Jun

12

I have started to look into modeling time series. One thing I can't understand is that all the models in the financial literature, such as GARCH and ARIMA, have the random walk as their base assumption. But if markets are assumed to be random from the onset, what good are models? Sure, they can be useful when pricing options and such, but they are useless for making accurate predictions on the time series itself. Am I right?

Philip McDonnell replies:

To an extent the premise of the question is true. Random walks are a pretty good model for markets. The purpose of time series analysis or any other is to detect subtle deviations from randomness. To the extent that the model is unable to detect deviations from randomness then a trader will not be able to profit from it except by luck alone.

The opportunities lie in the deviations from randomness. These can be identified by the model and their strength and statistical significance estimated. Significance testing always starts with the naive null hypothesis that the market is random and cannot be beaten. The burden of proof is upon the data to 'prove' that the null is incorrect and that the market can be beaten.


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2 Comments so far

  1. Jolin Majmin on June 13, 2007 10:52 am

    I think its more the errors of these structural models have randomness built into them. So there is a structure to the data ( some type of auto regression or moving average or both..etc..) but there is also randomness/noise/error terms that shock the data away from its “trend,” and these error terms are usually standard guassian with fixed volatility or conditional volatility, where the vol is time or level depending.

  2. Dyspeptic5423 on June 13, 2007 10:00 pm

    It is true that neither GARCH nor ARIMA models are useful in forecasting the stock market, but for different reasons. GARCH models assume that the direction of the time series is unpredictable and only the volatility is predictable. So they are not able to forecast direction “by construction” if you will (what you call the “base assumption”). The older ARIMA models can in principle forecast direction by exploiting autocorrelation in the data. They are used with success to forecast ice cream sales or long distance call traffic, etc. But when they are applied to the stockmarket they usually fail because they cannot find any autocorrelations to exploit. The first step of ARIMA modeling is to graph ACF’s and PACF’s; when you do this for the stock market you find that all these correlations are near zero. The ARIMA methodology then gives up and says “I can’t forecast this, it is close to a random walk”.

    But in substance I agree with you: these two models are not useful for directional stockmarket prediction.

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