# Time series price prediction and linear regression: using high/low rather than last quotes price

Discrete time series regression models, like ARIMA, are usually built around the assumption that we only have 1 available price for each period t, which I will call the Close.

In reality asset time series (bid, ask) are continuos processes and we might have more data than just the Close for each interval. Let's say we have, for each period, an Open, High, Low and Close price. t1(Low) will therefore be the lowest asset price during t1.

Now let's also assume we want to build a mean reversion model. We have reasons to believe that some of our predictors have significant negative correlation to the next period price, although we can't be confident that mean reversion will materialize precisely at t1(Close). If we want to make R-squared more meaningful, does it make sense to use the next period Close as the DV? Shouldn't we use the Low/High? That is, if the asset price at interval t0 as travelled from an Open of 10 to a Close of 20, we will want to regress t0 IVs against t1(Low), not t1(Close).

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Please edit your question for clarity. You say you are predicting prices but then define Y as a return in T1. Also you say you are predicting price at "any time" -- not sure that what means. Maybe you are trying to build a model that achieves some target return over the course of a horizon -- not clear from your question. – Quant Guy Dec 18 '11 at 15:32
I am, if anything, even more confused as to what you are asking after your most recent edits. At least, I am confused as to what you are proposing. I feel your initial goal of "maximizing prediction value" may be misguided. A model that overly depends on the specific regression you run is not very robust. Also, if I understand you right, rounding your dependent variable, particularly if you are trying to predict prices or returns, is rarely a good idea. Better to use robust regression, if outliers are a problem. – Tal Fishman Dec 18 '11 at 18:59
Alright, let's make it simple and I will walk you through: in time series analysis, be it ARIMA or any other forecasting model, what is the generally used observed value Y in the regression? If the answer is the last available differenced price at time t1 for the continuous process, why is that? Why not to regress against the differenced high or low price for the period t0-t1? And why to close the question anyway, other people might provide more specific critique than general "confused" comments. – Robert Kubrick Dec 18 '11 at 21:29
@RobertKubrick Closing need not be permanent. Closing only says that, as it stands right now, at least 5 active users believe your question is not clear. If you edit your question to be clearer, then it will be re-opened. If you wish, you could make your last comment, "Why not regress against the differenced high or low price?" your entire question, and perhaps that is good enough. – Tal Fishman Dec 18 '11 at 22:42
@RobertKubrick following your latest edits, is your question now "shouldn't we use high/low?" Please make it clear that that is your ultimate question. As it stands, the question still seems a bit overly chatty, more like giving your opinion than asking a question. – Tal Fishman Dec 19 '11 at 13:51
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$$\frac{O+C+\frac{H+L}2}3$$