Random Walk and Mean Reversion by Edu Pristine

Author of lecture Random Walk and Mean Reversion

Edu Pristine

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... normally distributed 3. The error variable must have a constant variance 4. The errors must be independent of each other "How can we diagnose violations of these conditions Residual Analysis, that is, examine the differences between the actual data points and those predicted by the linear equation ...

... Knowledge Management Pristine, Purposes Examine for linearity assumption Examine for constant variance for all levels of x Evaluate normal distribution assumption Graphical ...

... is violated, we have a condition of heteroscedasticity. We can diagnose heteroscedasticity by plotting the residual against the predicted y In Regression analysis we assumed the volatility ...

... are time series, the errors often are correlated. Error terms that are correlated over time are said to be auto-correlated. We can often detect auto-correlation by graphing the resid uals against the time periods. If a pattern emerges, it is likely that the independence requirement is violated. ...

... Knowledge Management Pristine Note the runs of positive residuals, replaced by runs of negative ...

... Exchange rates and stock prices do not exhibit mean reversion. Neev Knowledge Management Pristine A process in which the full path consists of series of small random steps. Complete path is called Random Walk. Used to model many processes, including returns on stocks, economics, physics, diffusion models, etc. Close to Markov processes. Stock returns are independent and have the identical distribution. The past movement or trend ...

... of the parameters would make them Maximum likelihood estimation gives a unique and easy way to determine solution in the case of the normal distribution For a normal distribution MLE for Mean ...