# What is a commonly accepted econometric model for volume?

What is the gold standard econometric model for volume? For example, a common model for price is the autoregressive (AR) model with GARCH(1,1) innovations. Do you know of any good survey articles about econometric models used for modeling volume?

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As an aside, GARCH models volatility (i.e. second moment), not price (first moment). –  Dirk Eddelbuettel May 22 '12 at 13:51
@Dirk Eddelbuettel but AR(1)-GARCH(1,1) does –  Qbik May 22 '12 at 14:16
@DirkEddelbuettel Every GARCH model will model the first moment through the mean equation. Even the plain GARCH(1,1) assumes $R(t) = \sigma(t)z(t)$ is the mean equation process. If the mean equation is misspecified then so is the variance equation so it's up to the modeller to try to get both as representative of the underlying process (not that this can be done through GARCH in reality). –  user2763361 Oct 27 '13 at 13:37

GARCH will work if volume has memory with some decay. AR will work if volume has mean reversion properties. Both of these are empirical questions and depend on the market. You should also consider if there are seasonal (day-of-week, monthly, quarterly effects) in which case you would want to add dummy variables. MA models will work well if volume behaves like a random-walk (not the case).

There is no "gold standard" since markets have different volume characteristics (for example, emerging markets have rising volumes; developed markets more recently are seeing less volume traded year-over-year with the rise of crossing networks and dark pools). I would start by observing the volume of interest to see what properties hold (i.e. trend, mean reversion, persistence, seasonality) for starters.

You may want to consider using the auto.arima function in the package forecast to fit a volume model to each security rather than looking for a global functional form for all securities.

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I deal recently with some analysis of the Volume time series, daily volume in € for European stocks. I found out that an ARIMA model works well. But, some EWMA could also provide good forecast if it's well parameterized.

You can also face some seasonality effect due to macroeconomic events, some you may need to clean you data and treat these days in a different way.

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Try the following :

1. perform the logarithmic transformation of the volume data.
2. check if the transformed data fits the normal distribution nicely.
3. if you are working with intraday volume, then adjust for the seasonality for time of the day effect, if using daily data, in some cases some special seasonalities like expiry day, etc might be applied but it may not be compulsory.
4. fit an ARMA model.
5. if you are still not satisfied, try using a long memory process.
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