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I'm developing a trading strategy which takes into account certain parameters (e.g. avg spread, weighted price, etc). Of course, these parameters can be calculated over different window types (i.e. last X minutes/ticks/trades) and sizes.

Obviously, there's no optimal window to be used in every instance, but I would appreciate a few pointers/references to papers discussing how to choose the right window type + size in different situations.

Also, are there any special measures to be taken when applying such windows to market data of illiquid assets?

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At the absolute core of any trading strategy should be a reflection of the admittance of total market dynamics. That means that there is no golden levels, no set parameters that optimize a strategy outcome over time. What works today may already stop working tomorrow. I would start with a verification of such dynamics and attempt to capture changes in dynamics and how you intend to react to those. –  Matt Wolf Aug 5 '13 at 2:57
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This may be a tricky question and I am curious to see whether there is indeed a statistical methodology that tries to answer this question.

To my experience it really varies with the data you are working with. For instance, one may choose a rolling window above an expanding window when there are structural breaks in the data, hence which can affect the structural estimates of the parameters.

The length of this rolling window is then usually determined by means of some economic explanation. Moreover, when you expect that a structural or dynamic change is in effect for a particular period of time X, then you choose a rolling window of X days/minutes/ticks.

As in your case, I would suggest to take a look at papers that discuss your trading strategies and why the authors choose this particular rolling window. It may be also useful to try a sensitivity analysis where you roughly `play' with various window sizes and see what happens.

Important! The latter is not genuine modelling as you are observing the data first. To avoid for this bias, try to play with a sub-sample (in-sample) of your data.

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