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

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Presentation transcript:

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

 Introduction  Methodology  Results  Limitations  References

 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.

 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.

 Identification Stage  Estimation and Diagnostic Stage  Forecasting Stage

 Identification stage: 1.Autocorrelation check for white noise: -Ho: none of the autocorrelations up to a given lag are significantly differently from 0. 2.Stationarity Test : -Stationarity in the variance must be present. 3.Autocorrelation: -Corr (Z t,Z t+k ) 4. Partial Autocorrelations: - Corr (Z t,Z t+k |Z t+1,Z t+2,….Z t+k-1 )

To LagChi-Square DFPr > Chi SqAutocorrelations To LagChi-Square DFPr > Chi SqAutocorrelations Autocorrelation Check for White Noise (S&P500) Autocorrelation Check for White Noise (DJI)

To LagChi-Square DFPr > Chi SqAutocorrelations < To LagChi-Square DFPr > Chi SqAutocorrelations < Autocorrelation Check for White Noise (S&P500) Autocorrelation Check for White Noise (DJI)

LagCovarianceCorrelation Std Error 02.91E-051 | |******************** | E |. |************* | E |. |********** | E |. |********* | E |. |***** | E |. |***** | E |. |***** |

LagCovarianceCorrelation Std Error 07.53E-051 | |******************** | E |. |*************** | E |. |********** | E |. |*******. | E |. |******. | E |. |****. | E |. |**. |

LagCorrelation |. |************* |. ****| |. |*** |. |* |. **| |. DJI S&P500 LagCorrelation |. |************* | |. |*** | |. |** | |. *|. | |. |** | |. |** |

ProcessACFPACF AR(p)Tails off as exponential decay or damped sine wave. Cuts off after lag p MA(q)Cuts off after lag qTails off as exponential decay or damped sine wave ARMA(p,q)Tails off after lag (q – p)Tails off after lag (p – q ) LagCorrelation |. |************* | |. |*** | |. |** | |. *|. |

ParameterEstimateStandard Errort Value Pr > |t| Lag MU < AR1, < To LagChi-SquareDFPr > ChiSqAutocorrelations < <

ProcessACFPACF AR(p)Tails off as exponential decay or damped sine wave. Cuts off after lag p MA(q)Cuts off after lag qTails off as exponential decay or damped sine wave ARMA(p,q)Tails off after lag (q – p)Tails off after lag (p – q ) LagCorrelation | |******************** |. |************* |. |********** |. |********* |. |***** |. |***** |. |***** LagCorrelation |. |************* |. |*** |. |** |. *| |. |**

To LagChi-SquareDFPr > ChiSqAutocorrelations

To LagChi-SquareDFPr > ChiSqAutocorrelations

ObsForecastStd Error 95% Confidence Limits Jan Feb March April May June July Aug Sept Oct Nov Dec ObsForecastStd Error95% Confidence Limits Jan Feb March April May June July Aug Sept Oct Nov Dec S&P500DJI

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.

[1] Yahoo Finance (finance.yahoo.com) [2] W.S. Wei, William. Time Series Analysis. New York: Greg Tobin, Print. [3] O’Rourke, Norm. Hatcher, Larry. Stepanksi, Edward. A Step-By-Step Approach to Using SAS for Univariate and Multivariate Statistics Print. [4] SAS Online Doc: Version 8, Chapter 7.

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.