A wavelet analysis for time series

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. This paper is mainly concerned with the analysis of regional house price cycles. Based on a newly available data set consisting of the 40 largest U.S. Metropolitan Statistical Areas (MSAs), we introduce a wavelet transform based metric to study the housing cycle synchronization across MSAs. We derive several conclusions: (i) We show that regional housing cycle dissimilarities are significantly and strongly connected to geography. Terms of use: Documents in(ii) We show that U.S. regional housing cycles are considerably shorter compared to business cycles. (iii) By employing statistical methods, we also show that regional housing prices significantly converge after the bursting of the bubble only at higher business cycle frequencies, whereas for lower business cycle frequencies this is not the case. This is a notable result, because it directly implies that housing cycles behavior is different even at the business cycle.JEL-Code: C320, C330, E320, R110, R310.

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“…See the FHFA FAQs. 13 For a detailed description of the properties of wavelets see also Chiann and Morettin (1998).…”

Section: Some Basic Ingredientsmentioning

confidence: 99%

On the cyclicity of regional house prices: New evidence for U.S. metropolitan statistical areas

Flor¹,

Klarl

2017

Journal of Economic Dynamics and Control

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“…We conclude by noting that the proposed NLT has potential applications not only in nonparametric regression problems, but also in spectral estimation where it can be used for obtaining a wavelet-like periodogram to estimate the spectrum (see for instance Chiann and Morettin (1999), Nason et al (2000)), which is a potential direction of future research. ) simulation results for test signals sampled at irregular locations and corrupted with noise at SNR=3, 5, respectively 7, for the lifting algorithm with AP1S prediction ('JNS' for amse JNS ) and for our NLT with AP1S prediction ('Perm' for amse perm ).…”

Section: Discussionmentioning

confidence: 99%

A ‘nondecimated’ lifting transform

Knight

Nason

2008

Stat Comput

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Classical nondecimated wavelet transforms are attractive for many applications. When the data comes from complex or irregular designs, the use of second generation wavelets in nonparametric regression has proved superior to that of classical wavelets. However, the construction of a nondecimated second generation wavelet transform is not obvious. In this paper we propose a new 'nondecimated' lifting transform, based on the lifting algorithm which removes one coefficient at a time, and explore its behaviour. Our approach also allows for embedding adaptivity in the transform, i.e. wavelet functions can be constructed such that their smoothness adjusts to the local properties of the signal. We address the problem of nonparametric regression and propose an (averaged) estimator obtained by using our nondecimated lifting technique teamed with empirical Bayes shrinkage. Simulations show that our proposed method has higher performance than competing techniques able to work on irregular data. Our construction also opens avenues for generating a 'best' representation, which we shall explore.

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“…Wavelet analysis is a special type of linear transformation of signals and physical data [2,3]. The basis of eigenfunctions employed by signals decomposition has many specific properties and possibilities.…”

Section: State Of the Art And Relevancementioning

confidence: 99%

Building Modern Vibration Diagnostics Systems Based on the Frequency-Time Transformations of A Measured Signal

Yasoveev

Akhmetshin

2016

MATEC Web Conf.

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Abstract. Basic methods of analysis of vibration transducers signals were reviewed. Continuous wavelet transform, being a time-frequency transform, was found to be an advanced mathematical tool for analysis of vibration signals. Experimental studies revealed obvious changes in the continuous wavelet transform spectrum depending on the existing defects. A method for detection and identification of technological violations based on the analysis of CWT spectrum components and normalized correlation coefficient was suggested. In accordance with the suggested method software for vibration diagnostics was developed.

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A wavelet analysis for time series

Cited by 64 publications

References 32 publications

On the cyclicity of regional house prices: New evidence for U.S. metropolitan statistical areas

On the cyclicity of regional house prices: New evidence for U.S. metropolitan statistical areas

A ‘nondecimated’ lifting transform

Building Modern Vibration Diagnostics Systems Based on the Frequency-Time Transformations of A Measured Signal

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