QA 10. Stationary Time-Series: LOs

a) Describe the requirements for a series to be covariance stationary.

b) Define the autocovariance function and the autocorrelation function.

c) Define white noise; describe independent white noise and normal (Gaussian) white noise.

d) Define and describe the properties of autoregressive (AR) processes.

e) Define and describe the properties of moving average (MA) processes.

f) Explain how a lag operator works.

g) Explain mean reversion and calculate a mean-reverting level.

h) Define and describe the properties of autoregressive moving average (ARMA) processes.

i) Describe the application of AR, MA and ARMA processes.

j) Describe sample autocorrelation and partial autocorrelation.

k) Describe the Box-Pierce Q-statistic and the Ljung-Box Q statistic.

l) Explain how forecasts are generated from ARMA models.

m) Describe the role of mean reversion in long-horizon forecasts.

n) Explain how seasonality is modeled in a covariance-stationary ARMA.

QA 11. Non-Stationary Time-Series: LOs

a) Describe linear and nonlinear time trends.

b) Explain how to use regression analysis to model seasonality.

c) Describe a random walk and a unit root.

d) Explain the challenges of modeling time series containing unit roots.

e) Describe how to test if a time series contains a unit root.

f) Explain how to construct an h-step-ahead point forecast for a time series with seasonality.

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