1. Econometric methods of analysis and forecasting of financial markets Lecture 3. Time series modeling and forecasting

2. From this lecture you will learn: How to make the forecast for autoregressive moving average (ARMA) models and exponential smoothing models How to estimate the accuracy of predictions with the use of different metrics How to estimate time series models and make the forecasts in EViews

3. Contents: The nature of time series AR, MA, ARMA models Box–Jenkins methodology ARCH-and GARCH-models Stationarity Unit roots Examples of time series modelling in finance

4. The nature of time series

6. AR, MA, ARMA models

9. AR, MA, ARMA models Box–Jenkins methodology Make the series stationary plot ACF and PACF graphs for lags up to T/4, choose appropriate number of lags p and q estimate chosen ARMA(p,q), check stability conditions and save residuals plot ACF and PACF for the series of residuals, compute the Q-statistics and perform the Q-tests If all the sample autocorrelations and partial autocorrelations are close to zero and if all the Q-tests do not reject the null hypothesis of no autocorrelation, then the estimated model might be the correct one. If not, then go back to step 1 and change the number of lags p and q.

10. AR, MA, ARMA models If several ARMA(p,q) models are possibly correct, choose the model that minimizes information criteria: Akaike information criterion (AIC): AIC = TlnSSR + 2n Schwarz Bayes information criterion (SBIC): SBIC = TlnSSR + nlnT Hannan-Quinn information criterion (HQIC): HQIC = TlnSSR + 2n(ln(lnT)) where SSR is the sum of residuals squares; n is the number of explanatory variables (n = p + q + 1 if a constant term is included); T is the number of usable observations.

11. ARCH-and GARCH-models

14. Stationarity and unit roots

15. Examples of time series modelling in finance

16. Conclusions We’ve covered how to make the forecast for autoregressive moving average (ARMA) models and exponential smoothing models How to estimate the accuracy of predictions with the use of different metrics How to estimate time series models and make the forecasts in EViews

17. References Brooks C. Introductory Econometrics for Finance. Cambridge University Press. 2008. Cuthbertson K., Nitzsche D. Quantitative Financial Economics. Wiley. 2004. Tsay R.S. Analysis of Financial Time Series, Wiley, 2005. Y. Ait-Sahalia, L. P. Hansen. Handbook of Financial Econometrics: Tools and Techniques. Vol. 1, 1st Edition. 2010. Alexander C. Market Models: A Guide to Financial Data Analysis. Wiley. 2001. Cameron A. and Trivedi P.. Microeconometrics. Methods and Applications. 2005. Lai T. L., Xing H. Statistical Models and Methods for Financial Markets. Springer. 2008. Poon S-H. A practical guide for forecasting financial market volatility. Wiley, 2005. Rachev S.T. et al. Financial Econometrics: From Basics to Advanced Modeling Techniques, Wiley, 2007.