UGC-NET 2025 Question 81: Binary-choice and time-series models

Let $\{\epsilon_t\}$ be a purely random process with mean zero and variance $\sigma^2$. Consider:

A. A process $\{x_t\}$ defined by $x_t = \alpha_1 x_{t-1} + \alpha_2 x_{t-2} + \dots + \alpha_r x_{t-r} + \epsilon_t$ is called an autoregressive process of order r
B. A process $\{x_t\}$ defined by $x_t = \beta_0 \epsilon_t + \beta_1 \epsilon_{t-1} + \dots + \beta_m \epsilon_{t-m}$ is called a moving average process of order m
C. A process $\{x_t\}$ defined by $x_t = \beta_0 \epsilon_t + \beta_1 \epsilon_{t-1} + \dots + \beta_m \epsilon_{t-m}$ is called an autoregressive process of order r
D. A process $\{x_t\}$ defined by $x_t = \alpha_1 x_{t-1} + \alpha_2 x_{t-2} + \dots + \alpha_r x_{t-r} + \epsilon_t$ is called a moving average process of order m