Two strings of magnets — the underlying linearity between randomness

On the last econometrics class, the professor didn’t talk about the econometric theory on the textbook. Instead, he told us the profound theory established by the nobel laureats Clive Granger and Robert Engle.

Their theory argues that there exists a highly significant linear relationship between two “random walk” processes.Short-run changes in time series are frequently stationary, even when the time series themselves are nonstationary in the long run. So one strategy in the face of nonstationary data was to study only short-run changes. But Granger (working with Engle) realized that such a strategy threw away valuable information. Not all long-run associations between nonstationary time series are nonsense. 

Suppose that the randomly walking drunk has a faithful (and sober) friend who follows him down the street from a safe distance to make sure he does not injure himself. Because he is following the drunk, the friend, viewed in isolation, also appears to follow a random walk, yet his path is not aimless; it is largely predictable, conditional on knowing where the drunk is.

The professor compared the two random walk processes to two strings of magnets. Although they seem to be independent from each other, their inner cointegration prevents them from separating.

The discovery is truly amazing, though based on very simple ideas. Personal development trajectory is sometimes like a random walk, but people of similar traits often end up on similar paths. The two random processes are closely related in an implicit way.

In reminiscing about his childhood, Sir Clive wrote, “A teacher told my mother that ‘I would never become successful,’ which illustrates the difficulty of long-run forecasting on inadequate data.” Forecasting is to reach the best based on what we have. It’s the same of achieving individual success.

Note: for more information of the theory, refer to


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