Forecasting Hourly Variance from Intraday Returns
Summary
The document considers how to forecast the next hour’s return variance when minute-level prices are available. It outlines two approaches: remove the recurring intraday volatility pattern before fitting ARCH or GARCH models, or use a heterogeneous autoregressive (HAR) model with volatility measures from multiple sampling intervals as predictors.
For a one-hour forecast, it suggests combining one-step-ahead forecasts over a rolling or expanding window. The discussion cites prior research for the intraday pattern and its filtering, but supplies no comparative tests or evidence that one approach is best. Its key caveat is that intraday absolute returns follow a time-of-day wave, creating dependence that can violate standard ARCH/GARCH assumptions. Model performance therefore depends on addressing this pattern and validating the forecast for the data at hand.
Key ideas
- Intraday absolute returns can follow a time-of-day pattern that creates autocorrelation.
- Filtering that pattern before ARCH or GARCH modeling may help meet model assumptions.
- A one-hour variance forecast can be assembled from successive one-step forecasts.
- HAR models can combine volatility measures sampled at different frequencies.
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Full text
# forecasting hourly variance with higher resolution data available
# forecasting hourly variance with higher resolution data available
Assume one has price data $P_{1}, P_{2}, \dots, P_{n}$ with one hour resolution and aims to forecast the variance for one hour ahead return. The first approach to try is ARCH or GARCH models. There are a lot of papers about that.
Next, assume that the goal is the same, i.e. forecasting the return's variance one-hour ahead, BUT with minute resolution data available.
What is the optimal way to use all the data?
## Answer by Martin Georg Haas (score 1, accepted)
https://quant.stackexchange.com/a/57740
Althoug I can only provide recommendation as to the forecasting task (see below), I want to point out one big caveat one has to account for: Intraday price volatility- or to be exact, the absolute returns, exhibit an intraday pattern which looks like a wave. This implies that the data is autocorrelated, which violates the assumptions of ARCH/GARCH models (see Andersen & Bollerslev 1997 https://doi.org/10.1016/S0927-5398(97)00004-2).
One solution is to model and filter out this pattern, e.g. using FFF-regression as in Behrendt & Schmidt 2018(https://doi.org/10.1016/j.jbankfin.2018.09.016). After that you can employ ARCH/GARCH forecasts.
One way to then retrieve a 1-hour (or 60-minute) forecast would be to use a rolling or expanding window of 60 one-step-ahead forecasts.
Additionally I can reccomend to look up HAR-models, these employ data on different frequencies, e.g. 1-minute, 5 -minute and 30-minute volatility as explanatory variables in an AR-model.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.