STAT 520
               Forecasting and Time Series


Exam Preparation
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 Durbin-Levinson 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.86-87
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 Yule-Walker equations for a simple ARMA model
Find the Yule-Walker estimates for a given model
Diagnostic checking of the final model
Chapter 6. Nonstationary and Seasonal Time Series Models
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 Dickey-Fuller (ADF) test, write down the regresion model(s) and stages to calculate ADF
Chapter 7. Multivariate Time Series
Bivariate VAR
Cross-correlations - interpretation
Prewhitening - definition
Granger causality - definition
Cointergration - definition

* BD: Brockwell and Davis, Introduction to Time Series and Forecasting, 2nd edition, 2002.

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