# Assessing Seasonal Covariates in a Seasonal ARIMA Time Series Model

I am using R to develop an ARIMA model to evaluate the influence of several seasonal covariates (e.g., meteorological data) upon the incidence of a seasonal disease. I have weekly data available and have set the period equal to 52 weeks. Using the auto.arima function the disease of interest has a form of ARIMA(0,1,2)(0,0,1).

Using the TSA package, I can then evaluate the influence of each of the covariates:

covariates <- data.frame(covariate1, covariate2, covariate3)
model <- arima(disease, order=c(0,1,2), seasonal=list(order=c(0,0,1), period=52), xreg=covariates)


However, I am worried that this approach is identifying spurious associations between the covariates, each of which has a seasonal component... Is it more appropriate to decompose the covariate data and subtract the seasonal component before fitting the ARIMA model?

covariate1_components <- decompose(covariate1)
[...]
model2 <- arima(disease, order=c(0,1,2), seasonal=list(order=c(0,0,1), period=52), xreg=covariates_adjust)


Any thoughts on which of the two approaches would be preferable for evaluating seasonal covariates?