Black Swan Outlook

May 2025: Special issue on cointegration in time series

This month’s Outlook is a special issue on cointegration in time-series analysis. While the concept is relatively old, it is still somewhat debated in the statistics literature. Its foundation lies in the assumption of stochastic trends. What is meant by them are random “stochastic” shocks that drive the behavior of a series of a variable through time. The characteristic of a stochastic trend process, or a random walk, is a time series that wanders through time, possibly around some upward-sloping trend. The forecasting of such a series is complicated by several factors, which we mapped last month.

Cointegration of two or more random-walk series establishes a (mathematical) bond between the variables. They tend to move through time ‘hand-in-hand.’ This, quite simply, makes the forecasting of the two (or more) cointegrated series easier and generally more effective because we can harvest information from both of the series and on their equilibrium relationship. Unit-root processes (a third name for the same process) are rather common in the economy, because the development of different economic variables, like gross domestic product, is dictated by the interaction of a multitude of other variables. This is the main reason why economic time-series tend to show wild fluctuations at times, while at times they can appear docile. This occurs, because they are driven by differing shocks, creating the stochastic trend process.

GDP Forecasts

We have updated our forecasts to reflect the findings of our recent forecasts. The debt stimulus enacted by Beijing and the (debt) stimulus to be enacted by President Trump are likely to carry the world economy for a while longer. However, we are assuming that further fiscal stimulus will not go down well with investors. President Trump risks a debt crisis in the U.S., like Tuomas explained in April. It is our current assessment that the ‘Big Beautiful Bill’ will pass, and, as a result, the U.S. will face growing issues in the Treasury markets heading into next year.

Forecasts for the quarter-to-quarter growth of real gross domestic product (GDP). Source: GnS Economics, Federal Reserve Bank of Atlanta, Bank of Finland, Banca D’Italia, Euroarea now-cast.

Our forecasts indicate that we would see robust growth in basically all countries/areas during this year, as indicated by our recent forecasts. Problems in the markets spilling over into the banking sector would become visible next year, which would start to dampen the growth prospects. We are thus assuming that the recession would start during H1 next year and would be accompanied by a financial crisis. We return to this in next week’s Weekly Forecasts.

Forecasts for the stimulus of China

Slowing down. The amount of money entering the Chinese economy grew by RMB1.160 trillion in April (our forecast was RMB1.191 trillion). This is a notable deceleration from previous months and from the previous April. The only times April has seen a lower flow of financing over the past 13 years we have been in 2012, 2015, 2016, 2018, 2022, and 2024. However, this is a major increase from the RMB72 billion that was withdrawn from the Chinese economy in April of last year.