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2017 | OriginalPaper | Chapter

1. Introduction

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Abstract

Research questions from various fields of science ranging from biology over engineering to economics are related to the problem of estimating latent time-dependent variables, based on noisy measurements. The associated estimation problems are called filter problems. Focusing on applications in economics, countless tasks exist which can be tackled by applying filter techniques.

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Footnotes
1
\(\int _{I_{1}}\ldots \int _{I_{d}}f\left (x_{1},\ldots,x_{d}\right )dx_{d}\ldots dx_{1} \approx \sum \limits _{l=1}^{n}f\left (\boldsymbol{\chi }_{l}\right )\alpha _{l}\), with \(I_{1},\ldots,I_{d} \subseteq \mathbb{R}\).
 
Literature
go back to reference Bayes, T., & Price, R. (1763). An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S. Philosophical Transactions of the Royal Society of London, 53(0), 370–418. Bayes, T., & Price, R. (1763). An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S. Philosophical Transactions of the Royal Society of London, 53(0), 370–418.
go back to reference Box, G. E., Jenkins, G. M., & Reinsel, G. C. (2008). Time series analysis: forecasting and control (4th ed.). Wiley series in probability and statistics. Hoboken, NJ: John Wiley and Sons. Box, G. E., Jenkins, G. M., & Reinsel, G. C. (2008). Time series analysis: forecasting and control (4th ed.). Wiley series in probability and statistics. Hoboken, NJ: John Wiley and Sons.
go back to reference Fernández-Villaverde, J. (2010). The econometrics of DSGE models. SERIEs, 1(1–2), 3–49.CrossRef Fernández-Villaverde, J. (2010). The econometrics of DSGE models. SERIEs, 1(1–2), 3–49.CrossRef
go back to reference Heiss, F., & Winschel, V. (2008). Likelihood approximation by numerical integration on sparse grids. Journal of Econometrics, 144(1), 62–80.MathSciNetCrossRefMATH Heiss, F., & Winschel, V. (2008). Likelihood approximation by numerical integration on sparse grids. Journal of Econometrics, 144(1), 62–80.MathSciNetCrossRefMATH
go back to reference Julier, S. J., Uhlmann, J., & Durrant-Whyte, H., editors (1995). A new approach for filtering nonlinear systems. Piscataway and N.J. Distributed through the IEEE Service Center. Julier, S. J., Uhlmann, J., & Durrant-Whyte, H., editors (1995). A new approach for filtering nonlinear systems. Piscataway and N.J. Distributed through the IEEE Service Center.
go back to reference Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35.CrossRef Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35.CrossRef
go back to reference Singer, H. (2015). Conditional Gauss–Hermite filtering with application to volatility estimation. IEEE Transactions on Automatic Control, 60(9), 2476–2481.MathSciNetCrossRefMATH Singer, H. (2015). Conditional Gauss–Hermite filtering with application to volatility estimation. IEEE Transactions on Automatic Control, 60(9), 2476–2481.MathSciNetCrossRefMATH
go back to reference Smolyak, S. A. (1963). Quadrature and interpolation formulas for tensor products of certain classes of functions. Soviet Mathematics Doklady, 4, 240–243.MATH Smolyak, S. A. (1963). Quadrature and interpolation formulas for tensor products of certain classes of functions. Soviet Mathematics Doklady, 4, 240–243.MATH
go back to reference Stroud, A. H., & Secrest, D. (1963). Approximate integration formulas for certain spherically symmetric regions. Mathematics of Computation, 17(82), 105.MathSciNetCrossRefMATH Stroud, A. H., & Secrest, D. (1963). Approximate integration formulas for certain spherically symmetric regions. Mathematics of Computation, 17(82), 105.MathSciNetCrossRefMATH
go back to reference Winschel, V., & Krätzig, M. (2010). Solving, estimating, and selecting nonlinear dynamic models without the curse of dimensionality. Econometrica, 78(2), 803–821.MathSciNetCrossRefMATH Winschel, V., & Krätzig, M. (2010). Solving, estimating, and selecting nonlinear dynamic models without the curse of dimensionality. Econometrica, 78(2), 803–821.MathSciNetCrossRefMATH
Metadata
Title
Introduction
Author
Dominik Ballreich
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-62130-2_1