series data. The course aims to provide students with techniques and receipts for estimation and assessment of quality of economic models with time series data. Special attention will be placed on limitations and pitfalls of different methods and their potential fixes. The course will also emphasize recent developments in Time Series Analysis and will present some open questions and areas of ongoing research. We will be using the software R, but students can do their homework using their own software.

The evaluation will be based on the final take-home exam (100% of the final grade). In addition, the students are expected to spend a significant amount of their time working on the theoretical homeworks and the applied homeworks. Serious and consistent work will count in the final grade (i.e. adding a positive bias).

The final take-home exam is available here . Please email me your work by Wednesday 2017/01/24 23:59pm.

The class follows Time Series Analysis (from J.D Hamilton) book content. We aim to cover Ch. 3-5 and Ch. 21 of the book.

- 2017/09/20 Lecture Introduction to statistics
- 2017/10/04 Lecture Ch. 3-1 to Ch. 3.3. We stopped at Equality [3.3.3].
- 2017/10/11 Lecture Ch. 3.3 until the end of Section The qth-Order Moving Average Process (p. 51).
- 2017/10/18 Lecture Ch. 3.3 infinite-order Moving Average Process-Ch. 3.4 up to expression [3.4.3] (p. 53).
- 2017/10/25 Lecture Ch. 3.3-3.5 and Introduction to Forecasting
- 2017/11/01 Lecture Ch. 4.1 Forecasts based on linear projection (p. 73-74)
- 2017/11/08 Lecture Applied R session
- 2017/11/15 Lecture Ch. 5 Maximum Likelihood Estimation
- 2017/11/29 Lecture Ch. 7 Asymptotic Distribution Theory
- 2017/12/06 Lecture Applied R session
- 2017/12/13 Lecture Ch. 21
- 2017/01/10 No class (Holiday)
- 2017/01/17 Office hours
- Due 2017/01/24 Take-home exam to return

- Due 2017/10/11 Prove Equality [3.3.4] and Equality [3.3.5] by yourself
- Due 2017/10/18 Ex 3.1 on p. 70. Equivalently to the lag operator that we haven't defined yet in class, the definition of Yt is Yt = et + 2.4et-1 + 0.8 et-2
- Due 2017/10/25 Compute [3.4.4] and [3.4.5] (p. 53)
- Due 2017/11/01 No theoretical homework
- Due 2017/11/08 Show that in the case where X_t = Y_t is a White noise, then the sample mean produce the smallest mean squared error among the class of linear forecasting rules. To do that, show that the forecast (introduced in class) satisfies [4.1.10].
- Due 2017/11/15 No theoretical homework
- Due 2017/11/29 No theoretical homework
- Due 2017/12/06 Compute the limit of [7.1.3] in probability when Y_t is a White noise + Exercice 7.2 (a)
- Due 2017/12/13 No theoretical homework

- Due 2017/10/11 Fix the horizon T=1000. Simulate the process [3.1.2] with sigma=1 and sigma=2. Also simulate the time trend plus Gaussian withe noise [3.1.7] with beta=1 and sigma=1. To do those, the function rnorm() will be useful in R.
- Due 2017/10/18 Fix the horizon T=1000. Simulate the processes MA(1) and MA(2) choosing reasonable parameter values.
- Due 2017/10/25 Fix the horizon T=1000. Simulate the process AR(1) choosing reasonable parameter values.
- Due 2017/11/01 Fix the horizon T=1000. Simulate the process ARMA(1,1) choosing reasonable parameter values, and make predictions at each time for the next period.
- Due 2017/11/08 No applied homework.
- Due 2017/11/15 No applied homework.
- Due 2017/11/29 No applied homework.
- Due 2017/12/06 Implement the seasonal effect on ccDeaths dataset.
- Due 2017/12/13 No applied homework