## A threshold cointegration analysis of Norwegian interest rates

##### Forfatter

Larsen, Berner##### Sammendrag

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.

##### Forlag

Universitetet i TromsøUniversity of Tromsø

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