A threshold cointegration analysis of Norwegian interest rates

Abstract

In this thesis we generalize the Hansen and Seo test in the R package tsDyn, which tests a linear cointegration model against a two-regime threshold cointegration model, to the case of three regimes in the alternative hypothesis. As the Lagrange Multiplier test statistic used in the Hansen and Seo test in tsDyn is different from the LM statistic described in Hansen and Seo (2002), we generalize both these LM statistics, and show that they are equal under certain conditions. The grid search algorithm, which is necessary when maximizing this LM statistic, is also extended to the case of three regimes, and it is rewritten such that if the cointegration value is given, it really maximizes the LM statistic under the constraints specified by the user. In our empirical studies we have examined thoroughly the bivariate time series consisting of the monthly NIBOR rates of the maturities tomorrow next and 12 months. When modeling this bivariate time series, we find strong evidence for a two-regime TVECM being superior to a linear VECM, and in our out-of-sample forecasting the two-regime SETAR model gives much better prediction of the cointegration relation than an AR model. When testing a two-regime SETAR model for the cointegration relation against a three-regime model, the two-regime model cannot be rejected at any reasonable significance level. In addition, we show how influential a few outliers may be by removing them from the time series and rerunning some of the statistical tests. Also, we have tested all the 66 possible pairs of Norwegian interest rates for cointegration, and we have tested the term spread of each pair for threshold effects, i.e., testing a linear model against a two-regime model, as well as testing a two-regime model against a three-regime model. We find a lot of cointegrated pairs, and we find evidence for a two-regime model in approximately 50 % of the cases, and evidence for a three-regime model in some cases in this univariate time series analysis. At last, we simulate a bivariate time series with a three-regime threshold cointegration model as data generation process, and estimate a three-regime threshold cointegration model from this simulated time series. Thus, we illustrate that the thresholds which our version of the Hansen and Seo test detects as optimal, are close to the original thresholds used in the simulation. As expected, a linear model for this bivariate time series is strongly rejected, and there is strong evidence for a three-regime threshold model for the cointegration relation being superior to both a linear model and a two-regime threshold model.