QA11 - Non-Stationary Time Series

Question 1

Describe linear and nonlinear time trends

Answer 1

Linear model with time trend has an issue if d < 1, as in finance Yt will become negative

Solve by using log model (non-linear time trend)

Question 2

Explain how to use regression analysis to model seasonality

Answer 2

Use dummy variable to increase or decrease intercept when in season x, can combine with ARMA components to capture cyclical nature

Question 3

Describe a random walk and a unit process

Answer 3

A unit process is the generalisation of a random walk by adding short-term stationary dynamics

Question 4

Explain the challenges of modelling time series containing unit roots

Answer 4

• Unit process does not mean revert
• Parameter estimates for ARMA models containing unit root are not normally-distributed
• Ruling out spurious relationships difficult

Question 5

Describe how to test if a time series contains a unit root

Answer 5

Use the Augmented Dickey-Fuller specification

1. Difference of a series regressed against lagged level, deterministic level, and lagged differences
2. H0: coefficient of lagged level = 0 means Yt does not contain a unit process

If trend-stationary, must also include a constant

Question 6

Calculate the estimated trend value and form an interval forecast for a time series

Answer 6

[E(Y_(t + h)) +/- e_(t+h)]