# Forecasting Multi-variate data using Arima errors with Fourier terms and covariate on a weekly data in R

I'm planning to do a multivariate time series forecasting using arima errors with fourier terms. Data assumptions-moderate seasonality. one independent variable(x) and dependent variable(y) Weekly data collected for 148 weeks. y has some good correlation with x. So planning to forecast y based on the correlation with x along with the fourier values of y.

df.y<-ts(y, frequency=52)
df.x<-ts(x,frequency=52)
zx.f<-fourier(df.x, K=2,h=26) #fourier values of x variable
forecast.x<-auto.arima(df.x,xreg=zx.f,approximation=F,h=26) #forecast values of x

zy.f<-fourier(df.y,K=2,h=26) #fourier values of y variable
forecast.y<-auto.arima(df.y,xreg=cbind(forecast.x,zy.f),approximation=F,h=26) #forecast y using
fourier values of y and forecast values of x

Is it right to use forecasted values of x and Fourier values of Y when forecasting the Y variable? i have just used cbind on the xreg parameter to use both forecasted variable(x) and Fourier values of y