scholarly journals Discrete Wavelet Analyses for Time Series

10.5772/16016 ◽  
2011 ◽  
Author(s):  
Jos S. ◽  
Haret C.
Keyword(s):  
Time Series ◽  
Discrete Wavelet ◽  
Wavelet Analyses

scholarly journals Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers

2021 ◽  
Vol 13 (2) ◽  
pp. 542
Author(s):  
Tarate Suryakant Bajirao ◽  
Pravendra Kumar ◽  
Manish Kumar ◽  
Ahmed Elbeltagi ◽  
Alban Kuriqi
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Suspended Sediment ◽  
River Basin ◽  
Time Series Data ◽  
Series Data ◽  
Discrete Wavelet ◽  
Original Time Series ◽  
Inference System ◽  
Original Time

Estimating sediment flow rate from a drainage area plays an essential role in better watershed planning and management. In this study, the validity of simple and wavelet-coupled Artificial Intelligence (AI) models was analyzed for daily Suspended Sediment (SSC) estimation of highly dynamic Koyna River basin of India. Simple AI models such as the Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) were developed by supplying the original time series data as an input without pre-processing through a Wavelet (W) transform. The hybrid wavelet-coupled W-ANN and W-ANFIS models were developed by supplying the decomposed time series sub-signals using Discrete Wavelet Transform (DWT). In total, three mother wavelets, namely Haar, Daubechies, and Coiflets were employed to decompose original time series data into different multi-frequency sub-signals at an appropriate decomposition level. Quantitative and qualitative performance evaluation criteria were used to select the best model for daily SSC estimation. The reliability of the developed models was also assessed using uncertainty analysis. Finally, it was revealed that the data pre-processing using wavelet transform improves the model’s predictive efficiency and reliability significantly. In this study, it was observed that the performance of the Coiflet wavelet-coupled ANFIS model is superior to other models and can be applied for daily SSC estimation of the highly dynamic rivers. As per sensitivity analysis, previous one-day SSC (St-1) is the most crucial input variable for daily SSC estimation of the Koyna River basin.

scholarly journals AUTOMATICALLY DETECTING "SIGNIFICANT EVENTS" ON SenseCam

2013 ◽  
Vol 11 (06) ◽  
pp. 1350050 ◽  
Author(s):  
NA LI ◽  
MARTIN CRANE ◽  
HEATHER J. RUSKIN
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Time Windows ◽  
Fluctuation Analysis ◽  
Discrete Wavelet ◽  
Dominant Eigenvalue ◽  
Multiple Time ◽  
Correlation Relationship ◽  
Significant Events ◽  
Detrended Fluctuation

SenseCam is an effective memory-aid device that can automatically record images and other data from the wearer's whole day. The main issue is that, while SenseCam produces a sizeable collection of images over the time period, the vast quantity of captured data contains a large percentage of routine events, which are of little interest to review. In this article, the aim is to detect "Significant Events" for the wearers. We use several time series analysis methods such as Detrended Fluctuation Analysis (DFA), Eigenvalue dynamics and Wavelet Correlations to analyse the multiple time series generated by the SenseCam. We show that Detrended Fluctuation Analysis exposes a strong long-range correlation relationship in SenseCam collections. Maximum Overlap Discrete Wavelet Transform (MODWT) was used to calculate equal-time Correlation Matrices over different time scales and then explore the granularity of the largest eigenvalue and changes of the ratio of the sub-dominant eigenvalue spectrum dynamics over sliding time windows. By examination of the eigenspectrum, we show that these approaches enable detection of major events in the time SenseCam recording, with MODWT also providing useful insight on details of major events. We suggest that some wavelet scales (e.g., 8 minutes–16 minutes) have the potential to identify distinct events or activities.

scholarly journals Technical Note: Using wavelet analyses on water depth time series to detect glacial influence in high-mountain hydrosystems

2013 ◽  
Vol 10 (4) ◽  
pp. 4369-4395 ◽  
Author(s):  
S. Cauvy-Fraunié ◽  
T. Condom ◽  
A. Rabatel ◽  
M. Villacis ◽  
D. Jacobsen ◽  
...  
Keyword(s):  
Time Series ◽  
Water Depth ◽  
Water Pressure ◽  
Methodological Approach ◽  
Technical Note ◽  
High Mountain ◽  
Tropical Andes ◽  
Glacial Meltwater ◽  
Depth Measurement ◽  
Wavelet Analyses

Abstract. Worldwide, the rapid shrinking of glaciers in response to ongoing climate change is currently modifying the glacial meltwater contribution to hydrosystems in glacierized catchments. Assessing the contribution of glacier run-off to stream discharge is therefore of critical importance to evaluate potential impact of glacier retreat on water quality and aquatic biota. This task has challenged both glacier hydrologists and ecologists over the last 20 yr due to both structural and functional complexity of the glacier-stream system interface. Here we propose a new methodological approach based on wavelet analyses on water depth time series to determine the glacial influence in glacierized catchments. We performed water depth measurement using water pressure loggers over ten months in 15 stream sites in two glacier-fed catchments in the Ecuadorian Andes (> 4000 m). We determined the global wavelet spectrum of each time series and defined the Wavelet Glacier Signal (WGS) as the ratio between the global wavelet power spectrum value at a 24 h-scale and its corresponding significance value. To test the relevance of the WGS we compared it with the percentage of the glacier cover in the catchments, a metric of glacier influence often used in the literature. We then tested whether one month data could be sufficient to reliably determine the glacial influence. As expected we found that the WGS of glacier-fed streams decreased downstream with the increasing of non-glacial tributaries. We also found that the WGS and the percentage of the glacier cover in the catchment were significantly positively correlated and that one month data was sufficient to identify and compare the glacial influence between two sites, provided that the water level time series were acquired over the same period. Furthermore, we found that our method permits to detect glacial signal in supposedly non-glacial sites, thereby evidencing glacial meltwater infiltrations. While we specifically focused on the tropical Andes in this paper, our approach to determine glacier influence would be applicable to temperate and arctic glacierized catchments. The WGS therefore appears as a powerful and cost effective tool to better understand the hydrological links between glaciers and hydrosystems and assess the consequences of rapid glacier melting.

Thailand tourism forecasting based on a hybrid of discrete wavelet decomposition and NARX neural network

2016 ◽  
Vol 116 (6) ◽  
pp. 1242-1258 ◽  
Author(s):  
Ratree Kummong ◽  
Siriporn Supratid
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Wavelet Decomposition ◽  
Tourism Industry ◽  
Relative Price ◽  
Discrete Wavelet ◽  
Content Type ◽  
Input Factor ◽  
Discrete Wavelet Decomposition ◽  
Forecasting Performance

Purpose – Accurate forecast of tourist arrivals is crucial for Thailand since the tourism industry is a major economic factor of the country. However, a nonstationarity, normally consisted in nonlinear tourism time series can seriously ruin the forecasting computation. The purpose of this paper is to propose a hybrid forecasting method, namely discrete wavelet decomposition (DWD)-NARX, which combines DWD and the nonlinear autoregressive neural network with exogenous input (NARX) to cope with such nonstationarity, as a consequence, improve the effectiveness of the demand-side management activities. Design/methodology/approach – According to DWD-NARX, wavelet decomposition is executed for efficiently extracting the hidden significant, temporal features contained in the nonstationary time series. Then, each extracted feature set at a particular resolution level along with a relative price as an exogenous input factor are fed into NARX for further forecasting. Finally, the forecasting results are reconstructed. Forecasting performance measures rely on mean absolute percentage error, mean absolute error as well as mean square error. Model overfitting avoidance is also considered. Findings – The results indicate the superiority of the DWD-NARX over other efficient related neural forecasters in the cases of high forecasting performance rate as well as competently coping with model overfitting. Research limitations/implications – The scope of this study is confined to Thailand tourist arrivals forecast based on short-term projection. To resolve such limitations, future research should aim to apply the generalization capability of DWD-NARX on other domains of managerial time series forecast under long-term projection environment. However, the exogenous input factor is to be empirically revised on domain-by-domain basis. Originality/value – Few works have been implemented either to handle the nonstationarity, consisted in nonlinear, unpredictable time series, or to achieve great success on finding an appropriate and effective exogenous forecasting input. This study applies DWD to attain efficient feature extraction; then, utilizes the competent forecaster, NARX. This would comprehensively and specifically deal with the nonstationarity difficulties at once. In addition, this study finds the effectiveness of simply using a relative price, generated based on six top-ranked original tourist countries as an exogenous forecasting input.

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 Multiband Prediction Model for Financial Time Series with Multivariate Empirical Mode Decomposition

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Md. Rabiul Islam ◽  
Md. Rashed-Al-Mahfuz ◽  
Shamim Ahmad ◽  
Md. Khademul Islam Molla
Keyword(s):  
Time Series ◽  
Empirical Mode Decomposition ◽  
Time Series Data ◽  
Financial Time Series ◽  
Arma Model ◽  
Series Data ◽  
Discrete Wavelet ◽  
Multivariate Empirical Mode Decomposition ◽  
Financial Time ◽  
Mode Decomposition

This paper presents a subband approach to financial time series prediction. Multivariate empirical mode decomposition (MEMD) is employed here for multiband representation of multichannel financial time series together. Autoregressive moving average (ARMA) model is used in prediction of individual subband of any time series data. Then all the predicted subband signals are summed up to obtain the overall prediction. The ARMA model works better for stationary signal. With multiband representation, each subband becomes a band-limited (narrow band) signal and hence better prediction is achieved. The performance of the proposed MEMD-ARMA model is compared with classical EMD, discrete wavelet transform (DWT), and with full band ARMA model in terms of signal-to-noise ratio (SNR) and mean square error (MSE) between the original and predicted time series. The simulation results show that the MEMD-ARMA-based method performs better than the other methods.

scholarly journals Wavelet-genetic programming conjunction model for flood forecasting in rivers

2018 ◽  
Vol 49 (6) ◽  
pp. 1880-1889 ◽  
Author(s):  
Mani Kumar ◽  
Rajeev Ranjan Sahay
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Genetic Programming ◽  
Flow Time ◽  
Discrete Wavelet ◽  
Mean Square ◽  
Performance Indices ◽  
Flow Rates ◽  
The World ◽  
Daily Flows

Abstract In this study we have developed a conjunction model, WGP, of discrete wavelet transform (DWT) and genetic programming (GP) for forecasting river floods when the only data available are the historical daily flows. DWT is used for denoising and smoothening the observed flow time series on which GP is implemented to get the next-day flood. The new model is compared with autoregressive (AR) and stand-alone GP models. All models are calibrated and tested on the Kosi River which is one of the most devastating rivers of the world with high and spiky monsoon flows, modeling of which poses a great challenge. With different inputs, 12 models, four in each class of WGP, GP and AR, are devised. The best performing WGP model, WGP4, with four previous daily flow rates as input, forecasts the Kosi floods with an accuracy of 87.9%, root mean square error of 123.9 m3/s and Nash–Sutcliffe coefficient of 0.993, the best performance indices among all the developed models. The extreme floods are also better simulated by the WGP models than by AR and GP models.

scholarly journals CIRCADA: Shiny Apps for Exploration of Experimental and Synthetic Circadian Time Series with an Educational Emphasis

2020 ◽  
Vol 35 (2) ◽  
pp. 214-222
Author(s):  
Lisa Cenek ◽  
Liubou Klindziuk ◽  
Cindy Lopez ◽  
Eleanor McCartney ◽  
Blanca Martin Burgos ◽  
...  
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Locomotor Activity ◽  
Body Temperature ◽  
Sampling Rate ◽  
Discrete Wavelet ◽  
Data Set ◽  
Maximum Entropy Spectral Analysis ◽  
Noise Characteristics ◽  
Synthetic Time Series

Circadian rhythms are daily oscillations in physiology and behavior that can be assessed by recording body temperature, locomotor activity, or bioluminescent reporters, among other measures. These different types of data can vary greatly in waveform, noise characteristics, typical sampling rate, and length of recording. We developed 2 Shiny apps for exploration of these data, enabling visualization and analysis of circadian parameters such as period and phase. Methods include the discrete wavelet transform, sine fitting, the Lomb-Scargle periodogram, autocorrelation, and maximum entropy spectral analysis, giving a sense of how well each method works on each type of data. The apps also provide educational overviews and guidance for these methods, supporting the training of those new to this type of analysis. CIRCADA-E (Circadian App for Data Analysis–Experimental Time Series) allows users to explore a large curated experimental data set with mouse body temperature, locomotor activity, and PER2::LUC rhythms recorded from multiple tissues. CIRCADA-S (Circadian App for Data Analysis–Synthetic Time Series) generates and analyzes time series with user-specified parameters, thereby demonstrating how the accuracy of period and phase estimation depends on the type and level of noise, sampling rate, length of recording, and method. We demonstrate the potential uses of the apps through 2 in silico case studies.

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