Answer: III only

**Explanation:** Let's analyze each statement: **Statement I:** "If the autoregressive (p) in an ARIMA model is 1, there is no autocorrelation in the series." - **INCORRECT** - In ARIMA models, p represents the autoregressive component. If p = 1, it means the current value depends on the previous value (lag 1), indicating autocorrelation at lag 1. - If p = 0, then there is no autoregressive component and no autocorrelation from the AR perspective. **Statement II:** "If (d), the integrated component in an ARIMA model is 0, the series is not stationary" - **INCORRECT** - The d parameter represents the number of differencing operations needed to make the series stationary. - If d = 0, it means no differencing is required, suggesting the original series is already stationary (or at least not integrated). - If d > 0, then the series is non-stationary and requires differencing to become stationary. **Statement III:** "There is autocorrelation in a series with lag 1 if the moving average component (q) in an ARIMA model is 1" - **CORRECT** - In ARIMA models, q represents the moving average component. - If q = 1, it means the current value depends on the previous error term (lag 1), which indicates autocorrelation at lag 1. - The moving average component captures the effect of past shocks/errors on the current value. Therefore, only Statement III is correct, making option C the correct answer. **Key Concepts:** - **ARIMA(p,d,q)**: Autoregressive Integrated Moving Average model - **p (AR)**: Number of autoregressive terms - captures relationship with past values - **d (I)**: Number of differencing operations - makes series stationary - **q (MA)**: Number of moving average terms - captures relationship with past error terms

Author: Nikitesh Somanthe