# Is the nominal interest stationary

## Introductory studies on interest structure models

Modeling the Interest Structure in Germany pp 23-76 | Cite as

### Summary

Interest structure models can be differentiated according to whether they model the short-term interest rate as an integrated or a stationary process. In particular, it assumes a stochastic differential equation with a mean value tendency (*mean reversion*) for the process of the underlying factor stationarity.^{1} While in the empirical financial literature on interest structure models, interest rates are regarded as random variables of satational processes, empirical macroeconomic studies mostly proceed *I.*(1) processes. Aït-Sahalia (1996) explains this with the fact that the data there is too low in frequency; Tests of his work on the basis of daily data allow for a *I.*Close (0) property.^{2} It can be countered that, according to the Monte Carlo studies in Perron (1991), the expressiveness (*power*) less common stationarity tests. Stock / Watson (1993) argue that interest rates are conceptually not as random variables of *I.*(1) processes can apply. A process with time-dependent variance results in negative observation values for an infinite time horizon, whereas nominal interest rates are always positive. Consequently, the test result of non-stationarity for interest rates can only be justified in the limited observation period. Against this, it must be countered that an integrated process can follow a path with exclusively positive values with a positive probability. Still is but *ex ante*the probability of negative observation values in the future is strictly positive. The first subsection of this chapter is devoted to this problem.

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