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ARMA Trading Signals and Intraday Volatility Periodicity

Article Quant Q&A · Author: David Hoareau
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Summary

The document describes a proposed EUR/USD forecasting workflow: take end-of-day closes, log-difference them to seek stationarity, fit an ARMA model using Box–Jenkins methods, inspect residuals, and use their assumed normal distribution to form cumulative probabilities for a next-day position. The author asks whether this is a sound trading strategy; no performance results or validation are supplied.

The response highlights intraday periodicity in volatility as a possible source of forecast error. It notes that volatility can vary systematically across the trading day, including around the European market open, and suggests removing this periodic pattern before applying an ARMA model to returns. The cited illustration describes average absolute five-minute returns for the Deutsche Mark against the dollar, including a lull associated with Asian-market lunch hours. These observations motivate modeling volatility by time of day, but they do not establish that the proposed strategy is profitable. The usefulness of the adjustment depends on sampling frequency and market, and the excerpt does not detail a full estimation procedure or out-of-sample test.

Key ideas

  • The proposed workflow fits ARMA to log differences of EUR/USD closing prices and uses residual probabilities to frame next-day positions.
  • The document assumes normally distributed model residuals but provides no evidence that the resulting signals are profitable.
  • Intraday volatility can vary predictably with the time of day, so a constant-volatility assumption may weaken forecasts.
  • Removing intraday periodicity before modeling returns is suggested as a way to account for the daily volatility pattern.
  • The cited pattern comes from five-minute Deutsche Mark and dollar returns and may not transfer unchanged across markets or timeframes.

Tags

ForexStatisticsVolatility
Full text
# Is that a good way to work with the ARMA model?


# Is that a good way to work with the ARMA model?












I would like to share with you what I am doing to get your point of view, and to make a better trading system in collaboration.

I am working on EURUSD forex, and I am trying to find a way to place order based on ARMA modelling.

Collecting Data, Data transformation, and Model fitting:

I am collecting each EOD Close of EURUSD instrument, and I calculate the log differencing to transform this time series in a stationary process. Then, using Box Jenkins, I fit the parameters of the ARMA Model.

Residuals Analysis:

After the model fitted, I analyze the residuals of the model. The process of the model residuals is a stationary process and follows a normal distribution.

Trading Strategy:

Like the model residuals is a normal distribution, I calculate the cumulative probability.

Then I am able to display on the chart with a minor timeframe H4 or H1 what will be the tomorrow position with their respecting probability based on volatility max of 2 standards deviations:

Is that a good way to work with the ARMA model? What do you think about this strategy? Can we improve it together?

Thanks

David

## Answer by Malick (score 1)

https://quant.stackexchange.com/a/22456

To improve your model I would recommend you to take into acount the intraday periodicity : ie the fluctuation of the exchange rate over the daily cycle.

For instance we observe strong increase on the volatility around 07:00 GMT (opening of European Market.)

The following image taken from Andersen, T. G., & Bollerslev, T. (1997) illustrates it. It is the average (across several days) absolute returns of the 5 min interval for DM-$ . The drop between intervals 40 and 60 corresponds to the lunch hour in the Tokyo and Hong Kong markets.

So we know that at some periodic time of day the volatility will decrease or increase for sure. You need to take it into account to improve your model. If you do not your forecast will be poor because in some way you are assuming a constant volatility over the day which is not true. Obviously the observed periodicity will depends of your timeframe.

As a basic strategy to tackle this fact, you can apply your ARMA model on a "de-periodicitized " returns serie...

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.