Economic Models - Convex Optimization

A Novel Method of Estimation Under Co-Integration 41
Due to the properties of SVD, we can easily and directly include in the
co-integrating vectors, as many deterministic components as we want to.
Besides, we found that the errors corresponding to the finally selected cointegration
vector, are characterized by the minimum variance property. It
should be noted that the procedure proposed here is not mentioned in the
relevant literature.
Further, we analyzed the stages of a relevant technique to obtain reliable
results regarding the order of integration of a given series provided that
it is DSS. We also demonstrated the properties of the so-called near integrated
series, which can be traced by applying this technique. It should be
emphasized that with this kind of series (NI), we show that the conventional
methods for unit root test may produce faulty results.
References
Banerjee, A, JJ Dolado, JW Galbraith and DF Hendry (1993). Co-integration, Error Correction,
and the Econometric Analysis of Non-Stationary Data. New York: Oxford
University Press.
Dickey, DA and WA Fuller (1981). Likelihood ratio statistics for autoregressive time series
with a unit root. Econometrica 49, 1057–1072.
Dickey, DA, DW Jansen and DL Thornton (1994). A primer on cointegration with an application
to money and income. In Cointegration for the Applied Economist, BB Rao
(ed.), UK: St. Martin’s Press, 9–45.
Enders, W (1995). Applied Econometrics Time Series. New York: John Wiley.
Harris, R (1995). Using Cointegration Analysis in Econometric Modelling. London: Prentice
Hall.
Holden, D and R Perman (1994). Unit roots and cointegration for the economist. In Cointegration
for the Applied Economist, BB Rao (ed.), UK: St. Martin’s Press, 47–112.
Johansen, S and K Juselius (1990). Maximum likelihood estimation and inference on cointegration
with application to the demand for money. Oxford Bulletin of Economics and
Statistics 52, 169–210.
Johnston, J and J DiNardo (1997). Econometric Models. New York: McGraw-Hill International.
Kleibergen, F and V Dijk (1994). Direct cointegration testing in error correction models.
Journal of Econometrics 63, 61–103.
Lazaridis, A and D Basu (1983). Stochastic optimal control by pseudo-inverse. Review of
Economics and Statistics 65(2), 347–350.
Lazaridis, A (1986). A note regarding the problem of perfect multicollinearity. Quantity and
Quality 120, 297–306.
McKinnon, J (1991). Critical values for co-integration tests. In Long-Run Economic Relationships,
RF Engle and CWJ Granger (eds.), New York: Oxford University Press.
Perron, P and T Vogelsang (1992a). Nonstationarity and level shifts with an application
to purchasing power parity. Journal of Business and Economic Statistics 10,
301–320.