T3. Deterministic and Stochastic Time Series

Question 1

Define deterministic time series

Answer 1

One which can be expressed explicitly by an analytic expression.

• It has no random or probabilistic aspects.
• Past and future are completely specified → we can always predict future behaviour and state past behaviour.

Question 2

Examples of deterministic model functions

Answer 2

Question 3

Define stochastic time series

Answer 3

A non-deterministic time series which cannot be described by an analytic expression. It has some as-if random aspect that prevents its behaviour from being described explicitly.

Question 4

Why might a time series by non-deterministic?

Answer 4

1. All the information necessary to describe it explicitly is not available although it might be in principle, or
2. The nature of the generating process is inherently random.

Question 5

Example: stochastic time process where

• first half are drawn independently from an N(0,1)
• second half from an N(5,1)

How are these probability models shown graphically?

Answer 5

Question 6

What do we mean by a structural break?

Answer 6

A sudden shift in the time series.

The dahed vertical line shows the regime shift.

Question 7

Example: stochastic process where:

• data drawn independently from N(μ,1)
• mean is increasing over time

What would the graph look like?

Answer 7

Stochastic graph with an upwards trend.

Question 8

Example: stochastic process where:

• data drawn independently from N(0,σ)
• variance is increaseing over time

What would the graph look like?

Answer 8