Cointegration tests with smooth breaks and co-movements of international reserves

Abstract

In the first essay, we propose a new Autoregressive Distributive Lag (ADL) cointegration test in the presence of structural breaks approximated by a Fourier function. The test offers a simple way to capture a smooth structural change in time series data. Exact break dates are not required, and the suggested methodology can accommodate various types of models with an unknown number and form of gradual structural changes. An empirical example of real oil prices, oil production, and real economic activity using the new test shows that these variables are cointegrated, while a conventional ADL test ignoring structural breaks yields an opposite result. In the second essay, we develop a new Fourier Engle-Granger (FEG2) co-integration test to approximate structural breaks in time-series. We note that a common-factor-restriction (CFR) is imposed in the Engle-Granger (EG) test. The restriction implies the identical long-run and short-run dynamics in the relationship among the variables of interest. This chapter develops a new Engle-Granger (FEG2) co-integration test that not only prevents the power loss issue from the existing EG test but also accommodates underlying nonlinearity in the data through a Fourier transformation. We allow for different long-run and short-run dynamics of the variables. The new EG2 co-integration test with a Fourier approximation detects the co-integration relationship among the crude oil price, crude oil production, and real economic activity even when the data is subject to higher frequencies. In contrast, the conventional EG test with a Fourier function fails to detect the co-integration in a similar situation due to the restrictive assumption of the CFR. In the third and final essay, we examine global co-movements of international reserves (IR) and their effects on the variations of IR holding in each country. To begin with, we evaluate how pervasive global co-movements of international reserves are. For this, we estimate the global, regional and country-specific factors of international reserves by using a dynamic factor model with time-varying factor loadings and stochastic volatility. We find that a global factor is a dominant component and it causes co-movements among international reserves in the world. Then the degree of association of each country’s reserve holding with the common global factor is analyzed. Results show that after the great financial crisis (GFC) the correlation of each country with the global factor drops remarkably compared to the pre-crisis period. Following the fact, we examine the driving forces of the IR through the estimated global factors of key macro-economic variables and notice that the dynamics of the driving forces become opposite after the financial crisis. Lastly, we examine the inter-temporal effects of the global factor of IR with the global factors of the key control variables by using a VAR model.