Mohammad Abdollahzadeh; Ataabak Baagherzadeh Hushmandi; Parisa Nabati
Abstract
In recent years, precise analysis and prediction of financial time series data have received significant attention. While advanced linear models provide suitable predictions for short and medium-term periods, market studies have indicated that stock behavior adheres to nonlinear patterns and linear models ...
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In recent years, precise analysis and prediction of financial time series data have received significant attention. While advanced linear models provide suitable predictions for short and medium-term periods, market studies have indicated that stock behavior adheres to nonlinear patterns and linear models capturing only a portion of the market's stock behavior. Nonlinear exponential autoregressive models have proven highly practical in solving financial problems. This article introduces a new nonlinear model that allocates coefficients to significant variables. To achieve this, existing exponential autoregressive models are analyzed, tests are conducted to validate data integrity and identify influential factors in data trends, and an appropriate model is determined. Subsequently, a novel coefficient allocation method for optimizing the nonlinear exponential Autoregressive model is proposed. The article then proves the ergodicity of the new model and determines its order using the Akaike Information Criterion (AIC). Model parameters are estimated using the nonlinear least squares method. To demonstrate the performance of the proposed model, numerical simulations of Kayson Corporation's stocks are analyzed using existing methods and the new approach. The numerical simulation results confirm the effectiveness and prediction accuracy of the proposed method compared to existing approaches.
Parisa Nabati
Abstract
This paper presents a nonlinear autoregressive model with Ornstein Uhlenbeck processes innovation driven with white noise. Notations and preliminaries are presented about the Ornstein Uhlenbeck processes that have important ...
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This paper presents a nonlinear autoregressive model with Ornstein Uhlenbeck processes innovation driven with white noise. Notations and preliminaries are presented about the Ornstein Uhlenbeck processes that have important applications in finance. The parameter estimation for these processes is constructed from the time continuous likelihood function that leads to an explicit maximum likelihood estimator. A semiparametric method is proposed to estimate the nonlinear autoregressive function using the conditional least square method for parametric estimation and the nonparametric kernel approach by using the nonparametric factor that is derived by a local L2-fitting criterion for the regression adjustment estimation. Then the Monte Carlo numerical simulation studies are carried out to show the efficiency and accuracy of the present work. The mean square error (MSE) is a measure of the average squared deviation of the estimated function values from the actual ones. The values of MSE indicate that the innovation in noise structure is performed well in comparison with the existing noise in the nonlinear autoregressive models.
