Solved – Modeling Time-Series with a lower bound

arimatime series

I am trying to fit a model to a time series that has a lower bound (at around -150). Using an ARIMA model, running simulations often leads to the time series hitting (and going underneath) this lower bound. How can I avoid this? Is there a better model I can use?

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The only way I can think of is to ignore values under 150

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Solved – High-Frequency Time-Series Forecast With A Lower Bound

Basically, you're looking for outliers in a time series. You're most interested in low outliers (but high outliers might be interesting too). This site already has a lot of information posted on this topic, but I'd like to specifically point you to this answer by Rob Hyndman:

The basic idea is to find robust estimates of the trend and seasonal components and subtract them. Then find outliers in the residuals.

(link to question)

In your case, it's a little trickier, as there's a 2 "seasonalities" in your data: minute-of-the-day and day-of-the week. One place to start might be a simple linear regression with dummy variables for minute-of-the-day and day-of-the-week and a simple linear trend variable (number of minutes since the start of the dataset). Fit this model to the data, and then look for outliers on the residuals.

Once you've got that working, you can look for more robust estimates of the 2 seasonal periods and the trend, using either loess smoothers, splines, or some variation of the stl function.

Solved – Time series modeling with dynamic regressors in SAS vs R

While it is not built in, it is easy enough to do:

library(forecast)
fity <- auto.arima(y, xreg=x)
fitx <- auto.arima(x)
forecast(fity,h=10,xreg=forecast(fitx,h=10)$mean)

However, the prediction intervals obtained do not account for the variance in the forecasts of x. I doubt that SAS handles this either.

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Related Solutions

Solved – High-Frequency Time-Series Forecast With A Lower Bound

Solved – Time series modeling with dynamic regressors in SAS vs R

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