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FRM Part I · FRM Exam Part I · Nonstationary Time Series

A series follows Y_t = Y_{t-1} + e_t with e_t white noise. A researcher regresses Y_t on an independent random walk X_t, both of length 500, and obtains a slope t-statistic of 9 and R-squared of 0.60, but the residuals are highly persistent with Durbin-Watson near 0.05. What is the most appropriate interpretation?

This is most likely a spurious regression. Regressing independent unit-root series on each other yields large t-statistics, high R-squared and highly autocorrelated residuals. The appropriate response is to difference the series or test for cointegration rather than trust the apparent relationship.

  1. AThe relationship is genuine because the t-statistic is large
  2. BThe result is likely a spurious regression; the variables should be differenced or tested for cointegrationCorrect
  3. CThe R-squared is too low; adding more lags of Y will confirm the relationship
  4. DThe persistent residuals show the series are stationary around a trend

Explanation

Regressing independent unit-root series produces inflated t-statistics and R-squared with strongly autocorrelated residuals, the signature of spurious regression. The remedy is differencing or cointegration testing. Large t-statistics are unreliable here because standard distributions fail.

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