Topics
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| Chapter
1. Introduction |
Use
backward shift operator and difference operator to write down TS models
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Derive
the ACVF and ACF for a particular model
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| Show
that particular TS is weakly stationary |
Write down the extended
form of ARMA model
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| 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.
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Chapter
3. ARMA Models
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ARMA(p,q)
- present in extended form and with backward shift operator and with
difference operator
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| 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.
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Calculate
the psi and pi coefficients for a simple model - see BD p.86-87
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Use a
ACF and PACF graphs to determine what model might be appropriate, i.e.
p=? q=?
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Chapter
4. Spectral Anaysis
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Spectral
density
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Use the
periodogram to find the lenght of cycle
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Derive the spectral
density for a process with given ACVF
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| 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)
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| 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
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Cross-correlations -
interpretation
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Prewhitening -
definition
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Granger causality - definition
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Cointergration - definition
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