Exponential Autoregressive Research Articles

Forecasting techniques based on the use of time series models for forecasting expenditures on social protection and social security

In the context of a military conflict, it is growing the number of people who are in difficult life circumstances and need state assistance. Therefore, the issue of forecasting spending on social protection and social security is becoming increasingly relevant. The aim of the paper is to consider modern methods of analyzing and forecasting time series and propose their application to determine the need for spending on social protection and social security. The article provides a brief overview of regression models, their advantages and features of use for analyzing and predicting nonlinear and linear processes described by time series of statistical indicators used in the population social protection system. The paper offers a combination of predictions that can be made based on locally linear and nonlinear models, such as threshold autoregression (TAR) and exponential autoregression (ExAR), which have known quality characteristics. This approach primarily concerns time series that contain data on structural changes in the analyzed processes. Using combined predictions, it is possible to estimate the contribution of each component for both different and selected time points using variable weights. To build forecasts, depending on the scenario of distribution of social protection and social security expenditures, it is proposed to use Bayes networks. Their advantages are flexibility, high quality of results, the possibility of structural and parametric optimization and adaptation to new data and conditions, support for quality assessment by appropriate sets of statistical criteria, which makes it possible to analyze thoroughly intermediate and final results. It helps to increase the adequacy of models and the high quality of the final result of their application.

Mathematical modeling and statistical analysis of Moroccan mean annual rainfall using EXPAR processes

In this work, we propose a study of the mean annual rainfall time series in order to evaluate the climate changes pattern over time. If the analysis of this time series is carried out correctly, it can contribute to improve planning and policy development. That is why we consider the problem of mathematical modeling and analysis of the mean annual rainfall of Morocco between 1901 and 2020 using descriptive statistics, structure changes analysis, spectral analysis and a nonlinear Exponential Autoregressive (EXPAR) processes to reproduce the behavior of this time series. The results indicate three main breakpoints and show that the time series has a remarkable cycles about 60, 18 and 6 years with a global decrease tendency about 0.56 mm per year. Furthermore, we have justified the choice of using a non-linear EXPAR processes rather than a linear traditional one and provided a good fitted EXPAR model.

Performance of a Novel Hybrid Model Through Simulation and Historical Financial Data

It is thoroughly acknowledged that the historical financial time series is not linear, exhibits structural changes, and is volatile. It has been noticed in the current literature that because of the existence of structural breaks in the historical time series, the GARCH family models provide misleading results and poor forecasts. Thus, it is unavoidable to incorporate models with nonlinearity in the conditional mean and conditional variance to capture volatility dynamics more precisely than the existing models. Therefore, inspiring in this matter, this study proposes a novel hybrid model of exponential autoregressive (ExpAR) with a Markov-switching GARCH (MSGARCH) model. This study also examines volatility dynamics and performances through simulation and real-world financial data. Moreover, this study investigates downside risk management performances using 5% VaR (Value-at-Risk) back-testing. The empirical findings showed that the proposed model outperforms the benchmark model for both simulation and real-world time series data. The VaR results also showed that the proposed model captures downside risk more meticulously than the benchmark model.

Aligned signed-rank tests of a linear autoregressive model against an exponential autoregressive one

In this work, we have established the aligned signed-rank tests for testing the ordinary dependence against exponential autoregression [] model. The considered tests are asymptotically valid under an arbitrary symmetric innovation density, and locally asymptotically most stringent against the EXPAR alternatives associated with some predetermined symmetric density type. Several simulation was curried out to show the good performance of these tests and an application for modeling the annual sunspots number is provided.

Joint Parameter and Time-Delay Estimation for a Class of Nonlinear Time-Series Models

Nonlinear time-series modeling is fundamental to a wide variety of control and prediction problems. This letter focuses on the joint parameter and time-delay estimation for an extended version of the nonlinear exponential autoregressive (ExpAR) time-series model. To address the difficulties posed by the unknown time-delay and improve the estimation accuracy, we first employ the redundant rule to transform the ExpAR model into an augmented identification model. Then we invoke the multi-innovation theory to enhance data utilization and propose a new algorithm that combines stochastic gradient descent with discrete search for estimating the unknown model parameters and time-delay. The simulation results show that by properly adjusting the innovation length, the estimation accuracy of the proposed multi-innovation algorithm can significantly exceed that of the single-innovation algorithm.

TAC Method for Fitting Exponential Autoregressive Models and Others: Applications in Economy and Finance

There are a couple of purposes in this paper: to study a problem of approximation with exponential functions and to show its relevance for economic science. The solution of the first problem is as conclusive as it can be: working with the max-norm, we determine which datasets have best approximation by means of exponentials of the form f(t)=b+aexp(kt), we give a necessary and sufficient condition for some a,b,k∈R to be the coefficients that give the best approximation, and we give a best approximation by means of limits of exponentials when the dataset cannot be best approximated by an exponential. For the usual case, we have also been able to approximate the coefficients of the best approximation. As for the second purpose, we show how to approximate the coefficients of exponential models in economic science (this is only applying the R-package nlstac) and also the use of exponential autoregressive models, another well-established model in economic science, by utilizing the same tools: a numerical algorithm for fitting exponential patterns without initial guess designed by the authors and implemented in nlstac. We check one more time the robustness of this algorithm by successfully applying it to two very distant areas of economy: demand curves and nonlinear time series. This shows the utility of TAC (Spanish for CT scan) and highlights to what extent this algorithm can be useful.

A wavelet approach of investing behaviors and their effects on risk exposures

Exposure to market risk is a core objective of the Capital Asset Pricing Model (CAPM) with a focus on systematic risk. However, traditional OLS Beta model estimations (Ordinary Least Squares) are plagued with several statistical issues. Moreover, the CAPM considers only one source of risk and supposes that investors only engage in similar behaviors. In order to analyze short and long exposures to different sources of risk, we developed a Time–Frequency Multi-Betas Model with ARMA-EGARCH errors (Auto Regressive Moving Average Exponential AutoRegressive Conditional Heteroskedasticity). Our model considers gold, oil, and Fama–French factors as supplementary sources of risk and wavelets decompositions. We used 30 French stocks listed on the CAC40 (Cotations Assistées Continues 40) within a daily period from 2005 to 2015. The conjugation of the wavelet decompositions and the parameters estimates constitutes decision-making support for managers by multiplying the interpretive possibilities. In the short-run, (“Noise Trader” and “High-Frequency Trader”) only a few equities are insensitive to Oil and Gold fluctuations, and the estimated Market Betas parameters are scant different compared to the Model without wavelets. Oppositely, in the long-run, (fundamentalists investors), Oil and Gold affect all stocks but their impact varies according to the Beta (sensitivity to the market). We also observed significant differences between parameters estimated with and without wavelets.

Parameter estimation for an exponential autoregressive time series model by the Newton search and multi-innovation theory

ABSTRACT This paper focuses on the recursive parameter estimation problem of the exponential autoregressive (ExpAR) model. Applying the Newton search and multi-innovation theory, a multi-innovation Newton recursive algorithm is presented for identifying the ExpAR model. In order to improve the computational efficiency, the hierarchical identification principle is employed to decompose an ExpAR model into two sub-models, and to derive a hierarchical multi-innovation Newton recursive algorithm. A simulation example is provided to demonstrate the effectiveness of the proposed algorithms.

Forecasting monthly rainfall of Sub-Himalayan region of India using parametric and non-parametric modelling approaches

Rainfall being a complex phenomenon governed by various meteorological parameters is difficult to model and forecast with high precision. For hilly regions such as state of Sikkim and adjoining areas of West Bengal, rainfall acts as lifeline. Several parametric models such as seasonal autoregressive integrated moving average (SARIMA) and exponential autoregressive (EXPAR) are very popular and extensively used to model and forecast rainfall. Owning to complex nature of rainfall series, non-parametric time delay neural network (TDNN) model has also gained substantial amount of attention by researchers. This study uses these two broad class of models and applies them to the monthly rainfall of Sub-Himalayan West Bengal and Sikkim. The models were compared based on their forecasting efficiencies and pattern prediction ability.

Comparison of Classical and Robust Estimates of Threshold Auto-regression Parameters

The exponential auto-regression model is a discrete analog of the second-order nonlinear differential equations of the type of Duffing and van der Pol oscillators. It is used to describe nonlinear stochastic processes with discrete time, such as vehicle vibrations, ship roll, electrical signals in the cerebral cortex. When applying the model in practice, one of the important tasks is its identification, in particular, an estimate of the model parameters from observations of the stochastic process it described. A traditional technique to estimate autoregressive parameters is the nonlinear least squares method. Its disadvantage is high sensitivity to the measurement errors of the process observed. The M-estimate method largely has no such a drawback. The M-estimates are based on the minimization procedure of a non-convex function of several variables. The paper studies the effectiveness of several well-known minimization methods to find the M-estimates of the parameters of an exponential autoregressive model. The paper demonstrates that the sequential quadratic programming algorithm, the active set algorithm, and the interior-point algorithm have shown the best and approximately the same accuracy. The quasi-Newton algorithm is inferior to them in accuracy a little bit, but is not inferior in time. These algorithms had approximately the same speed and were one and a half times faster than the Nelder-Mead algorithm and 14 times faster than the genetic algorithm. The Nelder-Mead algorithm and the genetic algorithm have shown the worst accuracy. It was found that all the algorithms are sensitive to initial conditions. The estimate of parameters, on which the autoregressive equation linearly depends, is by an order of magnitude more accurate than that of the parameter on which the auto-regression equation depends in a nonlinear way.

Gradient iterative-based kernel method for exponential autoregressive models

Two kernel method-based gradient iterative algorithms are proposed for exponential autoregressive (ExpAR) models in this study. A polynomial kernel function is utilised to transform the ExpAR model into a linear-parameter model. Since the order of the linear-parameter model is large, a momentum stochastic gradient algorithm and an adaptive step-length gradient iterative algorithm are developed. Both these two algorithms can estimate the parameters with less computational efforts. Finally, a simulation example shows that the proposed algorithms are effective.

A novel state estimation strategy for observation recovery in nonlinear systems based on ExpARMA algorithm

A more effective state estimation scheme of nonlinear systems having loss at output has been discussed in this paper. The existing model of reproducing lost measurement in nonlinear systems is Exponential Autoregressive or ExpAR which incorporates only output measurements for compensation. In this work, however, the compensated measurement is based on Exponential Autoregressive Moving Average (ExpARMA) series. The proposed model incorporates relatively more particulars compared to the existing models based on AR, ARMA or ExpAR etc. The ExpARMA scheme utilizes output, as well as input measurements, which bears more optimal outcomes at the cost of higher computational efforts. Important steps of calculating nonlinear prediction coefficients are carried out to assist the input signals. A trade-off could be considered between efficient results and computational time. To test and compare the performance of proposed algorithm with existing compensation techniques, two-phase Permanent Magnet Synchronous Motor (PMSM) has been simulated as a case study.

Comparison of Single Exponential Smoothing, Naive Model, and SARIMA Methods for Forecasting Rainfall in Medan

This study aims to compare the best method on the forecasting system of rainfall in Medan using Single Exponential Smoothing (SES), Naive Model, and Seasonal Autoregressive Integrated Moving Average (SARIMA) . The data used in this study is rainfall data for 10 years (2009 – 2019). From the simulation by comparing existing method, the best model is SES with and value of MAPE (Mean Absolut Percentage Error) sebesar 2,47%. And then SARIMA (1,01,1)(4,0,3)12 whit value of MAPE is2,93%. Both of this model is high accurate model because value of MAPE resulted < 10%.

Compensated closed-loop Kalman filtering for nonlinear systems

In this paper, we introduce new state estimation algorithm for nonlinear systems with the measurement loss at output channels. The goal of proposed methodology is to compensate for the output state-measurement losses through an advanced scheme that relies on the nonlinear prediction (NLP) and Kalman filter. Using NLP subsystem, based on Exponential Autoregressive (EXPAR) model, a compensated observation signal is first regenerated and then it is delivered to nonlinear discrete filtering or linearized Kalman filter in the form of closed-loop. Two proposed scheme versions (EXPAR-Substitution and EXPAR-Elimination) are presented in this paper. A two-phase permanent magnet synchronous motor (PMSM) case study is exposed to loss of measurements and then the loss is reconstructed using EXPAR-based schemes to demonstrate some capable results of the proposed algorithm. Simulation results of the proposed algorithm are found to be superior compared to other algorithms in the literature.

A remaining useful life prediction method for airborne fuel pump after maintenance

Remaining useful life prediction is the core of condition-based maintenance under the technology framework of prognostic and health management. But the remaining useful life of airborne fuel pump after maintenance is difficult to predict because of the multi-stage noise and small data size. A new method is proposed to solve the remaining useful life prediction of repaired fuel pump. Firstly, an alternative smooth transition auto-regression model logistic smooth transition auto-regression or exponential smooth transition auto-regression is proposed to reduce the multi-stage noise. Secondly, random effect Wiener process is utilized to model the de-noised degradation data, and the posterior parameters of remaining useful life prediction after maintenance are derived by the Bayesian method based on the parameters before maintenance. Finally, the method proposed above is compared with the methods which neglect the multi-stage noise and information before maintenance, comparative results show that the proposed method can improve the remaining useful life prediction accuracy significantly.

On some parameter estimation algorithms for the nonlinear exponential autoregressive model

SummaryModeling an exponential autoregressive (ExpAR) time series is the basis of solving the corresponding prediction and control problems. This paper investigates the hierarchical parameter estimation methods for the ExpAR model. By the hierarchical identification principle, the original nonlinear optimization problem is transformed into the combination of a linear and nonlinear optimization problem, and then, we derive a hierarchical least squares and stochastic gradient (LS‐SG) algorithm. Given the difficulty of determining the step‐size in the hierarchical LS‐SG algorithm, an approach is proposed to obtain the optimal step‐size. To improve the parameter estimation accuracy, the multi‐innovation identification theory is employed to develop a hierarchical least squares and multi‐innovation stochastic gradient algorithm for the ExpAR model. Two simulation examples are provided to test the effectiveness of the proposed algorithms.

Fitting the exponential autoregressive model through recursive search

This paper focuses on the recursive parameter estimation methods for the exponential autoregressive (ExpAR) model. Applying the negative gradient search and introducing a forgetting factor, a stochastic gradient and a forgetting factor stochastic gradient algorithms are presented. In order to improve the parameter estimation accuracy and the convergence rate, the multi-innovation identification theory is employed to derive a forgetting factor multi-innovation stochastic gradient algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms.

Modeling a nonlinear process using the exponential autoregressive time series model

The parameter estimation methods for the nonlinear exponential autoregressive (ExpAR) model are investigated in this work. Combining the hierarchical identification principle with the negative gradient search, we derive a hierarchical stochastic gradient algorithm. Inspired by the multi-innovation identification theory, we develop a hierarchical-based multi-innovation identification algorithm for the ExpAR model. Introducing two forgetting factors, a variant of the hierarchical-based multi-innovation identification algorithm is proposed. Moreover, to compare and demonstrate the serviceability of these algorithms, a nonlinear ExpAR process is taken as an example in the simulation.

Generalized exponential autoregressive models for nonlinear time series: Stationarity, estimation and applications

The generalized exponential autoregressive (GExpAR) models are extensions of the classic exponential autoregressive (ExpAR) model with much more flexibility. In this paper, we first review some development of the ExpAR models, and then discuss the stationary conditions of the GExpAR model. A new estimation algorithm based on the variable projection method is proposed for the GExpAR models. Finally, the models are applied to two real-world time series modeling and prediction. Comparison results show that (i) the proposed estimation approach is much more efficient than the classic method, (ii) the GExpAR models are more powerful in modeling the nonlinear time series.

Stability of a Non-Linear Exponential Autoregressive Model

In this paper, a non-linear exponential autoregressive model has been studied by applying the local linearization technique. The obtained results have been implemented in a time series which represents number of diabetic patients for ten years period.