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By: Arteid Memaj & Talal Butt

A time series approach to analyzing stock market volatility and returns. By: Arteid Memaj & Talal Butt. Outline. Introduction Methodology Results Limitations

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By: Arteid Memaj & Talal Butt

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  1. A time series approach to analyzing stock market volatility and returns. By: ArteidMemaj & Talal Butt

  2. Outline • Introduction • Methodology • Results • Limitations • References

  3. Background

  4. Purpose of the study • Develop a Model which predicts future values of S&P 500’s and DJI’s Returns and Volatility in a response time series as a linear combination of its past values and past errors. • Importance of study: • This information concerns economists and investors since the model developed could allow them to predict future risk and hedge against it.

  5. Hypothesis • Hypothesis 1: There is a time series model (ARMA(p,q)) that fits our data for Returns. • Hypothesis 2: There is a time series model(ARMA(p,q)) that fits our data for Volatility.

  6. Data

  7. Method • Identification Stage • Estimation and Diagnostic Stage • Forecasting Stage

  8. Method • Identification stage: • Autocorrelation check for white noise: -Ho: none of the autocorrelations up to a given lag are significantly differently from 0. • Stationarity Test : -Stationarity in the variance must be present. • Autocorrelation: -Corr (Zt,Zt+k) 4. Partial Autocorrelations: - Corr (Zt,Zt+k|Zt+1,Zt+2,….Zt+k-1)

  9. Returns Autocorrelation Check for White Noise (S&P500) Autocorrelation Check for White Noise (DJI)

  10. Volatility Autocorrelation Check for White Noise (S&P500) Autocorrelation Check for White Noise (DJI)

  11. Stationarity Test (S&P500)

  12. Stationarity Test (DJI)

  13. Partial Autocorrelation (Volatility) DJI S&P500

  14. Estimation & Diagnostic Stage

  15. Estimating a model (S&P500)

  16. Estimation & Diagnostic Stage

  17. Estimating a model (S&P500)

  18. Estimating a model (DJI)

  19. Forecasting Stage S&P500 DJI

  20. Predicted Vs. Actual (S&P500)

  21. Predicted VS. Actual (DJI)

  22. Conclusions • We can conclude that a ARMA(1,4) process forecasts volatility for both S&P500 and DJI with high precision. • Returns could not be forecasted with an AR(p) MA(q) or an ARMA(p,q) process.

  23. Limitations/Suggestion for Further Research

  24. Major Sources [1] Yahoo Finance (finance.yahoo.com) [2] W.S. Wei, William. Time Series Analysis. New York: Greg Tobin, 2006. Print. [3] O’Rourke, Norm. Hatcher, Larry. Stepanksi, Edward. A Step-By-Step Approach to Using SAS for Univariate and Multivariate Statistics. 2005. Print. [4] SAS Online Doc: Version 8, Chapter 7. <http://www.okstate.edu/sas/v8/saspdf/ets/chap7.pdf >

  25. Special Thanks to… • Dr. Chapman & Dr. Wolff for their valuable contributions and guidance during the process. • Xiana Clarke & Yanira Pichardo for contributions to data collections.

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