Solved – Multivariate ARIMA with regression

arimamultivariate regressionr

I have a dataset covering daily data for 3 years (3×365 rows) for multiple attributes TotalPhoneCall (main attribute that I want to predict), Christmas day, weekend, weekday, Easter, 4th_july, etc.(some are seasonal).

I would like to predict TotalPhoneCall for the following month. I have to use ARIMA with regression. I may filter out unnecessary attributes if needed. How can I do this in R?

Best Answer

Your data set / design matrix tells a lot about your assumptions. You are explicitly assuming that week days have a common effect and weekends have a common effect. It is much more general to estimate the individual effects for each day and upon finding a common pattern to possibly reduce the design matrix accordingly.

You are implicitly assuming that

  • there are no lead or lag effects around the known holidays that you are considering,
  • there are no Pulses, Level Shifts and/or Local Time Trends,
  • the day-of-the-week effect is constant over the 1126 observations,
  • there is no particular week-of-the-year effect by only introducing monthly indicators,
  • the parameters of the model don’t change over time,
  • the error variance is constant over time
  • there is no need for ARIMA structure to render the final model’s residuals uncorrelated.

Other than these items, you are good to go!

In a positive note I would strongly suggest that you find a consultant or a program/approach/solution that speaks to some/all of the above considerations. I would start with http://www.unc.edu/~jbhill/tsay.pdf .

after receipt of your data ..

The term Multivariate Arima is synonymous to VECTOR ARIMA i.e. multiple endogenous series. your problem has 1 endogenous (output) series thus and multiple inputs. This is called a Transfer Function. I note (but ignored) that you had negative phone calls. The data

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One can suggest Holiday impacts and identify lead and lag structure around these events. In addition, there may be unusual activity that needs to be isolated/accounted for in order to get robust estimates of the daily effects/the monthly effects, the day-of-the-month effects, the week of the month effects. Following is the Actual-Fit-Forecast graph

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and the residual plot

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A plot of the forecasts for the next 21 days is presented here.

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The actual equation is presented here in two parts

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and

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In summary your model has the following characteristics. enter image description here. In summary the third week of the month is statistically significant along with two level shifts at periods 5/15/09 and 5/20/10. Additionally, your series is impacted positively on Thursday and Monday and negatively on Saturday. There is a strong impact due to some specific months of the year and a few holidays.

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