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Financial Time Series

Financial Time Series. CS3. Financial Time Series. Outline. Discrete Time Series Analysis Continuous Time Series Analysis. Discrete Time Series Analysis. Comes from the same distribution. Auto-regressive model. ~. Moving Average Model. MA(1). Weighted Average of Shocks. Why?. ARMA.

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Financial Time Series

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  1. Financial Time Series CS3

  2. Financial Time Series

  3. Outline • Discrete Time Series Analysis • Continuous Time Series Analysis

  4. Discrete Time Series Analysis

  5. Comes from the same distribution

  6. Auto-regressive model ~

  7. Moving Average Model MA(1) Weighted Average of Shocks Why?

  8. ARMA • Combination of AR and MA

  9. Learning the Parameters • Easy !!! just apply normal regression analysis techniques • However, there are sophisticated method like Partial Auto-correlation (PACF).

  10. Non-stationary / Diverge US GDP

  11. A Simple Technique to convert to Stationary Model c as ARMA(p,q)

  12. Heteroscedasticity Robert Engle

  13. Continuous Time Series Analysis

  14. Why? • Interest rate • Prices for options, shares and bonds changes continuously

  15. Modeling Continuous Time Series W0 = 0 Wt is almost surely continuous

  16. Continuous Time Series with Jump

  17. Simple Levy Process /

  18. An example to estimate parameters is interest rate

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