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)?
 A: 
But it is sensless to include data from night hours if I trade only during day.

You have to distinguish two elements of your problem:


*

*understanding how a time series develops (e.g. by building a model for it);

*utilizing your understanding to find out a function of this development (e.g. a forecast for a specific time period).


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 $x_2$. 
Now back to your original problem: if the time series development at night were totally unrelated to its development at daytime, you could just ignore the night hours. But in all likelihood the relation is there, so better account for it.
In other words, I would address the two core elements of your problem in turns without taking shortcuts.
