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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 • Combination of AR and MA Learning the Parameters • Easy !!! just apply normal regression analysis techniques • However, there are sophisticated method like Partial Auto-correlation (PACF). Non-stationary / Diverge US GDP A Simple Technique to convert to Stationary Model c as ARMA(p,q) Heteroscedasticity Robert Engle Continuous Time Series Analysis Why? • Interest rate • Prices for options, shares and bonds changes continuously Modeling Continuous Time Series W0 = 0 Wt is almost surely continuous Continuous Time Series with Jump Simple Levy Process / An example to estimate parameters is interest rate
