Time Series Analysis

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
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
• lt0 ? (1-?)lt0 ? ?lt1

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
16
Forecasting of the Exchange Rate
17
References

• Burns, A and W. Michell, (1946), Measuring
  Business Cycles NBER, New York.
• Campbell J. Y. and R.J. Shiller (1987)
  Cointegration and Tests of Present Value Models,
  Journal of Political Economy, 95, 5, pp.
  1062-1087.
• Cooley and Thomas F. and S.F. LeRoy (1985)
  Atheoretical Macroeconometrics, Journal of
  Monetary Economics, North Holland 16 283-308.
• Dickey D.A. and W.A. Fuller (1979) Distribution
  of the Estimator for Autoregressive Time Series
  with a Unit Root, Journal of the American
  Statistical Association, June.
• Dickey D.A. and W. A. Fuller (1981) Likelihood
  Ratio Statistics for Autoregressive Time Series
  with a Unit Root, Econometrics, 494 July,
  1057-1071.
• Engle R E and C.W.J. Granger (1987)
  Co-integration and Error Correction
  Representation, Estimation and Testing.
  Econometrica, vol. 55, No. 2, pp. 251-276.
• Enders W. (1995) Applied Econometric Time Series,
  John Wiley and Sons
• Fair R.C.(1984) Specification, Estimation, and
  Analysis of Macroeconomic Models, Harvard.
• Garratt A., K. Lee, M.H. Pesaran and Y. Shin
  (2003) A Structural Cointegration VAR Approach to
  Macroeconometric Modelling, Economic Journal.
• Cooly Thomas F (1995) Frontiers of Business Cycle
  Research, Princeton.
• Doornik J.A and D.F. Hendry (2003) Econometric
  Modelling Using PCGive Volumes I, II and II,
  Timberlake Consultant Ltd, London.
• Hendry D.F. (1997) Dynamic Econometrics, Oxford
  University Press.
• Harris R. and R. Sollis (2003) Applied Time
  Series Modelling and Forecasting, John Willey.
• Holly S and M Weale Eds.(2000) Econometric
  Modelling Techniques and Applications, pp.69-93,
  the Cambridge University Press.
• Johansen Soren (1988) Estimation and Hypothesis
  Testing of Cointegration Verctors in Gaussian
  Vector Autoregressive Models, Econometrica, 596,
  1551-1580.
• Johansen Soren (1988) Statistical Analysis of
  Cointegration Vectors, Journal of Economic
  Dynamics and Control 12 231-254, North Holland.
• Nelson C. R. and C. I. Plosser (1982) Trends and
  Random Walks in Macroeconomic
• Time Series Some Evidence and Implications,
  Journal of Monetary Economics.
• Pagan A. and M. Wickens (1989) A Survey of Some
  Recent Econometric Methods, Economic Journal, 99
  pp. 962-1025.