Answer-first summary for fast verification
Answer: depends linearly on the squared errors from the previous two quarters.
## Explanation ARCH(2) stands for **Autoregressive Conditional Heteroskedasticity of order 2**. In an ARCH(2) process: - The conditional variance of the error term depends on the squared errors from the previous two periods - The general form is: $\sigma_t^2 = \alpha_0 + \alpha_1 \varepsilon_{t-1}^2 + \alpha_2 \varepsilon_{t-2}^2$ - This means the variance in the current quarter depends linearly on squared errors from quarters t-1 and t-2 **Why other options are incorrect:** - **ARMA process (A)**: ARMA models apply to the mean of the series, not the variance - **Time trend and previous quarter (C)**: ARCH models don't include time trends; they depend only on past squared errors The key characteristic of ARCH(p) processes is that the conditional variance depends on p lagged squared error terms.
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An analyst models the quarterly sales growth data of an online retailer and observes that the model's error term is heteroskedastic and follows an ARCH(2) process. This implies that the variance of the error term in the current quarter:
A
follows an autoregressive moving-average (ARMA) process.
B
depends linearly on the squared errors from the previous two quarters.
C
depends linearly on a time trend and the squared error from the previous quarter.
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