Relationships Between the American and Canadian Economies

Time Series Analysis Using Cointegration

July 2022

Understanding the behavior of a system of time series, and in particular how the interrelate, is an important topic in several fields.  Cointegration analysis is a powerful tool for uncovering relationships and long term  deterministic and stochastic trends in such a system. 

Exploring Data

The aim of this project is to better understand the relationship between the Canadian and American economies. Specifically, we are looking to uncover long term trends and interconnectedness of the following 5 macroeconomic time series

  • Consumer Price Index (CPI) in Canada and USA
  • Long term interest rates in Canada and USA
  • The exchange rate between CAD and USD

Note that, in line with common practice in econometrics, the analysis is conducted using log-transformed CPIs and exchange rate while the interest rates remain untransformed. The time series can be seen in the following figure

Uncovering Relationships

The analysis suggests that the system is cointegrated, that is, there exists a linear combination of the time series which is stationary.

Interestingly, the data suggests that the exchange rate and interest rate processes can be considered weakly exogenous, ie. their values are given outside the model. Intuitively, an explanation might be that interest rates are largely dictated by central banks and used as a tool to, for example, attempt to control inflation. In this way, the CPI would in turn react to adjustments in the interest rates. The CPI process enter the cointegration relation with coefficients of the same magnitude. This may not be too surprising, since Canada and USA are neighboring countries with a strong trade relationship.

Analysis of a cointegrating system of time series is very useful for drawing inference in order to better understand the system in terms of long term trends and how the time series relate to one another. However, we can also use a cointegration relation to forecast the system. This can be done since we are able to model the system as a Vector Error Correction Model (VECM), where lagged values of the error correction term is useful for predicting the differenced time series.

Cointegration analysis is thus a powerful tool when we are dealing with a system of integrated time series.