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Interview prep / ML/Data

Residual diagnostics and a trend

Question

A levels regression between two unrelated trending price series has a high R squared. What would you investigate?

Short answer

Investigate nonstationarity and the possibility of a spurious regression. Plot levels and changes, inspect residual persistence, and evaluate economically justified transformations or a defensible cointegration hypothesis. Ordinary iid significance calculations can be misleading for persistent series. A high in-sample R squared does not establish a stable forecasting relationship, and differencing is a modelling choice rather than a universal fix.

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