STAT 520
Forecasting and Time Series

 Exam Preparation
 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 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 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 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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