Final answer:
An AR Model shows heteroskedasticity when the error term variances are not constant, which can occur when a time series' variability is related to its past values. Heteroskedasticity can be detected with tests like Breusch-Pagan or White and addressed using GARCH models.
Step-by-step explanation:
An Autoregressive (AR) Model exhibits heteroskedasticity when the variances of the error terms are not constant across observations.
In time series data, this phenomenon implies that the variability of the time series is dependent on its own past values, and thus, the variance of the errors changes over time.
For example, in financial time series, periods of high volatility tend to cluster, leading to heteroskedastic error terms.
An AR Model should theoretically have constant variance in its error terms for valid inference; however, real-world data often violates this assumption.
To detect heteroskedasticity, tests such as the Breusch-Pagan or the White test can be used.
If heteroskedasticity is present, it can lead to inefficient estimates and affect the standard errors, which in turn can lead to invalid statistical inferences.
One way to address heteroskedasticity is by using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, which allow the conditional variance to change over time based on past squared residuals and past variances.