Which of the following is least likely a consequence of a model containing ARCH(1) errors? The:
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The presence of autoregressive conditional heteroskedasticity (ARCH) indicates that the variance of the error terms is not constant. This is a violation of the regression assumptions upon which time series models are based. The addition of another lag variable to a model is not a means for correcting for ARCH (1) errors.
Suppose you estimate the following model of residuals from an autoregressive model:
εt2 = 0.25 + 0.6ε2t-1 + μt, where ε = ε^
If the residual at time t is 0.9, the forecasted variance for time t+1 is:
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The variance at t=t+1 is 0.25 + [0.60 (0.81)] = 0.25 + 0.486 = 0.736.
Suppose you estimate the following model of residuals from an autoregressive model:
εt2 = 0.4 + 0.80εt-12 + μt, where ε = ε^
If the residual at time t is 2.0, the forecasted variance for time t+1 is:
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The variance at t=t+1 is 0.4 + [0.80 (4.0)] = 0.4 + 3.2. = 3.6.
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