Econometric methods of analysis and forecasting of financial

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

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

From this lecture you will learn: • How to make the forecast for autoregressive

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

Contents: • • The nature of time series AR, MA, ARMA models Box–Jenkins methodology

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

The nature of time series •

The nature of time series •

The nature of time series •

The nature of time series •

AR, MA, ARMA models •

AR, MA, ARMA models •

AR, MA, ARMA models •

AR, MA, ARMA models •

AR, MA, ARMA models •

AR, MA, ARMA models •

AR, MA, ARMA models Box–Jenkins methodology • Make the series stationary • plot ACF

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.

AR, MA, ARMA models • If several ARMA(p, q) models are possibly correct, choose

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 = Tln. SSR + 2 n • Schwarz Bayes information criterion (SBIC): SBIC = Tln. SSR + nln. T • Hannan-Quinn information criterion (HQIC): HQIC = Tln. SSR + 2 n(ln(ln. T)) 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.

ARCH-and GARCH-models •

ARCH-and GARCH-models •

ARCH-and GARCH-models •

ARCH-and GARCH-models •

ARCH-and GARCH-models •

ARCH-and GARCH-models •

Stationarity and unit roots

Stationarity and unit roots

Examples of time series modelling in finance •

Examples of time series modelling in finance •

Conclusions • We’ve covered how to make the forecast for autoregressive moving average (ARMA)

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

References • Brooks C. Introductory Econometrics for Finance. Cambridge University Press. 2008. • Cuthbertson

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, 1 st 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 forecasting financial market volatility. Wiley, 2005. • Rachev S. T. et al. Financial Econometrics: From Basics to Advanced Modeling Techniques, Wiley, 2007.