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Analyzing Stock Market Volatility Using Time Series Approach

This study develops a model predicting S&P 500 and DJI returns and volatility using a time series method. Hypotheses are tested, methods detailed, and results analyzed. The study's significance lies in aiding economists and investors in predicting future market risks. Limitations and suggestions for further research are also discussed.

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Analyzing Stock Market Volatility Using Time Series Approach

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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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