DYNAMIC / w2

Example of MA(1)

AR(1) process

Stable vs Unstable Processes

Coefficient Values and their Behavior

Positive vs Negative Coefficient Values

AR(1) process

Backward Substitution
Writing as MA(∞) Process

AR(1) process

Deriviations + Covariance Stationarity

Initial Conditions

AR(p) Process

AR(p) Process

Example

MA(∞) representation of an AR(p) process

Population moments of an AR(p)

AR(∞)

AR(∞) representation of an MA(q) process

Why is the conversion between MA and AR useful?

ARMA(p,q) process

ARMA(p,q) process

Properties

Forecasting

Forecast Error

Mean Squared Forecast Error

Optimal Forecast Theorem

Example

Forecasting MA(1)

Truncate?

Forecasting ARMA

Volatility clustering

GARCH(1,1)

Intermediate Summary