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Journal of Economics and Finance

Erschienen in:

01.01.2016

Persistence and cyclical dependence in the monthly euribor rate

verfasst von: Guglielmo Maria Caporale, Luis A. Gil-Alana

Erschienen in: Journal of Economics and Finance | Ausgabe 1/2016

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Abstract

This paper analyses two well-known features of interest rates, namely their time dependence and their cyclical structure. Specifically, it focuses on the Euribor rate, using monthly data from January 1994 to May 2011. Two models are considered, one with fractional integration at the long run or zero frequency, and the other replacing the zero frequency with a cyclical one. The results indicate that the latter outperforms the former as well as other standard specifications. Future directions for research (such as nonlinearities, volatility behaviour, and multivariate models) are also discussed.

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Recently, Gil-Alana and Moreno (2012) have proposed a fractional integration model for the short-term interest rate and the term premium.

See Doukhan et al. (2003) and Gil-Alana and Hualde (2009) for a review of fractional integration in economic time series.

Note that these two conditions, which can be expressed as γ_j ~ c j^2d-1 as j → ∞, and f(λ) ~ c^*λ^-2d as λ → 0⁺, for 0 < c, c^* < ∞, are not always equivalent but Zygmund (1995, Cap. V, Section 2) and Yong (1974) in a more general case give conditions under which both expressions are equivalent.

Such processes were first considered in the 1960s by Granger (1966) and Adelman (1965) who pointed out that for most aggregate economic time series the spectral density function increases sharply as the frequency approaches zero and that differencing the data leads to overdifferencing at the zero frequency.

Note that, strictly speaking, the spectral density function of x_t only exists for d < 0.5. If of d ≥ 0.5, one can use the term “quasi spectral density function”. The same applies to the autocovariances above, where the term “quasi autocovariances” can be used for nonstationary processes.

Note that if │μ│ < 1 and d in (2) increases beyond 0.5, the process becomes “more nonstationary” in the same sense as before, i.e. the variance of the partial sums increases in magnitude.

Alternatively daily data, which are also available from the ECB, could have been used. However, this paper focuses on two specific features of the Euribor, i.e. cyclicality and dependence, and for our purposes monthly data are more appropriate.

Burn and Mitchell (1946), Romer (1986, 1994), Stock and Watson (1999), Diebold and Rudebusch (1992), Canova (1998), Baxter and King (1999), King and Rebelo (1999) among others showed that the average length of the cycle is approximately 6 years.

Diebold and Rudebusch (1991), Hassler and Wolters (1994), and Lee and Schmidt (1996) inter alia have shown that standard unit root tests have very low power against fractional alternatives.

This method is based on the Lagrange Multiplier (LM) principle. A Wald testing approach (Lobato and Velasco 2007) was also implemented, using the Whittle estimates of d. The results were completely in line with those reported here.

The t-values for the time trend coefficients (not reported) indicate that these are insignificant in all cases, whilst the intercept is always significant. Moreover, the inclusion of non-linear deterministic trends (in the the form of the Chebyshev polynomials, Bierens 1997; Cuestas and Gil-Alana 2012) also leads to insignificant coefficients.

This method is fairly general since it allows to test any integer or fractional order of integration on the unit circle in the complex plane, including roots at both zero and non-zero frequencies.

The time trend in the undifferenced process in (6) does not necessarily mean that there is a decreasing trend in the process noting that for values of d in the interval (0, 1) the time trend disappears in the long run.

Note, however, that these forecasting methods have under some circumstances very low power, especially for non-linear models (see, e.g., Costantini and Künst 2011).

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Titel: Persistence and cyclical dependence in the monthly euribor rate
verfasst von: Guglielmo Maria Caporale
Luis A. Gil-Alana
Publikationsdatum: 01.01.2016
Verlag: Springer US
Erschienen in: Journal of Economics and Finance / Ausgabe 1/2016
Print ISSN: 1055-0925
Elektronische ISSN: 1938-9744
DOI: https://doi.org/10.1007/s12197-014-9296-0

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