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.

ADF Test for the model residuals

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:

Chart with the Probability for the next day

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



  • $\begingroup$ Not sure if I understood this, but what is the rationale of doing a unit-root test on the residuals? They will of course be stationary around 0. $\endgroup$
    – Slug Pue
    Dec 22, 2015 at 15:29
  • $\begingroup$ Same as @SlugPue and you should produce one step ahead forecast and then apply the confidence interval on the point forecast. You should also consider that on the forex, the volatility has a periodic behaviour. $\endgroup$
    – Malick
    Dec 22, 2015 at 20:31
  • $\begingroup$ @SlugPue Hi thanks for your reply. In fact I am doing a unit root test to check that the residuals of the model are stationary. But I agree with you that there is no doubt on that, it was just a checking. $\endgroup$ Dec 22, 2015 at 23:51
  • $\begingroup$ @Malick Hi Thanks for your reply. In the last image that I published, I have already produced the forecast, and then I calculate the probability based on the new forecast. Can you explain be better what do you mean by: periodic behaviour of the volatility? Do you mean GARCH model? $\endgroup$ Dec 22, 2015 at 23:57

1 Answer 1


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.

Avg Absolute Return

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...

  • $\begingroup$ Hi Malick, thanks you very much for your suggestion. I am sure that if I include the volatility into the algorithm, the model will be better. But in fact, my question was about how interpret residuals from ARMA model. If we consider that the residuals distribution is normal (Shapiro Test or QQPlot), can we use the cumulative distribution in order to take decision on trading opportunity. What do you think? $\endgroup$ Jan 5, 2016 at 16:53
  • 1
    $\begingroup$ No you should perform points forecasts to obtain with a certain level of confidence the next returns. And based on it you can place orders. If you just use the volatility you are losing the autoregressive framework on the mean process. $\endgroup$
    – Malick
    Jan 5, 2016 at 17:04
  • $\begingroup$ Hi Malick, yes you are right. In my case, the forecasting is not really confident if I use the ARMA model only: 53% of right direction forecasting. I would like to quantify, the forecasting signal , do you have any idea how to do that using the ARMA model? $\endgroup$ Jan 6, 2016 at 16:18

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