Suppose we find a significant positive relationship between X and Y because of the trend in both series. We can solve this problem by:

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The question concerns a situation where a significant positive relationship between X and Y may arise due to common trends in both series rather than a substantive association.

Option presented: a. Detrending.

Explanation of the option: Detrending is a preprocessing step used to remove deterministic trends from time series data, such as a steady upward or downward drift over time. By removing the trend component, you reduce the chance that spurious correlations driven by shared trends will inflate the apparent relationship between X and Y. This aligns with standard time series practices to address non-stationarity in mean level.

Why this helps: If both series share a similar upward trend, a naive regression or correlation can pick up that trend rather than any underlying causal or associative link. Detrending helps test for a relationship in the stationary residuals, where changes rather than levels are examined.

Potential caveats: Detrending may also remove meaningful long-run relationships if those trends reflect structural connections between X and Y. In such cases, alternative approaches like cointegration analysis or modeling common trends explicitly might be more appropriate. It is important to check whether the relationship persists in detrended data before drawing substantive conclusions.

Absence of other options: The provided information lacks any additional answer choices to compare. If other options existed (e.g., differencing, using growth rates, applying cointegration tests, incorporating time-fixed effects), they could offer different pathways to address spurious correlations due to trends. Without them, the assessment must focus on the stated option and its rationale within the context described.

ECON7950 (1) [2024 B2] In-Class Quiz 1

Suppose we find a significant positive relationship between X and Y because of the trend in both series. We can solve this problem by:

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