scholarly journals MONEY, CREDIT, HOUSE PRICES AND QUANTITATIVE EASING – THE WAVELET PERSPECTIVE FROM 1970 TO 2016

2019 ◽  
Vol 20 (3) ◽  
pp. 546-572 ◽  
Author(s):  
Maciej Ryczkowski
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
European Central Bank ◽  
House Prices ◽  
House Price ◽  
Quantitative Easing ◽  
Continuous Wavelet ◽  
Price Inflation ◽  
European Central ◽  
Long Run

This paper investigates the relationship between money/credit growth and house price inflation for a sample of twelve developed countries. The novel application of the continuous wavelet transform showed significant but time-varying linkages between these two variables. During quantitative easing in the United States and the United Kingdom, growth of respectively broad money and bank credit was leading house price inflation for the 2-8 years cycle. In contrast to this, the Bank of Japan and the European Central Bank either did not assign a separate role to house prices in their reaction functions or the two central banks were not capable to significantly increase house prices by extending money/credit during the business cycle. The significant co-movements of financial variables and house prices around booming episodes warn us that a new asset price boom might appear within the length of a business cycle as a consequence of overly expansionary monetary policy. In the euro area, the significant, long run, and close to a one-for-one link between growth of M3 and house price inflation is an argument for the monetary pillar of the European Central Bank. The present study contributes significantly to the literature by introducing a novel application of a continuous wavelet transform to study the housing prices in relation to money, credit and quantitative easing. The article uses a long-term dataset covering a period of almost half a century to analyse their varying relationship in the short-run to the long-run and from the historical perspective.

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

scholarly journals Automatic ECG Classification Using Continuous Wavelet Transform and Convolutional Neural Network

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 119
Author(s):  
Tao Wang ◽  
Changhua Lu ◽  
Yining Sun ◽  
Mei Yang ◽  
Chun Liu ◽  
...  
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Convolutional Neural Network ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Ecg Signals ◽  
Rr Interval ◽  
Frequency Components ◽  
Fully Connected

Early detection of arrhythmia and effective treatment can prevent deaths caused by cardiovascular disease (CVD). In clinical practice, the diagnosis is made by checking the electrocardiogram (ECG) beat-by-beat, but this is usually time-consuming and laborious. In the paper, we propose an automatic ECG classification method based on Continuous Wavelet Transform (CWT) and Convolutional Neural Network (CNN). CWT is used to decompose ECG signals to obtain different time-frequency components, and CNN is used to extract features from the 2D-scalogram composed of the above time-frequency components. Considering the surrounding R peak interval (also called RR interval) is also useful for the diagnosis of arrhythmia, four RR interval features are extracted and combined with the CNN features to input into a fully connected layer for ECG classification. By testing in the MIT-BIH arrhythmia database, our method achieves an overall performance of 70.75%, 67.47%, 68.76%, and 98.74% for positive predictive value, sensitivity, F1-score, and accuracy, respectively. Compared with existing methods, the overall F1-score of our method is increased by 4.75~16.85%. Because our method is simple and highly accurate, it can potentially be used as a clinical auxiliary diagnostic tool.

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