Using High, Low, and VWAP Prices in Mean-Reversion Models
Summary
The discussion considers whether a mean-reversion regression should predict the next interval's high or low instead of its close when the expected reversal may occur within the interval. High and low prices are useful for some tasks, including volatility estimation, and established estimators use the range between them. But they may be brief, unreliable, or difficult to trade at meaningful size, so they can give a misleading measure of whether a strategy captured a reversal.
For evaluating realized execution or returns, the answer recommends interval VWAP calculated from tick data as a more representative alternative to the close. When only OHLC data is available, it gives a formula that approximates VWAP for short horizons. That approximation is presented as a fallback, not a substitute for actual transaction-level VWAP. The response provides methodological advice rather than an empirical comparison of regression targets.
Key ideas
- High and low prices are used in some contexts, including volatility estimation.
- An interval extreme may be brief and may not represent a price available for practical execution.
- Tick-based VWAP can be a more meaningful interval price for evaluating mean reversion than the close alone.
- An OHLC-based formula can approximate short-horizon VWAP when transaction data is unavailable.
- The choice of regression target should reflect tradability and the intended performance evaluation.
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Full text
# Time series price prediction and linear regression: using high/low rather than last quotes price
# 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).
## Answer by Tal Fishman (score 6, accepted)
https://quant.stackexchange.com/a/2625
High and low prices are frequently used in many contexts, such as estimating volatility. See, for example, the Garman-Klass and Yang-Zhang estimators. Brandt and Kinlay provide a nice summary of some of these estimators.
However, it sounds like you are more interested in using high/low information for evaluating whether mean reversion has taken place. In that case, I would counsel against using the range to measure whether the predicted mean reversion materialized. Having worked with real financial time series, I can tell you that the high/low quotes are much less reliable. The high or low of a given period is often only the active price for a very short period, and may not be tradeable, particularly in large size and/or without expensive high-frequency execution (for which you should really be using tick data, not OHLC data, anyhow).
Instead, I would recommend that you use the VWAP over the interval (calculated from actual ticks) as a slightly more meaningful alternative to the close alone. I've seen some research that approximates VWAP over short horizons for typical equities from OHLC data as
$$\frac{O+C+\frac{H+L}2}3$$
If OHLC data is all you have, this may be your best bet.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.