Cointegration and Valid Inference with Integrated Time Series

Summary

The document examines why regressions or correlation tests between nonstationary integrated time series can appear significant even when the relationship is spurious. It refers to early econometric work documenting biased significance tests and later asymptotic analysis explaining that standard statistics may lack convergent behavior for unrelated I(1) series. It then asks whether cointegration resolves this problem because the regression error is stationary.

The author highlights an important distinction: an I(0) residual is not necessarily independent, identically distributed, or normally distributed. The text asks for references establishing when conventional OLS or correlation inference is valid for cointegrated series, and whether cointegration is necessary as well as sufficient. It provides no answer, estimation procedure, or empirical evidence of its own, so it is best read as a question about the assumptions and limits of statistical inference rather than a practical trading method.

Key ideas

• The document notes that regressions between unrelated I(1) series can produce misleading significance.
• It raises cointegration as a possible condition for avoiding spurious inference.
• It distinguishes stationarity of residuals from independent, identically distributed normal residuals.
• It asks whether cointegration is sufficient or necessary for standard OLS inference to be valid.

Tags

# How do brokerage firms provide liquidity?


# How do brokerage firms provide liquidity?












Do they directly put limit orders on the order book? Or do they automatically fill limit/market orders from customers and have offsetting position with their market maker(LP) to offset their net position?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.