Robust speech processing using ARMA spectrogram models

Three important parametric models for describing the correlation functions and spectra of stationary stochastic processes are the autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Quite recently, the MATLAB toolbox “ARMASA” has been made publicly available. This toolbox provides state-of-the-art algorithms to perform automatic identification and selection between the models based on the estimated prediction error. ARMASA works on a single segment of data, whereas in some applications, the data are available as multiple segments. We could process each segment independently and average the estimated autocorrelation functions or spectra afterward. Better performance, however, can be expected when all segments are processed simultaneously, for two reasons. Initially, the bias in the estimated model parameters depends on the number of observations in a segment. Averaging models from segments does not reduce this bias, in contrast to identification from all the data at once. In either case, the variance of the estimated model parameters will decrease. By considering all the data at once this variance reduction can be considered in the order selection stage, decreasing the selection bias. In this paper, we extend the parameter estimation algorithms of the ARMASA toolbox to the case of multiple segments. AR parameter estimation from segments has been considered before, but not for the MA and ARMA models. In addition, in the AR case, model order selection can be done easily when the segments are independent. But, in the application we are primarily interested in, the segments are formed by lines of scanning transmission electron microscopy (STEM) images, which can be correlated with each other. Because the correlation among data segments influences the effective number of independent observations available it becomes necessary to estimate that number. This is not an easy problem in general. For observations from a stochastic process with an isotropic 2-D autocorrelation function we can, however, formulate an accurate estimator in terms of the line autocorrelation function. This situation arises, for example, in STEM images of amorphous specimens. From the AR model identification for segments, the extension to the MA and ARMA models is rather straightforward because MA and ARMA algorithms are based on Durbin's methods, whose first step is the estimation of a long AR model. We compare the segment-based algorithms to conventional ARMASA with simulations of stationary stochastic processes. An illustrative example involving simulated STEM images shows large potential benefits.

Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir

The focus of this chapter is on autoregressive moving average (ARMA) models, which were introduced in a simple form in Chapter 1. These models are not only of interest in their own right, they serve to provide a background to interpret many of the issues arising in the context of unit roots and integrated time series. The ‘ARMA’ notation indicates that there are two components to the structure of these models. The first part is the autoregressive (AR) component and the second the moving average (MA) component. The ARMA model is said to be integrated if a unit root, or roots, can be extracted from the AR component, in which case the appropriate notation is ARIMA, for an autoregressive, integrated moving average model. The kind of structure of interest in this chapter is where one of the roots of the AR polynomial might be a unit root whilst the others are outside the unit circle. The case of two unit roots is considered in Chapter 11 and the roots of a polynomial are considered extensively in Appendix 2.

Autoregressive moving average models of crown profiles for two California hardwood species

The performance of Autoregressive Moving Average and Multiple Linear Regression Models in predicting minimum and maximum temperatures of Ogun State is herein reported. Maximum and Minimum temperatures data covering a period of 29 years (1982 -2009) obtained from the Nigerian Meteorological Agency (NiMet), Abeokuta office, Nigeria, were used for the analyses. The data were first processed and aggregated into annual time series. Mann-Kendal non-parametric test and spectral analysis were carried out to detect whether there is trend, seasonal pattern, and either short or long memory in the time series. Mann-Kendal Z-values obtained are –0.47 and –2.03 for minimum and maximum temperatures respectively, indicating no trend, though the plot shows a slight change. The Lo’s R/S Q(N,q) values for minimum and maximum temperatures are 3.67 and 4.43, which are not within the range 0.809 and 1.862, thus signifying presence of long memory. The data was divided into two and the first 20 years data was used for model development, while the remaining was used for validation. Autoregressive Moving Average (ARMA) model of order (5, 3) and Autoregressive (AR) model of order 2 are found best for predicting minimum and maximum temperatures respectively. Multiple Linear Regression (MLR) model with 4 features (moving average, exponential moving average, rate of change and oscillator) were fitted for both temperatures. The ARMA and AR models were found to perform better with Mean Absolute Percentage Error (MAPE) values of -2.89 and -1.37 for minimum and maximum temperatures, compared with the Multiple Linear Regression Models with MAPE values of 141 and 876 respectively. Results of ARMA model can be relied on in generating forecast of temperature of the study area because of their minimal error values. However, it is recommended other climatic elements that were not captured in this paper due to unavailability of information be considered too in order to see which model is best for them.

Objective To establish an autoregression moving average (ARMA) model for predicting general traffic accidents and analyzing distributional difference on time series and frequency of common traffic accident so as to provide certain basis for a prediction model with better stability and accuracy. Methods The data of road traffic accidents in one newly developed zone of Chongqing in 2000-2005 were collected. The monthly distribution regularity of road traffic accidents was analyzed with descriptive epidemiologic method. ARMA model was set up for retrospective and prospective prediction. The predicted data were compared. Results Based on the characteristics of monthly distribution, the frequency of general traffic accidents in this area showed a cyclic fashion. The frequency of general traffic accidents predicted by ARMA model had over 80% of coincidence with the actual value. Conclusion The ARMA model can be used to predict the frequency of general traffic accidents, with better accuracy of short-term prediction than the long-term prediction. Key words: Accidents, traffic; ARMA; Time series; Prediction model

The seemingly complex nature of river flow and the significant variability it exhibits in both time and space, have largely led to the development and application of the stochastic process concept for its modelling, forecasting, and other ancillary purposes. Towards this end, in this study, attempt was made at stochastic modelling of the daily streamflow process of the Benue River. In this regard, Autoregressive Moving Average (ARMA) models and its derivative, the Periodic Autoregressive (PAR) model were developed and used for forecasting. Comparative forecast performances of the different models indicate that despite the shortcomings associated with univariate time series, reliable forecasts can be obtained for lead times, 1 to 5 day-ahead. The forecast results also showed that the traditional ARMA model could not robustly simulate high flow regimes unlike the periodic AR (PAR). Thus, for proper understanding of the dynamics of the river flow and its management, especially, flood defense, in the light of this study, the traditional ARMA models may not be suitable since they do not allow for real-time appraisal. To account for seasonal variations, PAR models should be used in forecasting the streamflow processes of the Benue River. However, since almost all mechanisms involved in the river flow processes present some degree of nonlinearity thus, how appropriate the stochastic process might be for every flow series may be called to question.

Time series modeling and analysis provides means of predicting the future and has been widely used in a variety of fields ranging from seismology for predicting earthquake and volcanic eruption, to finance for risk assessment, and to quantum information processing. The conventional integer order models can only capture short-range dependence; for example, Poisson processes, Markov processes, autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) processes. In time series analysis, one of the conventional assumptions is that the coupling between values at different time instants decreases rapidly as the time difference or distance increases. However, there are situations where strong coupling between values at different times exhibit properties of long range dependence which cannot be processed by the conventional time series analysis. Typical examples of long range dependence signals include financial time series, underwater noise, electroencephalography (EEG) signal, etc. ARFIMA, a fractional order signal processing technique, is the generalization of the conventional integer order techniques, namely, ARIMA and ARMA methods. Hence, it is capable of capturing both short-range dependence and long-range dependence in signals. Compared to conventional integer order models, the ARFIMA model gives a better fit and result when dealing with the data which possess the long range dependence property. In this paper, we investigate the application of the ARFIMA as well as AR methods to model EEG signals obtained from different brain channels. We analyze the resulting correlations for comparison the benefits of ARFIMA over AR on the EEG data exhibiting the long range dependency property. The results showed that the prediction results have a better performance compared to the conventional ARMA models.

The stationary data tests in time series data are the most common idea to create the model with an autoregressive (AR) model, moving average (MA) model, autoregressive moving average (ARMA) model, and autoregressive integrated moving average (ARIMA) model. In this chapter, we present the tseries package in the R program to investigate stationary data on the time series. This package offers Augmented Dickey-Fuller (ADF), Kwiatkowski-Phillips-Schmidt-Shin (KPSS), and Phillips-Perron (PP) tests. Three tests also provide the statistics test and p-value to decide the acceptance or rejection of the null hypothesis. This chapter also aims to present the calculation of these tests proposes step-by-step and the available coding commands under similar time series data. The performance of these tests considers the probability of type I error and the power of the test. The time series data in this study is simulated from the stationary in term of random walk process and non-stationary in term of MA model. This simulation is also conducted to recommend that the user select the appropriate stationarity tests. The R program employs to simulate and analyzes data on 1,000 replications for several sample sizes. The simulation results showed that the ADF and PP tests could control the best probability of type I error on non-stationary time series data. For the power of the test, ADF and PP tests give the highest power of the test on stationary time series data.

In this paper, we proposed a new method able to select, simultaneously, from finite length time-series sequence, the suitable model type; pure Autoregressive (AR) or Autoregressive Moving Average (ARMA), which best describes the process that generated data. This is also a new way for estimating ARMA model order. The proposed method is different in its concept from all other methods found in the literature, direct and far simpler to implement. We proposed new empirical criteria basing on specific AR order selection criteria for finite length time series. We tested the proposed criteria on 10000 realizations of different broadband and narrow band processes. We also studied effects of additive noise and data length on their performance. The best mean recognition rate of model type was 92%. [Formula: see text]-value of Fisher’s exact test was always strictly under [Formula: see text]. Power spectral densities of selected models managed to recover the true Power spectral density (PSDs) shapes by resolving close spectral peaks and by finding their positions and their bandwidths with negligible spectral biases. Efficiency of our method was proved by its application in automatic segmentation of electrohysterographic signals (EHG) in the aim of predicting preterm deliveries with a mean rate of 90%.

Background/Objective: To provide an efficient predictive technique to foresee future workload as well as to handle the resources efficiently by performing hybrid auto scaling for Cloud applications. Cloud applications might expertise completely different workload at different times, automatic provisioning has to work with efficiency at any point of time. Auto scaling is a feature of cloud computing that potentially scale the resources in line on demand. Considering this expectation, they are generally categorized into Reactive scaling which adds or reduces resources based on a fixed threshold value. The predictive scaling is used provide necessary scaling actions beforehand. Methods/Statistical Analysis: To perform the hybrid auto scaling (reactive plus predictive auto scaling), a time series technique should be used. Auto-regressive Moving Average (ARMA) model, the Exponential Smoothing (ES) model, the Autoregressive model (AR), the Moving Average model (MA) and the Trend- Adjusted Exponential Smoothing (TAES), Auto Regressive Integrated Moving Average (ARIMA) Time-series model, Naïve bayes algorithm, Recurrent Neural Network- Long Short Term Memory (RNN-LSTM), Independent Recurrent Neural Network (IndRNN) are time series techniques used to foresee the future workload. To find the effectiveness of predictive techniques, Mean Absolute Error (MAE), Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) performance metrics are evaluated. Findings: Based on the evaluation, IndRNN gives the minimum error rate. IndRNN is used to predict the future resource requisites in order to ascertain adequate resource are available ahead of time. Application: The predicted result from IndRNN method is integrated on private cloud to autoscale the resources for cloud applications. Keywords: Cloud Applications, Hybrid Autoscaling, Independent Recurrent Neural Network (IndRNN), Private Cloud, Workload

The application of time series analysis to describe the dynamic movements of suspension bridges

This article is intended to complement previous research (Sivo, 1997; Sivo & Willson, 1998, in press) by discussing the propriety and practical advantages of specifying multivariate time series models in the context of structural equation modeling for time series and longitudinal panel data. Three practical considerations motivated this article. Unlike Marsh (1993), Sivo and Willson (2000) did not offer multiple indicator (latent order) equivalents to their autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Moreover, such models have yet to be discussed, despite Marsh's (1993) advocacy for multiple indicator models in general. Further motivating multiple indicator extensions of the AR, MA, and ARMA equivalent models is the fact that longitudinal studies often collect data on more than 1 related variable per occasion. Such multiple indicator models capitalize on 1 of the chief analytical advantages of structural equation modeling in that measurement error may be estimated directly.

A comparative study and assessment of doppler ultrasound spectral estimation techniques part II: Methods and results

A third-order cumulants based adaptive recursive least-squares (CRLS) algorithm for the identification of time-invariant nonminimum phase systems, as well as time-variant nonminimum phase systems, has been successfully developed. As higher order cumulants preserve both the magnitude and the phase information of received signals, they have been considered as powerful signal processing tools for nonminimum phase systems. In this paper, the development of the CRLS algorithm is described and examined. A cost function based on the third-order cumulant and the third-order cross cumulant is defined for the development of the CRLS system identification algorithm. The CRLS algorithm is then applied to different moving average (MA) and autoregressive moving average (ARMA) models. In the case of identifying the parameters of an MA model, a direct application of the CRLS algorithm is adequate. When dealing with an ARMA model, the poles and the zeros are estimated separately. In estimating the zeros of the ARMA model, the construction of a residual time-series sequence for the MA part is required. Simulation results indicate that the CRLS algorithm is capable of identifying nonminimum phase and time-varying systems. In addition, because of the third-order cumulant properties, the CRLS algorithm can suppress Gaussian noise and is capable of providing an unbiased estimate in a noisy environment.