# What is the sample size for this time series ARIMA model?

If the ARIMA model is: $Y= X_1+X_2+X_3+X_4$

I have data of 50 years.

What is the sample size here?

1. 50 (50 years of observations)
2. 250 (each variable/series has 50 years of observations, total 5 variables, 50*5=250)

The sample size ($n$) is the number of observations you have of the response variable and the corresponding explanatory variables $(y_i, x_i)$. The correct sample size is thus $n=50$, since you have $50$ such pairs of response and explanatory variables.