T5. Time Series Models Flashcards
What are the 4 types of basic time series models?
- White Noise processes
- Random Walks
- Random Walks with Drift
- Auto-regressive processes
When is a time series white noise?
Properties of white noise
(3)
When is a time series random walk?
White noise and distributions
They do not have to come from normal distributions, but if they do they are called Gaussian White Noise and have distribution N(0, σ2)
Show that the mean of Xt is constant under a random walk
Is random walk stationary?
Show workings for the answer.
NO, despite mean is constant, variance depends on time.
Graph for random walk
(and correlogram)
Generalised equation for random walk with drift
Graph for random walk with drift
What is an auto-regressive model?
Generalised equation for auto-regressive models
How are the other time series related to AR(1)?
What does the random walk model say?
That the value at time t will be equal to the last period value plus a stochastic (non-systematic) component that is a white noise (can go up and down but averages at zero).
- A random walk can move away from its starting point (either +ve or -ve) but will eventually come back.
What is a random walk with drift?
A time series model that predicts that the value at time t will be equal to the last period value plus a constant movement up or down given by θ0, plus a random component that is white noise.
