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This study analyzes drought conditions in the Aegean region using monthly precipitation data from nine stations between 1972 and 2020. The Standardized Precipitation Index (SPI) was calculated for 1-, 3-, 6-, 9-, and 12-month periods to evaluate drought conditions at different timescales and station-specific conditions. The results indicate that short-term droughts are more frequent but shorter in duration, while longer periods exhibit fewer but more prolonged droughts. The relative frequency of drought across all periods ranges between 9% and 27%. The İzmir and Denizli stations were highlighted due to their representation of coastal and inner regions, respectively. The findings show that coastal stations, like İzmir, experience more frequent wet years compared to inner stations like Denizli, which have more dry years. Time series linear autoregressive (AR) models, using SPI-12 data, were developed to represent long-term drought trends and forecasts. The best-fitting models were determined using AIC, AICC, FPE, and Var(e) criteria, with AR(2) generally being the most suitable, except for Denizli. This integrated analysis of SPI and AR models provides a robust basis for understanding regional precipitation regimes and predicting future droughts, aiding in the development of effective drought mitigation strategies and water resource management. Future research is anticipated to extend this analysis to encompass all of Turkey and explore various time series models' applicability. [ABSTRACT FROM AUTHOR]

This study analyzes drought conditions in the Aegean region using monthly precipitation data from nine stations between 1972 and 2020. The Standardized Precipitation Index (SPI) was calculated for 1-, 3-, 6-, 9-, and 12-month periods to evaluate drought conditions at different timescales and station-specific conditions. The results indicate that short-term droughts are more frequent but shorter in duration, while longer periods exhibit fewer but more prolonged droughts. The relative frequency of drought across all periods ranges between 9% and 27%. The İzmir and Denizli stations were highlighted due to their representation of coastal and inner regions, respectively. The findings show that coastal stations, like İzmir, experience more frequent wet years compared to inner stations like Denizli, which have more dry years. Time series linear autoregressive (AR) models, using SPI-12 data, were developed to represent long-term drought trends and forecasts. The best-fitting models were determined using AIC, AICC, FPE, and Var(e) criteria, with AR(2) generally being the most suitable, except for Denizli. This integrated analysis of SPI and AR models provides a robust basis for understanding regional precipitation regimes and predicting future droughts, aiding in the development of effective drought mitigation strategies and water resource management. Future research is anticipated to extend this analysis to encompass all of Turkey and explore various time series models’ applicability.

This study considers a goodness of fit test based on the quadratic distance (QD) in composite hypotheses. Lindsay et al. [Quadratic distances on probabilities: a unified approach. Ann Statist. 2008;36:983–1006] established a general theory of QD measures for the goodnees of fit test. Using the spectral decomposition of centred kernels, they verified that the QD test asymptotically follows a sum of weighed chi-square distributions. In this study special attention is paid to a smoothing kernel-based QD test and its bootstrap version. Their performances are compared via Monte Carlo simulations with those of the Bickel-Rosenblatt test and those of the Fisher's dispersion test for the normality and the testing for the Poisson distribution in IID samples and AR(1) models. The comparison results demonstrate the validity of our method. [ABSTRACT FROM AUTHOR]

The monitoring of condition variables for maintenance purposes is a growing trend amongst researchers and practitioners where decisions are based on degradation levels. The two approaches in Condition-Based Maintenance (CBM) are diagnosing the level of degradation (diagnostics) or predicting when a certain level of degradation will be reached (prognostics). Using diagnostics determines when it is necessary to perform maintenance, but it rarely allows for estimation of future degradation. In the second case, prognostics does allow for degradation and failure prediction, however, its major drawback lies in when to perform the analysis, and exactly what information should be used for predictions. This encumbrance is due to previous studies that have shown that degradation variable could undergo a change that misleads these calculations. This paper addresses the issue of identifying explosive changes in condition variables, using Control Charts, to determine when to perform a new model fitting in order to obtain more accurate Remaining Useful Life (RUL) estimations. The diagnostic-prognostic methodology allows for discarding pre-change observations to avoid contamination in condition prediction. In addition the performance of the integration methodology is compared against adaptive autoregressive (AR) models. Results show that using only the observations acquired after the out-of-control signal produces more accurate RUL estimations.

Autoregressive models have played an important role in time series. In this paper, an autoregressive model based on the skew-normal distribution is considered. The estimation of its parameters is carried out by using the expectation–maximization algorithm, whereas the diagnostic analytics are conducted by means of the local influence method. Normal curvatures for the model under four perturbation schemes are established. Simulation studies are conducted to evaluate the performance of the proposed procedure. In addition, an empirical example involving weekly financial return data are analyzed using the procedure with the proposed diagnostic analytics, which has improved the model fit.

ADHD affects a major portion of our children, predominantly boys. Upon diagnosis treatment can be offered that is usually quite effective. Diagnosis is generally based on subjective observation and interview. As a result, an objective test for the detection or presence of ADHD is considered very desirable. Based on EEG, across multiple channels, using autoregressive model parameters as features, ADHD detection is approached here in analogy with the imposter problem known from speaker verification. Gaussian mixture models are used to define ADHD and universal background models so that a likelihood ratio detector can be designed. The efficacy of this approach is reflected in the traditional detector performance measures of the area-under-the-curve and equal-error-probability. The results – based on a limited database of males, approximately 6 years of age – indicate that high probability of detection and low equal error rate can be achieved simultaneously with the proposed approach, when using EEG collected during an attention network task. The effect of using contaminated data is investigated as well. [ABSTRACT FROM AUTHOR]

Advances in the development of micro-electromechanical systems (MEMS) have made possible the fabrication of cheap and small dimension accelerometers and gyroscopes, which are being used in many applications where the global positioning system (GPS) and the inertial navigation system (INS) integration is carried out, i.e., identifying track defects, terrestrial and pedestrian navigation, unmanned aerial vehicles (UAVs), stabilization of many platforms, etc. Although these MEMS sensors are low-cost, they present different errors, which degrade the accuracy of the navigation systems in a short period of time. Therefore, a suitable modeling of these errors is necessary in order to minimize them and, consequently, improve the system performance. In this work, the most used techniques currently to analyze the stochastic errors that affect these sensors are shown and compared: we examine in detail the autocorrelation, the Allan variance (AV) and the power spectral density (PSD) techniques. Subsequently, an analysis and modeling of the inertial sensors, which combines autoregressive (AR) filters and wavelet de-noising, is also achieved. Since a low-cost INS (MEMS grade) presents error sources with short-term (high-frequency) and long-term (low-frequency) components, we introduce a method that compensates for these error terms by doing a complete analysis of Allan variance, wavelet de-nosing and the selection of the level of decomposition for a suitable combination between these techniques. Eventually, in order to assess the stochastic models obtained with these techniques, the Extended Kalman Filter (EKF) of a loosely-coupled GPS/INS integration strategy is augmented with different states. Results show a comparison between the proposed method and the traditional sensor error models under GPS signal blockages using real data collected in urban roadways.

The economic history literature on Fascism points out that its policies were strongly oriented towards capital accumulation. In this paper we analyse capital accumulation in Italy between 1881 and 1938 to verify its stability. If these policies were successful, we should observe a discontinuity in the data generation process with respect to the previous period. However, this analysis shows that the process is quite stable over time, and possible discontinuities cannot be attributed to the economic policy of the Fascist government. [ABSTRACT FROM AUTHOR]

Structural Health Monitoring (SHM) methodologies are taking advantage of the development of new families of MEMS sensors and of the available network technologies. Advanced systems rely on intelligent bus-connected sensing units performing locally data filtering, elaboration and model identification. This paper describes a family of enhanced multivariate autoregressive models that can be used in SHM-oriented identification procedures and the implementation of a new advanced SHM system in the tower of the Engineering School of Bologna University. It describes also the results given by the considered procedure and a comparison of the implemented MEMS-based system with a traditional solution based on piezoelectric seismic accelerometers. [ABSTRACT FROM AUTHOR]

Advances in the development of micro-electromechanical systems (MEMS) have made possible the fabrication of cheap and small dimension accelerometers and gyroscopes, which are being used in many applications where the global positioning system (GPS) and the inertial navigation system (INS) integration is carried out, i.e., identifying track defects, terrestrial and pedestrian navigation, unmanned aerial vehicles (UAVs), stabilization of many platforms, etc. Although these MEMS sensors are low-cost, they present different errors, which degrade the accuracy of the navigation systems in a short period of time. Therefore, a suitable modeling of these errors is necessary in order to minimize them and, consequently, improve the system performance. In this work, the most used techniques currently to analyze the stochastic errors that affect these sensors are shown and compared: we examine in detail the autocorrelation, the Allan variance (AV) and the power spectral density (PSD) techniques. Subsequently, an analysis and modeling of the inertial sensors, which combines autoregressive (AR) filters and wavelet de-noising, is also achieved. Since a low-cost INS (MEMS grade) presents error sources with short-term (high-frequency) and long-term (low-frequency) components, we introduce a method that compensates for these error terms by doing a complete analysis of Allan variance, wavelet de-nosing and the selection of the level of decomposition for a suitable combination between these techniques. Eventually, in order to assess the stochastic models obtained with these techniques, the Extended Kalman Filter (EKF) of a loosely-coupled GPS/INS integration strategy is augmented with different states. Results show a comparison between the proposed method and the traditional sensor error models under GPS signal blockages using real data collected in urban roadways. [ABSTRACT FROM AUTHOR]

The main purpose of this study was to develop an optimum flow prediction model, based on data mining process. The data mining process was applied to predict river flow of Seyhan Stream in the southern part of Turkey. Hydrological time series modeling was applied using monthly historical flow records to predict Seyhan Stream flows. Seyhan Stream flows were modeled by Markov models and it was seen that it adapted AR(2). Hence, Ft-2 and Ft-2 flows in (t-2) and (t-1) months were the taken inputs. For monthly streamflow predictions, data were taken from the General Directorate of Electrical Power Resources Survey and Development Administration. Used data covered 35 years between 1969 and 2003 for monthly streamflows. Furthermore, for the effect of monthly periodicity in hydrological time series cos (2π/12), sin (2π/12) (I = 1, 2,..., 12) were included as inputs. Then, Ftt flows in (t) months were modeled by data mining process. It was concluded that with using data mining process for streamflow prediction, it was possible to estimate missing or unmeasured data. [ABSTRACT FROM AUTHOR]

Selecting the correct lag order is necessary in order to avoid model specification errors in autoregressive (AR) time series models. Here we explore the problem of lag order selection in such models. This study provides an in-depth but easy understanding of the model selection mechanism to the practitioners in various fields of applied research. Several interesting findings are reported and through these the pitfalls of the model selection procedures are exposed. In particular, we show that the whole exercise of model selection and subsequent statistical inference invariably depends upon unknown entities, namely the true values of parameters in the model. The model averaging technique is proposed as an alternative to the common practice of model selection and it is shown that, as a result, the properties of post-model-selection estimates substantially improve. [ABSTRACT FROM AUTHOR]

Heat waves are a serious threat to society, the environment, and the economy. Estimates of the recurrence probabilities of heat waves may be obtained following the successful modeling of daily maximum temperature, but working with the latter is difficult as we have to recognize, and allow for, not only a time trend but also seasonality in the mean and in the variability, as well as serial correlation. Furthermore, as the extreme values of daily maximum temperature have a different form of nonstationarity from the body, additional modeling is required to completely capture the realities. We present a time series model for the daily maximum temperature and use an exceedance over high thresholds approach to model the upper tail of the distribution of its scaled residuals. We show how a change-point analysis can be used to identify seasons of constant crossing rates and how a time-dependent shape parameter can then be introduced to capture a change in the distribution of the exceedances. Daily maximum temperature series for Des Moines, New York, Portland, and Tucson are analyzed. In-sample and out-of-sample goodness-of-fit measures show that the proposed model is an excellent fit to the data. The fitted model is then used to estimate the recurrence probabilities of runs over seasonally high temperatures, and we show that the probability of long and intense heat waves has increased considerably over 50 years. We also find that the increases vary by city and by time of year. [ABSTRACT FROM AUTHOR]

In this paper we develop a statistic test in order to compare two discrete stochastic dynamical systems with autoregressive structures under heteroskedasticity, more specifically the variance of the errors follows a general function depending on time. The random disturbances or errors can also be contemporaneously correlated through some structure varying in time. The approach is based on a Wald test and we present three consistent estimates for the asymptotic covariance matrix. The study of the asymptotic properties is based on the L-mixingale processes theory since we consider errors generated from martingale difference processes. In order to evaluate the performance of the test in finite samples, we ran some simulations with satisfactory results. A real application is also provided. [ABSTRACT FROM AUTHOR]

We use state space methods to estimate a large dynamic factor model for the Norwegian economy involving 93 variables for 1978Q2–2005Q4. The model is used to obtain forecasts for 22 key variables that can be derived from the original variables by aggregation. To investigate the potential gain in using such a large information set, we compare the forecasting properties of the dynamic factor model with those of univariate benchmark models. We find that there is an overall gain in using the dynamic factor model, but that the gain is notable only for a few of the key variables. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper focuses on parameter estimation problems of auto-regression (AR) time series models with missing observations. The standard estimation algorithms cannot be applied to such AR models with missing observations. The polynomial transformation technique is employed to transform the AR models into models which can be identified from available scarce observations, then the extended stochastic gradient algorithm is proposed to fit the time series with missing observations. The convergence properties of the proposed algorithm are analyzed and an example is given to test and illustrate the conclusions in the paper. [Copyright &y& Elsevier]

Abstract: This paper presents a two-stage least squares based iterative algorithm, a residual based interactive least squares algorithm and a residual based recursive least squares algorithm for identifying controlled autoregressive moving average (C-ARMA) models. The simulation studies indicate that the proposed algorithms can effectively estimate the parameters of the C-ARMA models. [Copyright &y& Elsevier]

In this paper we study the dependence structure for AR(1) models with symmetric α-stable innovations and time-varying coefficients. In this case the covariance function is not defined and therefore other measures of dependence have to be used. We formulate conditions providing the bounded solutions of such systems and give the form of the solution. Then the covariation and the codifference for stable AR(1) models are studied and the asymptotic relation between these two measures of dependence for the considered models is examined. [ABSTRACT FROM AUTHOR]

Starting from the Durbin algorithm in polynomial space with an inner product defined by the signal autocorrelation matrix, an isometric transformation is defined that maps this vector space into another one where the Levinson algorithm is performed. Alternatively, for iterative algorithms such as discrete all-pole (DAP), an efficient implementation of a Gohberg-Semencul (GS) relation is developed for the inversion of the autocorrelation matrix which considers its centrosymmetry. In the solution of the autocorrelation equations, the Levinson algorithm is found to be less complex operationally than the procedures based on GS inversion for up to a minimum of five iterations at various linear prediction (LP) orders. [ABSTRACT FROM AUTHOR]

In this work we will explore the theoretical connections existing between fuzzy rule-based systems (FRBS) applied on univariate time series and two statistical reference tools, the autoregressive (AR) models and the smooth transition autoregressive (STAR) model. We will show that a TSK fuzzy rule happens to be a localised AR model and that a STAR model can hence be interpreted as a restricted FRBS. Several consequences derive from this fact, and we will explore some of them, including a statistical inference-based procedure to incrementally build FRBS or the linguistic interpretation of STAR models. Finally an econometric example is given to illustrate the core idea. [Copyright &y& Elsevier]

Abstract: In this paper we study cellular automata (CAs) that perform the computational Majority task. This task is a good example of what the phenomenon of emergence in complex systems is. We take an interest in the reasons that make this particular fitness landscape a difficult one. The first goal is to study the landscape as such, and thus it is ideally independent from the actual heuristics used to search the space. However, a second goal is to understand the features a good search technique for this particular problem space should possess. We statistically quantify in various ways the degree of difficulty of searching this landscape. Due to neutrality, investigations based on sampling techniques on the whole landscape are difficult to conduct. So, we go exploring the landscape from the top. Although it has been proved that no CA can perform the task perfectly, several efficient CAs for this task have been found. Exploiting similarities between these CAs and symmetries in the landscape, we define the Olympus landscape which is regarded as the “heavenly home” of the best local optima known (blok). Then we measure several properties of this subspace. Although it is easier to find relevant CAs in this subspace than in the overall landscape, there are structural reasons that prevent a searcher from finding overfitted CAs in the Olympus. Finally, we study dynamics and performance of genetic algorithms on the Olympus in order to confirm our analysis and to find efficient CAs for the Majority problem with low computational cost. [Copyright &y& Elsevier]

Linear prediction (LP) analysis, split in two stages, is proposed for a combined time-frequency analysis. The first-stage LP is used to obtain the residual signal and extract each one of its cycles, whose harmonic spectrum is then modeled by the second-stage estimate from discrete all-pole algorithms. Thus, harmonic cycle spectra are modeled with less than 1 dB in log spectral distortion (SD). Further, a method is proposed to approximate the log SD target. A linear approximation to the log power spectral ratio in the log SD gradient is shown to provide better model fit to harmonic cycle spectra. [ABSTRACT FROM AUTHOR]

A new tool for robust tracking of fundamental frequency is proposed, along with an objective measure of main singing voice parameters, such as vibrato rate, vibrato extent, and vocal intonation. High-resolution Power Spectral Density estimation is implemented, based on AutoRegressive models of suitable order, allowing reliable formant tracking also in vocalizations characterized by highly varying values. The proposed techniques are applied to about 1000 vocalizations, coming from both professional and non-professional singers, and show better performance as compared to classical Fourier-based approaches. If properly implemented, and with a user-friendly interface, the new tool would allow real-time analysis of singing voice. Hence, it could be of help in giving non-professional singers and singing teachers reliable measures of possible improvements during and after training. [ABSTRACT FROM AUTHOR]

This paper provides a novel passive underwater acoustic method to track a moving object called source or target, with the following constraints: the sensors location is fixed and imposed, and classical array processing techniques cannot be applied. The method proposed has been successfully used to track a surface vessel (2D problem) or an underwater target (3D problem). All the results presented have been obtained with real signals. The localization of the target requires the estimation of propagation delays, that means the duration between the instant of the signal emission and its reception on each receiver. The cross-correlation function is a suitable tool when the target is motionless, but needs to be extended to the ambiguity function when it is moving. The signal to noise ratio, the uniformity of power spectral density and the integration time are determining factors for the accuracy of the localization. We show that a whitening method and a Doppler compensation are necessary, and we propose a way to eliminate the significant problem of the reflected signals. Furthermore, a new configuration of the receivers is proposed, based on the idea of coupling receivers whose distance is chosen from experiment derived results. Furthermore, the algorithm proposed is susceptible to parallel implementation, thereby facilitating real-time uses. Experimental results with real time domain data are presented and compared to trajectories obtained by an active method. [Copyright &y& Elsevier]

An estimating method for spectral densities of Gaussian time series that belong to a parametric model is proposed. Spectral density estimators are evaluated by using average Kullback–Leibler divergence from the true spectral density to estimated spectral densities. In the classical approach, unknown spectral densities are estimated by replacing the unknown parameters by asymptotically efficient estimates. In the alternative method introduced in the present paper, spectral density estimates usually do not belong to the model. The alternative spectral density estimators asymptotically dominate the classical ones. The difference in average Kullback–Leibler divergence between them can be regarded as the mixture mean curvature of the model in the space of all spectral densities. The explicit expression for the proposed estimators of spectral densities of autoregressive processes is obtained. The accuracy of prediction can be improved by using predictors that correspond to the alternative spectral density estimators. [ABSTRACT FROM AUTHOR]

In this paper we consider time series models belonging to the autoregressive (AR) family and deal with the estimation of the residual variance. This is important because estimates of the variance are involved in, for example, confidence sets for the parameters of the model, estimation of the spectrum, expressions for the estimated error of prediction and sample quantities used to make inferences about the order of the model. We consider the asymptotic biases for moment and least squares estimators of the residual variance, and compare them with known results when available and with those for maximum likelihood estimators under normality. Simulation results are presented for finite samples [ABSTRACT FROM AUTHOR]

In many one-dimensional (1-D) and two-dimensional (2-D) digital signal processing applications, auto-regressive (AR) models are very useful and powerful tools. Most of the development work done so far in 2-D AR modeling was limited to causal models. Recently, noncausal models have generated a great deal of interest because these models are a more natural choice for many applications in image processing. In this paper, we generalize the 1-D problems of noncausal linear-phase signal mdoeling and system modeling to their 2-D counterparts. The purpose of this paper is twofold. First, for homogeneous random fields, we introduce and investigate the 2-D symmetric (zero-phase) noncausal AR signal and system modeling problems. We then develop two computationally efficient algorithms for the determination of model parameters. Finally, we investigate an application in stochastic texture modeling and provide experimental results. [ABSTRACT FROM AUTHOR]

P. M. Djuric, etc.(1992) researched on the segmentation of nonstationary stochastic process into piecewise stationary stochastic process by Bayesian criterion, and gave a dynamic equation about the number of segments, their boundaries and AR model orders for each segment, but did not give detailed solution for the equation. Because the solution for the equation is very complex, this paper investigates the solution, derives some recursive relations, simplifies the problem, saves computation time and goes further into the segmentation of nonstationary stochastic process into piecewise stationary stochastic process. [ABSTRACT FROM AUTHOR]

Autoregressive models have played an important role in time series. In this paper, an autoregressive model based on the skew-normal distribution is considered. The estimation of its parameters is carried out by using the expectation–maximization algorithm, whereas the diagnostic analytics are conducted by means of the local influence method. Normal curvatures for the model under four perturbation schemes are established. Simulation studies are conducted to evaluate the performance of the proposed procedure. In addition, an empirical example involving weekly financial return data are analyzed using the procedure with the proposed diagnostic analytics, which has improved the model fit. [ABSTRACT FROM AUTHOR]