Some Important Time Series Processes Fin250f: Lecture 8.3 Spring 2010.

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Presentation transcript:

Some Important Time Series Processes Fin250f: Lecture 8.3 Spring 2010

Outline  Basic finance price dynamics Random walk Geometric random walk Martingale  Random walk + noise  Trend + noise

Random Walk

Geometric Random Walk

Martingale

Random Walk + Noise

 Why interesting?  Exponential smoother is the optimal forecast  History: Muth, and rational expectations

Trend + Noise Model  Model returns as Small persistent trend Plus noise  Can generate significant predictability which is invisible to most tests

Covariance Reminder

Trend + Noise

Trend Plus Noise

Parameter Example  A small   big  A = 0.02, 

Trend Plus Noise ACF

AR(1) ACF’s

Trend Plus Noise  Can show Returns are ARMA(1,1) ARMA’s can generate persistent, but small autocorrelations for certain parameters  This is useful to model returns Low correlations Trends for momentum/moving average trading rules