Seasonality, daily data, business calendar

[Vincent Haan]

Hello,

I have some daily macroeconomic variables, which I only use on working days. I would like to check if these variables exhibit any form of seasonality, and tried to use a ARIMA (1, 0, 0) model on each of the variables. The model would look something like this.

 arima MacroVariable Q2 Q3 Q4, arima(1,0,0)

However, for none of my macroeconomic variables any of the seasonality dummies are significant. Would this imply that my data does not exhibit seasonality? Or should I undertake more steps?

[Nick Cox]

It's far from clear what you're doing here. You have daily data but without any other information I can only guess that Q2 Q3 Q4 are indicators for quarters. Many macroeconomic variables (what? where?) are pre-adjusted for seasonality any way. What is it that you fear? Time of week? month? year?

Plotting the data on a relevant time scale is simplest and often best for checking.

[Vincent Haan]

Nick,

First of all, thank your for responding, and my fault, I'll try to be more precise.

I have 4 macroeconomic variables (first-differenced, daily, on working days, spanning roughly 20 years), which I intent to use as some sort of control variables in the conditional variance of a GARCH model. A 3 Month Treasury Bill Rate variable and a variable for the Trade-adjusted Dollar value are not seasonally adjusted, and therefore I was interested if they were. The Q2 Q3 Q4 are indeed indicators for quarters, but of course half-yearly or monthly indicators are also possible. I was just wondering that if I test in this ARIMA form, I can conclude anything from it.

[Nick Cox]

If your model is inadequate you should see patterns in the residuals.