scholarly journals Wavelet Transform as an Alternative to Power Transformation in Time Series Analysis

2016 ◽  
Vol 17 ◽  
pp. 57-74
Author(s):  
Chukwudi Justin Ogbonna ◽  
C. Jeol Nweke ◽  
Eleazer C. Nwogu ◽  
Iheanyi Sylvester Iwueze
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Goodness Of Fit ◽  
Discrete Wavelet ◽  
Power Transformation ◽  
Rate Data ◽  
Forecast Performance ◽  
Constant Variance

This study examines the discrete wavelet transform as a transformation technique in the analysis of non-stationary time series while comparing it with power transformation. A test for constant variance and choice of appropriate transformation is made using Bartlett’s test for constant variance while the Daubechies 4 (D4) Maximal Overlap Discrete Wavelet Transform (DWT) is used for wavelet transform. The stationarity of the transformed (power and wavelet) series is examined with Augmented Dickey-Fuller Unit Root Test (ADF). The stationary series is modeled with Autoregressive Moving Average (ARMA) Model technique. The model precision in terms of goodness of fit is ascertained using information criteria (AIC, BIC and SBC) while the forecast performance is evaluated with RMSE, MAD, and MAPE. The study data are the Nigeria Exchange Rate (2004-2014) and the Nigeria External Reserve (1995-2010). The results of the analysis show that the power transformed series of the exchange rate data admits a random walk (ARIMA (0, 1, 0)) model while its wavelet equivalent is adequately fitted to ARIMA (1,1,0). Similarly, the power transformed version of the External Reserve is adequately fitted to ARIMA (3, 1, 0) while its wavelet transform equivalent is adequately fitted to ARIMA (0, 1, 3). In terms of model precision (goodness - of - fit), the model for the power transformed series is found to have better fit for exchange rate data while model for wavelet transformed series is found to have better fit for external reserve data. In forecast performance, the model for wavelet transformed series outperformed the model for power transformed series. Therefore, we recommend that wavelet transform be used when time series data is non-stationary in variance and our interest is majorly on forecast.

MULTIVARIATE SPECTRAL ANALYSIS USING HILBERT WAVELET PAIRS

2004 ◽  
Vol 02 (04) ◽  
pp. 567-587 ◽  
Author(s):  
BRANDON WHITCHER ◽  
PETER F. CRAIGMILE
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Multivariate Time Series ◽  
Discrete Wavelet ◽  
Pass Filter ◽  
Wavelet Filters ◽  
The Hilbert Transform ◽  
High Pass

We investigate the use of Hilbert wavelet pairs (HWPs) in the non-decimated discrete wavelet transform for the time-varying spectral analysis of multivariate time series. HWPs consist of two high-pass and two low-pass compactly supported filters, such that one high-pass filter is the Hilbert transform (approximately) of the other. Thus, common quantities in the spectral analysis of time series (e.g., power spectrum, coherence, phase) may be estimated in both time and frequency. Compact support of the wavelet filters ensures that the frequency axis will be partitioned dyadically as with the usual discrete wavelet transform. The proposed methodology is used to analyze a bivariate time series of zonal (u) and meridional (v) winds over Truk Island.

scholarly journals The Shift Invariant Discrete Wavelet Transform (SIDWT) with Inflation Time Series Application

2016 ◽  
Vol 8 (4) ◽  
pp. 14
Author(s):  
Suparti Suparti ◽  
Rezzy Eko Caraka ◽  
Budi Warsito ◽  
Hasbi Yasin
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Well Being ◽  
Discrete Wavelet ◽  
Time Series Modeling ◽  
The Government ◽  
Determining Factor ◽  
Analysis Of Time Series ◽  
Economic Well Being

<p>Analysis of time series used in many areas, one of which is in the field economy. In this research using time series on inflation using Shift Invariant Discrete Wavelet Transform (SIDWT).Time series decomposition using transformation wavelet namely SIDWT with Haar filter and D4. Results of the transformation, coefficient of drag coefficient wavelet and scale that is used for modeling time series. Modeling done by using Multiscale Autoregressive (MAR). In a certain area, inflation to it is an important that he had made the standard-bearer of economic well-being of society, the factors Directors investors in selecting a kind of investment, and the determining factor for the government to formulate policy fiscal, monetary, as well as non-monetary that will be applied. Inflation can be analyzed using methods Shift Invariant Discrete Wavelet Transform (SIDWT) which had been modeled for them to use Mulitiscale Autoregressive (MAR) with the R2 value 93.62%.</p>

scholarly journals Application of Discrete Wavelet Transform in Shapelet-Based Classification

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Lijuan Yan ◽  
Yanshen Liu ◽  
Yi Liu
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Weight Vector ◽  
Majority Voting ◽  
Discrete Wavelet ◽  
Time Series Classification ◽  
Original Time Series ◽  
Time Frequency ◽  
Original Time

Recently, several shapelet-based methods have been proposed for time series classification, which are accomplished by identifying the most discriminating subsequence. However, for time series datasets in some application domains, pattern recognition on the original time series cannot always obtain ideal results. To address this issue, we propose an ensemble algorithm by combining time frequency analysis and shape similarity recognition of time series. Discrete wavelet transform is used to decompose the time series into different components, and the shapelet features are identified for each component. According to the different correlations between each component and the original time series, an ensemble classifier is built by weighted majority voting, and the Monte Carlo method is used to search for optimal weight vector. The comparative experiments and sensitivity analysis are conducted on 25 datasets from UCR Time Series Classification Archive, which is an important open dataset resource in time series mining. The results show the proposed method has a better performance in terms of accuracy and stability than the compared classifiers.

scholarly journals New Deconvolution Method for a Time Series Using the Discrete Wavelet Transform.

1997 ◽  
Vol 40 (4) ◽  
pp. 630-636 ◽  
Author(s):  
Arata MASUDA ◽  
Sizuo YAMAMOTO ◽  
Akira SONE
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Discrete Wavelet ◽  
Deconvolution Method

scholarly journals Multiscale Analysis of GPS Time Series from Non-decimated Wavelet to Investigate the Effects of Ionospheric Scintillation

2015 ◽  
Vol 16 (2) ◽  
pp. 119 ◽  
Author(s):  
Gabriela De Oliveira Nascimento Brassarote ◽  
Eniuce Menezes de Souza ◽  
João Francisco Galera Monico
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Artificial Satellite ◽  
Stationary Time Series ◽  
Ionospheric Scintillation ◽  
Discrete Wavelet ◽  
The Time Domain ◽  
Gps Time Series ◽  
Redundant Discrete Wavelet Transform

Due to the numerous application possibilities, the theory of wavelets has been applied in several areas of research. The Discrete Wavelet Transform is the most known version. However, the downsampling required for its calculation makes it sensitive to the origin, what is not ideal for some applications,mainly in time series. On the other hand, the Non-Decimated Discrete Wavelet Transform (or Maximum Overlap Discrete Wavelet Transform, Stationary Wavelet Transform, Shift-invariant Discrete Wavelet Transform, Redundant Discrete Wavelet Transform) is shift invariant, because it considers all the elements of the sample, by eliminating the downsampling and, consequently, represents a time series with the same number of coefficients at each scale. In the present paper, the objective is to present the theorical aspects of the a multiscale/multiresolution analysis of non-stationary time series from non-decimated wavelets in terms of its implementation using the same pyramidal algorithm of the decimated wavelet transform. An application with real time series of the effect of the ionospheric scintillation on artificial satellite signals is investigated. With this analysis some information and hidden patterns which can not be detected in the time domain, may therefore be explained in the space-frequency domain.

Sign in / Sign up

Export Citation Format

Share Document