scholarly journals Sea Spectral Estimation Using ARMA Models

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4280
Author(s):  
Marta Berardengo ◽  
Giovanni Battista Rossi ◽  
Francesco Crenna
Keyword(s):  
Spectral Estimation ◽  
Arma Model ◽  
Arma Models ◽  
Reconstruction Procedure ◽  
Spectral Estimates ◽  
Wave Elevation ◽  
Accuracy Of Results ◽  
Auto Covariance ◽  
Signal Time ◽  
Sea Wave

This paper deals with the spectral estimation of sea wave elevation time series by means of ARMA models. To start, the procedure to estimate the ARMA coefficients, based on the use of the Prony’s method applied to the auto-covariance series, is presented. Afterwards, an analysis on how the parameters involved in the ARMA reconstruction procedure—for example, the signal time length, the number of poles and data used—affect the spectral estimates is carried out, providing evidence on their effect on the accuracy of results. This allowed us to provide guidelines on how to set these parameters in order to make the ARMA model as accurate as possible. The paper focuses on mono-modal sea states. Nevertheless, examples also related to bi-modal sea states are discussed.

Vortex Characterization and Identification by Ultrasound Doppler

1981 ◽  
Vol 3 (3) ◽  
pp. 271-293 ◽  
Author(s):  
L. J. D'Luna ◽  
V. L. Newhouse
Keyword(s):  
Spectral Estimation ◽  
Entropy Method ◽  
Channel Flows ◽  
Spectral Estimates ◽  
System A ◽  
Novel Approach ◽  
Doppler Signals ◽  
Invasive Method ◽  
Short Time ◽  
Pulsed Rf

The detection of vortices is of potential interest in physiology (e.g. the detection of weak stenoses), and in fluid mechanics. In this paper a non-invasive method of detecting vortices in channel flows using pulsed RF Doppler ultrasound is described. A novel approach involving hybrid operation is taken in implementing a directional Doppler system. A scattering model of a vortex crossing an ultrasound beam is presented and theoretical simulations of the Doppler signals show good agreement with experiment. Experimental results showing the detection of both periodic and isolated vortices in channel flows are given. The Autoregressive or Maximum Entropy Method of spectral estimation is used to obtain the spectral estimates of the Doppler signals over short time intervals. It is shown that these spectral estimates can be used to estimate the velocity profiles of the detected vortices.

scholarly journals A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 324 ◽  
Author(s):  
Dabuxilatu Wang ◽  
Liang Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Empirical Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Complex Data ◽  
Arma Models ◽  
Linguistic Data ◽  
Series Analysis

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

scholarly journals Sleep Neurophysiological Dynamics Through the Lens of Multitaper Spectral Analysis

Physiology ◽  
2017 ◽  
Vol 32 (1) ◽  
pp. 60-92 ◽  
Author(s):  
Michael J. Prerau ◽  
Ritchie E. Brown ◽  
Matt T. Bianchi ◽  
Jeffrey M. Ellenbogen ◽  
Patrick L. Purdon
Keyword(s):  
Spectral Analysis ◽  
Spectral Estimation ◽  
Sleep Eeg ◽  
Sleep Stages ◽  
Subcortical Structures ◽  
Sleep State ◽  
Time Frequency ◽  
Oscillatory Dynamics ◽  
Spectral Estimates ◽  
The Rich

During sleep, cortical and subcortical structures within the brain engage in highly structured oscillatory dynamics that can be observed in the electroencephalogram (EEG). The ability to accurately describe changes in sleep state from these oscillations has thus been a major goal of sleep medicine. While numerous studies over the past 50 years have shown sleep to be a continuous, multifocal, dynamic process, long-standing clinical practice categorizes sleep EEG into discrete stages through visual inspection of 30-s epochs. By representing sleep as a coarsely discretized progression of stages, vital neurophysiological information on the dynamic interplay between sleep and arousal is lost. However, by using principled time-frequency spectral analysis methods, the rich dynamics of the sleep EEG are immediately visible—elegantly depicted and quantified at time scales ranging from a full night down to individual microevents. In this paper, we review the neurophysiology of sleep through this lens of dynamic spectral analysis. We begin by reviewing spectral estimation techniques traditionally used in sleep EEG analysis and introduce multitaper spectral analysis, a method that makes EEG spectral estimates clearer and more accurate than traditional approaches. Through the lens of the multitaper spectrogram, we review the oscillations and mechanisms underlying the traditional sleep stages. In doing so, we will demonstrate how multitaper spectral analysis makes the oscillatory structure of traditional sleep states instantaneously visible, closely paralleling the traditional hypnogram, but with a richness of information that suggests novel insights into the neural mechanisms of sleep, as well as novel clinical and research applications.

The Use of ARMA Models in Earthquake Response Spectra

2006 ◽  
Author(s):  
Malek Brahimi ◽  
Sidi Berri
Keyword(s):  
Linear Response ◽  
Energy Demand ◽  
Arma Model ◽  
Response Spectra ◽  
Response Analysis ◽  
Arma Models ◽  
Maximum Displacement ◽  
Ductility Demand ◽  
Displacement Ductility ◽  
Hysteretic Energy

Structural design spectra are based on smoothed linear response spectra obtained from different events scaled by their peak values. Such an approach does not incorporate other characteristics of the excitation represented by measured data. This study investigate the use of non-stationary models which can be considered characteristic and representative of specific historical earthquakes. An earthquake record is regarded as a sample realization from a population of such samples, which could have been generated by the stochastic process characterized by an Autoregressive Moving Average (ARMA) model. ARMA models are developed for four major earthquakes after processing by a variance stabilizing transformation. Samples of acceleration records are generated for each event. In this earthquake modeling procedure, parameters describing the modulating function of the record and the stabilized series are estimated. Maximum displacement ductility demand and normalized hysteretic energy demand for linear and stiffness softening single degree of freedom system systems are computed for the samples generated for each event. The sensitivity and dependence of demand spectra on earthquake model characteristics are examined to develop a response prediction model. Non linear response analysis of the four events indicates that ARMA (2,1) process using samples of twenty simulated earthquakes provide a reliable description of the information contained within acceleration records. Empirical relationships for displacement ductility and Normalized hysteretic energy demand spectra are developed.

scholarly journals Machine Learning Modeling of Water Use Patterns in Small Disadvantaged Communities

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2312
Author(s):  
Yang Zhou ◽  
Bilal Muhammad Khan ◽  
Jin Yong Choi ◽  
Yoram Cohen
Keyword(s):  
Water Use ◽  
Model Development ◽  
Model Performance ◽  
Arma Model ◽  
Water Source ◽  
Arma Models ◽  
Treatment Needs ◽  
Use Patterns ◽  
Average Absolute Relative Error ◽  
Water Use Patterns

Water use patterns were explored for three small communities that are located in proximity to agricultural fields and rely on their local wells for potable water supply. High-resolution water use data, collected over a four-year period, revealed significant temporal variability. Monthly, daily, and hourly water use patterns were well described by autoregressive moving average (ARMA) models. Model development was supported by unsupervised clustering analysis via self-organizing maps (SOMs) that revealed similarities of water use patterns and confirmed the time-series water use model attributes. The inclusion of ambient temperature and rainfall as model attributes improved ARMA model performance for daily and hourly water use from R2 ~0.86–0.87 to 0.94–0.97 and from R2 ~0.85–0.89 to 0.92–0.98, respectively. Water use predictions for an entire year forward in time was feasible demonstrating ARMA models’ performance of (i) R2 ~0.90–0.94 and average absolute relative error (AARE) of ~2.9–4.9% for daily water use, and (ii) R2 ~0.81–0.95 and AARE ~1.9–3.8% for hourly water use. The study suggests that ARMA modeling should be useful for analysis of temporally variable water use in support of water source management, as well as assessing capacity building for small water systems including water treatment needs and wastewater handling.

Conversion Among Arma Models And State-Space Representation

2021 ◽  
Vol 9 (2) ◽  
pp. 53-59
Author(s):  
William W.S. Chen
Keyword(s):  
State Space ◽  
Arma Model ◽  
The State ◽  
Space Representation ◽  
Arma Models ◽  
State Space Representation ◽  
Markovian Representation

We present the ARMA models (or Non-Markovian) and state-space (or Markovian) representation relationship. Then we break the problem into three different cases to discuss how one form could be converted to another form. In case A, we assume that we know the state-space representation then we convert it into the ARMA model. In case B, we reverse the situation, given the ARMA model we convert into state-space representation. In Case C, we combine the first two cases, conversion the two forms in either directions. 

scholarly journals Pendugaan Imbal Hasil Saham dengan Model Autoregressive Moving Average

2021 ◽  
Vol 3 (2) ◽  
pp. 140-154
Author(s):  
Grifin Ryandi Egeten ◽  
Berlian Setiawaty ◽  
Retno Budiarti
Keyword(s):  
Maximum Likelihood ◽  
Central Asia ◽  
Stock Returns ◽  
Stock Return ◽  
Moving Average ◽  
Arma Model ◽  
Ar Model ◽  
Autoregressive Moving Average ◽  
Arma Models ◽  
Unknown Parameters

ABSTRAKSeorang investor pada umumnya berharap untuk membeli suatu saham dengan harga yang rendah dan menjual saham tersebut dengan harga yang lebih tinggi untuk memperoleh imbal hasil yang tinggi. Namun, kapan waktu yang tepat melakukannya menjadi tantangan tersendiri bagi para investor. Oleh sebab itu, dibutuhkan suatu model yang mampu menduga imbal hasil saham dengan baik, salah satunya adalah model autoregressive moving average (ARMA). Tujuan dari penelitian ini adalah untuk menerapkan model autoregressive (AR), model moving average (MA), atau model autoregressive moving average (ARMA) pada data observasi untuk menduga imbal hasil saham bank central asia (BCA). Terdapat empat prosedur dalam membangun sebuah model AR, MA atau ARMA. Pertama, data yang digunakan harus weakly stationary. Kedua, orde dari model harus diidentifikasi untuk memperoleh model yang terbaik. Ketiga, parameter setiap model harus ditentukan. Keempat, kelayakan model harus diperiksa dengan melakukan analisis residual untuk memperoleh model yang terbaik. Pada akhirnya, model ARMA (1,1) adalah model terbaik dan akurat dalam menduga imbal hasil saham BCA. ABSTRACTGenerally, investor always wish to be able to buy a stock at a low price and sell it at a higher price to obtain high returns. However, when is the best time to buy or sell it is a challenge for investor. Therefore, proper models are needed to predict a stock return, one of them is autoregressive moving average (ARMA) model. The first purpose of this paper is to apply the autoregressive (AR), moving average (MA) or ARMA models to the observations to predict stock returns. There are four procedures which is used to build an AR, MA, or ARMA model. First, the observations must be weakly stationary. Second, the order of the models must be identified to obtain the best model. Third, the unknown parameters of the models are estimated by maximum likelihood. Fourth, through residual analysis, diagnostic checks are performed to determine the adequacy of the model. In this paper, stock returns of BCA are used as data observation. Finally, the ARMA (1,1) model is the best model and appropriate to predict the stock returns BCA in the future.

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