# ARIMA with high frequency data of only one month

I'm analyzing some data I collected for 4 weeks I would like to correlate a dependent variable ($y$) to other 10 independent metereological variables ($x_1, \dots, x_{10}$). ARIMA was suggested as possible statistical method: https://stackoverflow.com/questions/36789439/multivariate-analysis-on-time-series-data.

The problem is that my measurements are made every five minutes and I have only one month of measures. I was thinking that ARIMA could not work so well with this little temporal interval, is it right?

• Do you have 288 measurements? That seems like a reasonable amount to me at first blush. – gung May 23 '16 at 10:41

If you have independent data, you will want to either run an ARIMAX model or a regression with ARIMA errors. There is a difference. Parameter estimates are easier to interpret in regressions with ARIMA errors, which R's auto.arima() and other functions fit.

If you have meteorological data, I'd expect intra-daily seasonality. With data in 5 minute buckets, this translates to a season length of 288, which is quite a lot. Fitting an ARIMA model to long-season data will take a while. In R, you can simulate four weeks' worth of white noise with a seasonal period of 288 and then check how long fitting an ARIMA model will take like this:

library(forecast)
set.seed(1)
foo <- ts(rnorm(4*7*24*12),frequency=24*12)
system.time(auto.arima(foo))


I'd love to tell you how long this took on my machine, but after five minutes, it's still running, and I'm getting bored. It might be better not to let auto.arima() choose the seasonality, but to force seasonality by setting the parameter D=1 - this might speed up matters a bit.

Other software may have similar possibilities of prespecifying the seasonality, and of including covariates.

• Thank you Stephan, I tried to run your example code and my computer crashed, so I think this frequency is too high to run the code. I'll try to set the parameter D=1 and I'll write for new responses. I read the site you suggested me, robjhyndman.com/hyndsight/arimax , and I'll try also to run regression on the arima residuals (run without covariates). – Phalaen May 24 '16 at 12:54
• You are welcome. If my post answered your question, please consider accepting it by clicking the little checkmark under the voting buttons. You get reputation, I get reputation, the next user to come along sees that the post answers the question - everyone wins. – Stephan Kolassa May 24 '16 at 13:00