Abstract
In this paper, we develop robust methods for forecasting term structures of interest rates. We implement a deep long short-term memory (LSTM) neural network based on keras. Our input data is based on the bootstrapped bid, mid and ask multiple (tenor-dependent) yield curves reflecting different risk categories over the period 2005–2018. We use the bid-ask spreads as an additional input factor modelling the market depth. Since there is only a limited amount of data available, there is a lack of a sufficiently large training data set. We cope with that difficulty by generating data based on fitted time series models in order to enlarge the training data. Furthermore, we apply support vector machines to predict trends in the term structures. For this approach, we include different market variables to investigate the relationship of these quantities to future yields.
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Notes
- 1.
The European market publishes the swap rate of an OIS at every business date for maturities ranging from 1 week to 60 years. The floating leg is indexed on the EONIA rate and the payments are based on annual frequency.
- 2.
We did not use a pre-implemented loss of keras as most of these functions are applicable only for categorization problems, and hence, fail to be of any value for our application.
References
Ang, A., Piazzesi, M.: A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. J. Monet. Econ. 50, 745–787 (2003)
Bennett, K.P., Campbell, C.: Support vector machines: hype or hallelujah? ACM SIGKDD Explor. Newsl. 2, 1–13 (2000)
Bergstra, J., Bengio, Y.: Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13, 281–305 (2012)
Burges, C.J.: A tutorial on support vector machines for pattern recognition. Data Min. Knowl. Discov. 2, 121–167 (1998)
Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20, 273–297 (1995)
Decoste, D., Schölkopf, B.: Training invariant support vector machines. Mach. Learn. 46, 161–190 (2002)
DePooter, M., Ravazzolo, F., van Dijk, D.: Term structure forecasting using macro factors and forecast combination. Working Paper 2010/01, Norges Bank (2009)
Diebold, F., Li, C.: Forecasting the term structure of government bond yields. J. Econ. 130, 337–364 (2006)
Evgeniou, T., Pontil, M., Poggio, T.: Regularization networks and support vector machines. Adv. Comput. Math. 13, 1–50 (2000)
Exterkate, P., Van Dijk, D., Heij, C., Groenen, P.J.: Forecasting the yield curve in a data-rich environment using the factor-augmented Nelson–Siegel Model. J. Forecast. 32(3), 193–214 (2013)
Friedman, J., Hastie, T., Tibshirani, R.: The Elements of Statistical Learning, vol. 2. Springer (2017)
Gerhart, C., Lütkebohmert, E.: Empirical analysis and forecasting of multiple yield curves (2019). Available on https://ssrn.com/abstract=3311998
Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9, 1735–1780 (1997)
Huang, W., Nakamori, Y., Wang, S.Y.: Forecasting stock market movement direction with support vector machine. Comput. Oper. Res. 32, 2513–2522 (2005)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: Proceedings of the 3rd International Conference on Learning Representations (2014)
Koopman, S.J., van der Wel, M.: Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model. Int. J. Forecast. 29(4), 676–694 (2013)
Lantz, B.: Machine Learning with R, 2nd ed. Packt Publishing Ltd. (2015)
Moench, E.: Term structure surprises: the predictive content of curvature, level, and slope. J. Appl. Econ. 27(4), 574–602 (2012)
Nelson, C., Siegel, A.: Parsimoneous modeling of yield curves. J. Bus. 60, 473–489 (1987)
Steinwart, I., Christmann, A.: Support Vector Machines. Springer Science & Business Media (2008)
Witten, I., Frank, E., Hall, M.: Data Mining: Practical Machine Learning Tools and Techniques, 3rd ed. Morgan Kaufmann Publishers Inc. (2011)
Wolpert, D.: Stacked generalization. Neural Netw. 5, 241–259 (1992)
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Gerhart, C., Lütkebohmert, E., Weber, M. (2019). Robust Forecasting of Multiple Yield Curves. In: Valenzuela, O., Rojas, F., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis. ITISE 2018. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-26036-1_13
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