What is a fundamental difference between typical time series data and cross-sectional data that violates a standard OLS assumption?

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BlackTom AI · Accepted Answer

The question asks about a fundamental difference between typical time series data and cross-sectional data that breaches a standard OLS assumption.
Option 1: 'Time series observations are typically not independently drawn (violates MLR.2).' This is a core issue with time series: observations are often correlated over time (serial correlation or autocorrelation), which means the independence assumption (MLR.2) is violated, potentially biasing standard errors.
Option 2: 'Time series data always exhibits perfect collinearity (violates MLR.3).' Perfect collinearity is a problem for estimating the model when a regressor is a perfect linear combination of others; this is not a general or fundamental feature of time series versus cross-sectional data, and it is not a universal property of time series data.
Option 3: 'Time series errors never have a zero conditional mean (violates MLR.4).' In OLS, the zero conditional mean of errors is a key assumption; time series data can have heteroskedasticity or autocorrelation, but the statement that errors never have zero conditional mean is incorrect as a general rule. The assumption concerns E[u|X]=0, not a time-series-specific outcome that errors never have zero conditional mean.
Option 4: 'Time series data cannot be linear in parameters (violates MLR.1).' The linearity in parameters (MLR.1) is a property of the model specification, not something inherently violated by time series data; many time series models are linear in parameters, so this claim misstates the nature of time series modeling.
In summary, the essential distinction here is the dependence structure: time series data tend to display autocorrelation, which clashes with the independence requirement of MLR.2, making Option 1 the correct characterization among the choices provided.

What is a fundamental difference between typical time series data and cross-sectional data that violates a standard OLS assumption?

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