# ARIMA model coefficients from discontinuous data series

Stock prices are not stationary processes during all week or all day. For example EURGBP has low variability at night in Europe but during working hours is changing much more dynamic because of market liquidity.

I want to collect history data (15 minutes interval), calculate ARIMA coefficients and get prediction in R. But it is sensless to include data from night hours if I trade only during day.

So, is it possible to create ARIMA model based on discontinous data series (like 10:00 - 16:00 Monday, 10:00 - 16:00 Tuesday, 10:00 - 16:00 Wednesday, etc.)? How to merge this data minimizing the error (price from Tuesday 10:00 de facto is not next price after Monday 16:00)?

• I was going through my old answers and noticed this one was not accepted. Do you perhaps need further clarification? – Richard Hardy Feb 24 '17 at 14:07

Think of an analogy: if the true model is $$y=\beta_0+\beta_1 x_1 + \beta_2 x_2 + u$$ and you are only interested in $\beta_0$ and $\beta_1$ but not $\beta_2$, you are still better off estimating $\beta_0$ and $\beta_1$ from the true model rather than the submodel $$y=\beta_0+\beta_1+v.$$ Your estimates from the full model will be more accurate, and considerably so if $x_1$ is (highly) correlated with $x_2$.