Topics

Chapter
1. Introduction 
Use
backward shift operator and difference operator to write down TS models

Derive
the ACVF and ACF for a particular model

Show
that particular TS is weakly stationary 
Write down the extended
form of ARMA model

Present the parameters of
ARMA model e.g. phi(1)=?, theta(1)=? 
Chapter
2. Stationary Processes 
Determine
causality
and invertibility for AR(1), MA(1), ARMA(1,1) 
ARMA(1,1),
express in backward shift operator and in extended form 
Apply
manually the Innovations and DurbinLevinson algorithm for a simple
model  e.g. BD page 74.

Chapter
3. ARMA Models

ARMA(p,q)
 present in extended form and with backward shift operator and with
difference operator

Present the parameters of
ARMA(p,q) model e.g. phi(1)=?, theta(1)=?, etc. 
Determine the causality
and invertibility for ARMA(p,q) with p,q =0,1,2.

Calculate
the psi and pi coefficients for a simple model  see BD p.8687

Use a
ACF and PACF graphs to determine what model might be appropriate, i.e.
p=? q=?

Chapter
4. Spectral Anaysis

Spectral
density

Use the
periodogram to find the lenght of cycle

Derive the spectral
density for a process with given ACVF

Derive the spectral
density for a simple ARMA model 
Chapter 5. Modeling and Forecasting
with ARMA Processes 
Write YuleWalker
equations for a simple ARMA model 
Find the YuleWalker
estimates for a given model 
Diagnostic checking
of the final model 
Chapter 6. Nonstationary and Seasonal Time
Series Models 
ARIMA(p,d,q) 
Seasonal ARIMA:
SARIMA(p,d,q)(P,D,Q)s_{  write in extended and backward shift
operator form} 
Unit Roots (UR),
what does it mean, what to do when there are k UR (k=0,1,2)

Test for AR UR 
Augmented DickeyFuller (ADF) test, write down the regresion
model(s) and stages to calculate ADF 
Chapter
7. Multivariate Time Series 
Bivariate VAR

Crosscorrelations 
interpretation

Prewhitening 
definition

Granger causality  definition

Cointergration  definition

