1 - Introduction to time series analysis

Question 1

How can the time points of measurement be?

Answer 1

They can be:
- regularly spaced (monthly, yearly, …) and also regularly spaced with missing values
- irregularly spaced
- high frequency (continuous time)

They can be also in:
- discrete time
- continuous time
- continuous time, but observed at discrete time points

Question 2

How can the different types of data be?

Answer 2

They can be:
- categorical (QUALITATIVO)
- discrete
- continuous

They can also be:
- univariate
- multivariate

Question 3

What can be the aims of time series analysis?

Answer 3

• Exploratory/descriptive analysis
• Forecasting with algorithms, but they do not describe uncertainty and risk nor give a ‘vision’ of the phenomenon
• Explain
• Modeling and inference: which is a task of explaining
• Forecasting but with probability to express uncertainty and risk
• Control

Question 4

What is the exploratory/descriptive analysis?

Answer 4

• Describe trend, seasonality, cycle, etc.
• Often thi is done in order to de-trend, de-seasonalize, etc.
• In multivariate/high dimensional time series we may want to summarize; find common patterns, clusters, or perform dimension reduction

Question 5

What do we mean with explain and modeling and inference in the time series analysis?

Answer 5

Explain
- We may want to explain the phenomenon: understand the relationships among variables, or how one variable of interest Y depends on other variables
- These will not be determinist relationships, but ‘statistical ’. The main tool is regression, but here the variables evolve over time.

Modeling and inference
- In this “explain” task, the info on the phenomenon is formalized through a probabilistic (statistical) model.
- The statistical model will have unknown parameters, that will have to be estimated: so we need to do inference.
- Statistical inference is based on probability.

Question 6

What is a time series?

Answer 6

A time series is no longer just a sequence of measurements over time, but a stochastic process (Yt , t ≥ 1).
- Here Yt is a random variable
- So a time series is not just a collection of numbers
- In the course we will study some of the main probabilistic models for time series analysis, with focus on models for NON-stationary processes.