An Introduction to univariate financial time series analysis

An Introduction to univariate financial time series analysis

1 Introduction: what is a time-series?
Time-series is a sequence
{x1, x2, ..., xT } or {xt} , t = 1, ..., T, where t is an index denoting the period in time in which x occurs. We shall treat xt as a random variable; hence, a time-series is a sequence of random variables ordered in time. Such a sequence is known as a stochastic process. The probability structure of a sequence of random variables is determined by the joint distribution of a stochastic process.
A possible probability model for such a joint distribution is: xt = α +

References: Amisano, G., and Giannini, C. (1997). Topics in Structural VAR Econometrics Banerjee, A., Dolado, J. J., Hendry, D. F. and Smith, G. W. (1986). Banerjee, A., Dolado, J. J., Galbraith, J. W. and Hendry, D. F. (1993). Banerjee, A., and Hendry, D. F. (1992). ‘Testing Integration and Cointegration’. Beveridge, S., and Nelson, C. (1981). ‘A New Approach to the Decomposition of Economic Time Series into Permanent and Transitory Bhargava, A. (1986). ‘On the Theory of Testing for Unit Roots in Observed Time Series’ Cuddington, J. T., and Winters, L. A. (1987). ‘The Beveridge-Nelson decomposition of economic time-series DeJong, D. N., and Whiteman, C. H. (1991). ‘Reconsidering Trends and random walks in macroeconomic time-series’ Dickey, D. A., and Fuller, W. A. (1981). ‘Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root’ Doornik, J., and Hendry, D. F. (1994). PcFiml 8.0. Interactive Econometric Modelling of Dynamic Systems Enders, W. (1995). Applied Econometric Time Series. New York: Wiley Series in Probability and Mathematical Statistics. Engle, R. F., Granger, C.W. J., and Hallman, J. J. (1987). ‘Combining Short and Long Run Forecasts: an Application of Seasonal Cointegration Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: J Giannini, C. (1992). ‘Topics in Structural VAR Econometrics’. Lecture Notes in Economics and Mathematical Systems, Springer-Verlag. Giannini, C., Lanzarotti, S., and Seghelini, M. (1994). ‘A Traditional Interpretation of Macroeconomi Fluctuations: the Case of Italy’. Gonzalo, J. (1994). ‘Five Alternative Methods of Estimating Long-run Equilibrium Relationships’ Granger, C. W. J. (1986). ‘Developments in the Study of Cointegrated Economic Variables’ Granger, C. W. J., and Newbold, P. (1974). ‘Spurious Regressions in Econometrics’ Hamilton, J. (1994). Time-Series Analysis. Princeton: Princeton University Press. Hansen, H., and Juselius, K. (1995). CATS in RATS. Cointegration Analysis of Time Series Harvey, A. C., and Jaeger, A. (1993). ‘Detrending, Stylized Facts and the Business Cycles’ Harvey, A. C., and Koopman, S. J.(1996) ‘Multivariate Structural Time Series Models’ in C Hatanaka, M. (1987). Time-Series-based-econometrics. Oxford: Oxford University Press. Hendry, D. F. (1987) ‘Econometric Modelling with Cointegrated Variables’. Hendry, D. F., and Ericsson, N. (1991). ‘Modeling the demand for narrow money in the United Kingdom and the United States’. Hodrick, R. J., and Prescott, E. C. (1997). ‘Postwar U.S. Business Cycles: An Empirical Investigation’ Horvath, M. T. K., and Watson, M. W. (1995). ‘Testing for cointegration when some of the cointegrating vectors are known’ Johansen, S. (1988). ‘Statistical Analysis of Cointegration Vectors’. Johansen, S. (1989). ‘Likelihood-based Inference on Cointegration: Theory and Applications’ Johansen, S. (1992). Identifying Restrictions of Linear Equations. University of Copenaghen, Institute of Mathematical Statistics. Johansen, S. (1994). ‘The role of the Constant and Linear Terms in Cointegration Analysis of Nonstationary Variables’ Johansen, S. (1995). Likelihood Based Inference on Cointegration in the Vector Autoregressive Model Johansen, S., and Bartlett, A. (1999). ‘Correction Factor for Tests on the Cointegrating Relationships’ Johansen, S., and Juselius, K. (1990). ‘Maximum Likelihood Estimation and Inference on Cointegration with Applications to the Demand Johansen, S., and Nielsen, B. G. (1993). ‘Asymptotics for the cointegration rank test tests in the presence of intervantion dummies’