1. Time Series Analysis Definition of a Time Series process
AR, MA, ARMA, ARIMA
Vector Autoregression
Impulse Response
Forecasting

2. Four Components of a Time Series
Trend
Season
Cycle
Random
(refer STAMP manual p.140)

3. Iterative Substitution in AR(1) Model

4. AR(1) Time Series as a Function of Past Innovations (Impulses or Shocks)

5. Time Dependent Variance

6. Dicky-Fuller and Augmented Dicky-Fuller Tests
Null hypotheses:
There is unit root and time series in non-stationary
=0  (1-)=0
Alternative hypothesis:
There is no unit root and time series is stationary
<0  (1-)<0  <1

7. Moving Average-MA Process

8. MA(2) Process

9. Autoregressive Process

10. ARMA(1,1) Process

11. Co-integration

12. Error Correction Model

13. Structure of a VAR Model.
Simple Example

14. Impulse Response Analysis in a VAR Model

15. Stamp Program for Time Series Analysis
Estimation sample is (T = 116, n = 111).
Log-Likelihood is (-2 LogL = ).
Prediction error variance is
Summary statistics ER
Std.Error
Normality
H( 37)
r( 1)
r( 9) DW
Q( 9, 6)
Rs^
ER = Trend + Trigo seasonal + Expl vars + Irregular
Eq 3 : Estimated coefficients of final state vector.
Variable Coefficient R.m.s.e t-value
Lvl [ ]
Slp [ ]
Sea_ [ ]
Sea_ [ ]
Sea_ [ ]
Eq 3 : Estimated coefficients of explanatory variables.
ER_ [ ]
ER_ [ ]
ER_ [ ]
ER_ [ ]
Eq 3 : Seasonal analysis (at end of period).
Seasonal Chi^2( 3) test is [0.9818].
Seas Seas Seas Seas 4
Value

16. Forecasting of the Exchange Rate

17. References
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Hendry D.F. (1997) Dynamic Econometrics, Oxford University Press.
Harris R. and R. Sollis (2003) Applied Time Series Modelling and Forecasting, John Willey.
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Johansen Soren (1988) Estimation and Hypothesis Testing of Cointegration Verctors in Gaussian Vector Autoregressive Models, Econometrica, 59:6,
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Time Series: Some Evidence and Implications, Journal of Monetary Economics.
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Prescott, E.C. (1986), “Theory Ahead of Business Cycle Measurement,” Federal Reserve Bank of Minneapolis, Quarterly Review; Fall.
Pindyck R.S and Robinfeld D.L. (1998) Econometric Models and Economic Forecasts, 4th edition, McGraw Hill.
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Hypothesis, Econometrics 48:1, pp,