Financial Time Series CS3. Financial Time Series.

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Presentation transcript:

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 Weighted Average of Shocks Why? MA(1)

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 W 0 = 0 W t is almost surely continuous

Continuous Time Series with Jump

Simple Levy Process /

An example to estimate parameters is interest rate