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

W0 = 0Wt is almost surely continuous

Continuous Time Series with Jump

Simple Levy Process

/

An example to estimate parameters

is interest rate