Nonlinear Time Series Models Research Articles

A Three-Stage Nonparametric Kernel-Based Time Series Model Based on Fuzzy Data

In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by LR fuzzy numbers. To this end, we present a three-stage nonparametric kernel-based estimation procedure for the center as well as the left and right spreads of the unknown nonlinear fuzzy smooth function. In each stage, the nonparametric Nadaraya–Watson estimator is used to evaluate the center and the spreads of the fuzzy smooth function. A hybrid algorithm is proposed to estimate the unknown optimal bandwidths and autoregressive order simultaneously. Various goodness-of-fit measures are utilized for performance assessment of the fuzzy nonlinear kernel-based time series model and for comparative analysis. The practical applicability and superiority of the novel approach in comparison with further fuzzy time series models are demonstrated via a simulation study and some real-life applications.

Subordinated Gaussian processes for solar irradiance

AbstractTraditionally the power grid has been a one‐way street with power flowing from large transmission‐connected generators through the distribution network to consumers. This paradigm is changing with the introduction of distributed renewable energy resources (DERs), and with it, the way the grid is managed. There is currently a dearth of high fidelity solar irradiance datasets available to help grid researchers understand how expansion of DERs could affect future power system operations. Realistic simulations of by‐the‐second solar irradiances are needed to study how DER variability affects the grid. Irradiance data are highly non‐stationary and non‐Gaussian, and even modern time series models are challenged by their distributional properties. We develop a subordinated non‐Gaussian stochastic model whose simulations realistically capture the distribution and dependence structure in measured irradiance. We illustrate our approach on a fine resolution dataset from Hawaii, where our approach outperforms standard nonlinear time series models.

Constraining nonlinear time series modeling with the metabolic theory of ecology

Forecasting the response of ecological systems to environmental change is a critical challenge for sustainable management. The metabolic theory of ecology (MTE) posits scaling of biological rates with temperature, but it has had limited application to population dynamic forecasting. Here we use the temperature dependence of the MTE to constrain empirical dynamic modeling (EDM), an equation-free nonlinear machine learning approach for forecasting. By rescaling time with temperature and modeling dynamics on a "metabolic time step," our method (MTE-EDM) improved forecast accuracy in 18 of 19 empirical ectotherm time series (by 19% on average), with the largest gains in more seasonal environments. MTE-EDM assumes that temperature affects only the rate, rather than the form, of population dynamics, and that interacting species have approximately similar temperature dependence. A review of laboratory studies suggests these assumptions are reasonable, at least approximately, though not for all ecological systems. Our approach highlights how to combine modern data-driven forecasting techniques with ecological theory and mechanistic understanding to predict the response of complex ecosystems to temperature variability and trends.

Pakistan CO2 Emission Modelling and Forecasting: A Linear and Nonlinear Time Series Approach.

Pakistan is considered among the top five countries with the highest CO2 emissions globally. This calls for pragmatic policy implementation by all stakeholders to bring finality to this alarming situation since it contributes greatly to global warming, thereby leading to climate change. This study is an attempt to make a comparative analysis of the linear time series models with nonlinear time series models to study CO2 emission data in Pakistan. These linear and nonlinear time series models were used to model and forecast future values of CO2 emissions for a short period. To assess and select the best model among these linear and nonlinear time series models, we used the root mean square error (RMSE) and the mean absolute error (MAE) as performance indicators. The outputs showed that the nonlinear machine learning models are the best among all other models, having the lowest RMSE and MAE values. Based on the forecasted value of the nonlinear machine learning neural network autoregressive model, Pakistan's CO2 emissions will be 1.048 metric tons per capita by 2028. The increasing trend in emissions is a frightening and clear warning, suggesting that innovative policies must be initiated to reduce the trend. We encourage the Pakistan government to price CO2 emissions by companies and entities per ton, adapt electricity production from hydro, wind, and different sources with no emissions of CO2, initiate rigorous planting of more trees in the populated areas of Pakistan as forest covers, provide incentives to companies, organisations, institutions, and households to come out with clean technologies or use technologies with no CO2 emissions or those with lower ones, and fund more studies to develop clean and innovative technologies with less or no CO2 emissions.

On portmanteau-type tests for nonlinear multivariate time series

A general framework to devise portmanteau-type test statistics for a general class of multivariate nonlinear time series models with vector martingale difference errors is formulated. Based on this framework a suite of individual and mixed multivariate test statistics is considered. Two applications are developed: single- and multiple-lag test statistics. In each case, the resulting portmanteau test statistic is based on multivariate residuals and multivariate squared residuals. Moreover, single- and multiple-lag mixed multivariate portmanteau-type tests are introduced. These test statistics are designed to detect different forms of inadequacies in the model residuals jointly. All proposed tests take uncertainty due to model estimation properly into account. The asymptotic null distribution of each test statistic follows from the asymptotic distribution of the general portmanteau-type test statistic in a natural way. Some considerations are given to the empirical size and power of six test statistics via a simulation study. All tests have satisfactory size and power properties in finite samples. To demonstrate their practical use, the proposed test statistics are applied to the residuals of a vector bivariate nonlinear threshold model fitted to U.S. interest rates.

Gradient-based Parameter Estimation for a Nonlinear Exponential Autoregressive Time-series Model by Using the Multi-innovation

Gradient-based Parameter Estimation for a Nonlinear Exponential Autoregressive Time-series Model by Using the Multi-innovation

Stability Conditions for a Nonlinear Time Series Model

This research aims to determine whether the proposed time series model is stable or not. To achieve this, Ozaki’s approximation method was utilized, where the nonlinear part is a function that approaches zero, similar to Ozaki’s imposed function. The study produced examples of both stable and unstable models, and it was discovered that the stability and instability of the model are affected by the enforced optional constants. The researchers used the approximation method to obtain an asymptotic linear model that satisfied the singular point of the proposed model. The study first identified the singular points of the suggested model and then focused on determining the stability conditions, which was the main objective of the study. Last, the stability conditions of the limit cycle were established.

Consumer product prediction using machine learning

Time-series forecasting is an approach that uses historical and current data to project future values over time or at a given point in time, while forecasting and prediction are often synonymous, there is one interesting detail. In some professions, forecasting may refer to data at a specific future point in time, whereas prediction refers to future data in general. Most widely used to determine the nature of stock prices. A series of analyses and modeling by a finance committee is to guide investors, professors of legal sciences, and processes. And that is why he proposes that this series argument not include a sliding window; they were wise to back then, and they gave up everything, anticipating stock values relative to her. The system presents the (GUI) Graphical User Interface as a stand-alone application. The proposed findings demonstrate a highly predicted accurate approach for nonlinear time series models that are difficult to obtain from traditional models.

Prediction of heading date, culm length, and biomass from canopy-height-related parameters derived from time-series UAV observations of rice.

Unmanned aerial vehicles (UAVs) are powerful tools for monitoring crops for high-throughput phenotyping. Time-series aerial photography of fields can record the whole process of crop growth. Canopy height (CH), which is vertical plant growth, has been used as an indicator for the evaluation of lodging tolerance and the prediction of biomass and yield. However, there have been few attempts to use UAV-derived time-series CH data for field testing of crop lines. Here we provide a novel framework for trait prediction using CH data in rice. We generated UAV-based digital surface models of crops to extract CH data of 30 Japanese rice cultivars in 2019, 2020, and 2021. CH-related parameters were calculated in a non-linear time-series model as an S-shaped plant growth curve. The maximum saturation CH value was the most important predictor for culm length. The time point at the maximum CH contributed to the prediction of days to heading, and was able to predict stem and leaf weight and aboveground weight, possibly reflecting the association of biomass with duration of vegetative growth. These results indicate that the CH-related parameters acquired by UAV can be useful as predictors of traits typically measured by hand.

Uncertain Threshold Autoregressive Model via LASSO Procedure

Uncertain time series models have been proposed to forecast future data based on imprecise known data. As an uncertain time series model, the uncertain threshold autoregressive model was proposed to deal with nonlinear data. The previous study estimated the unknown parameters in the uncertain threshold autoregressive model with the least-squares estimation. However, for nonlinear time series models, the least-squares estimation may cause overfitting of the model. To deal with this problem, this paper adds the least absolute shrinkage and selection operator penalty to the uncertain threshold autoregressive model to alleviate the level of overfitting. In addition, this paper uses the sum of square errors criterion to select the optimum order of the model. Finally, a real stock price example is provided to compare two different parameter estimation methods.

Modelling Period Effect of Lee-Carter Mortality Model with SETAR Model

Mortality dynamics plays an important role in understanding mortality and life expectancy that will impact on economy of the countries. Many studies have considered Lee Carter method with time index as an indicator to do the forecasting. In order to forecast the mortality rates, the period index in the Lee Carter model is applied to the random walk with drift model. Despite its performance on the forecasting ability on the Lee Carter model, it is lack in term of time varying parameter that leads to higher error when fitted with random walk of drift and less accurate when forecasting the model. This is because the random walk with drift model is only adequate to data with linear series. In this study, we used the concept of non-linear time series model and then proposed a self-exciting threshold autoregressive (SETAR) to the period index. It shows that our model outperformed the random walk with drift (RWD) model for forecasting accuracy when Malaysian mortality data from 1980-2010 are considered. Long term forecasting analysis up to 2017 comparing the two models are then performed.

A Novel Short-Term Power Load Forecasting Method Based on TSNE-EEMD-LSTM

In this paper, a novel power load forecasting model is proposed to fully extract the periodic characteristics of short-term load at various time scales and explore the potential correlations between influencing factors and characteristics of load components. Firstly, the t-distributed stochastic neighbor embedding algorithm is used to map sample points of high-dimensional load influencing factors to low-dimensional space, and the ensemble empirical mode decomposition algorithm is employed to split the historical load curve into multiple signal components with different frequencies. Then, several long short-term memory networks including nonlinear mapping and time series models are established to mine the relationship between low-dimensional comprehensive influencing factors and each intrinsic mode function component by utilizing different inputs. Finally, the effectiveness of the hybrid model is verified via using the short-term load dataset of 3-hour data granularity in a certain region, and the influence of key parameters of the model on the forecasting effect is discussed.

Modeling and Forecasting Stock Market Volatility of CPEC Founding Countries: Using Nonlinear Time Series and Machine Learning Models

The highly sensitive, nonlinear, and unpredictable stock marketbehaviours are always challenging for researchers. Stock markets ofPakistan and China, i.e., KSE-100 and SSE-100, respectively, are thetwo most attractive stock markets after the official announcementof CPEC. Thus, the daily closing price of KSE-100 and SSE-100 Stockreturns are used to evaluate the volatility forecast performance ofthe machine learning technique, GARCH family and the nonlinearregime-switching models. The findings of this study revealed that thestandard GARCH model is the best-fitted model based on Akaike’sInformation Criteria (AIC) and Bayesian Information Criteria (BIC).Furthermore, the forecast performance of the machine learning LSTMmodel outperforms other models based on RMSE for SSE-100. Incontrast, the forecast performance of CGARCH for SSE-100 and theMarkov-regime-switchingmodelforKSE-100outperformsothermodelsbased on MAE, MAPE, and SMAPE evaluation criteria. It is also revealedthat the predictive power of the machine learning model is very closeto CGARCH and MRS model; therefore, the LSTM model can be used asan alternative to GARCH and regime-switching models for stock marketvolatility. These findings will help national and international investors,policy-makers, geographical economists, and industrialists to use thebestforecastmodeltomakebetterpoliciesandgaintremendousprofit.

Bayesian nonlinear expectation for time series modelling and its application to Bitcoin

This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or misspecification in the conditional mean and volatility. At the first stage, a reference or approximating time series model is specified and estimated. At the second stage, Bayesian nonlinear expectations are introduced to incorporate model uncertainty or misspecification in prediction via specifying a family of alternative models. The Bayesian nonlinear expectations for prediction are constructed from closed-form Bayesian credible intervals evaluated using conjugate priors and residuals of the estimated approximating model. Using real Bitcoin data including some periods of Covid 19, applications of the proposed method to forecasting and risk evaluation of Bitcoin are discussed via three major parametric nonlinear time series models, namely the self-exciting threshold autoregressive model, the generalized autoregressive conditional heteroscedasticity model and the stochastic volatility model.

Air Pollution Exposure and the Relative Risk of Sudden Sensorineural Hearing Loss in Taipei.

(1) Background: The etiologies of sudden sensorineural hearing loss (SSHL) remain unclear. The level of mean particulate matter with a diameter of 2.5 μm or less (PM2.5) was not associated with SSHL, but the maximum PM2.5 level exhibited a negative association with SSHL in Korea. Exposure to nitrogen dioxide (NO2) for 2 weeks increased the risk of SSHL. The lag effects of SSHL after air pollution exposure were limited. We aimed to evaluate the association of SSHL with air pollution exposure to determine whether air pollution exposure caused delayed effects. (2) Methods: This observational study used inpatient data obtained from electronic health records at the Tri-Service General Hospital from 2011 to 2019. The data of all SSHL patients were retrieved. The air quality dataset from Songshan station from 2011 to 2019 was used. The main outcomes were the relative risks (RRs) of SSHL associated with PM2.5, O3, and NO2 exposures within 1 month. The relationships between these factors were examined using distributed lag nonlinear time series models. (3) Results: The RR of SSHL associated with PM2.5 exposure was 1.195 (95% confidence interval (C.I.: 1.047–1.363) for a 10 unit increase at a lag of 7 days. The RR of SSHL associated with O3 exposure was 1.14 (95% C.I.: 1.003–1.3) for a 10 unit increase at a lag of 9 days. The RR of SSHL associated with NO2 exposure was 1.284 (95% C.I.: 1.05–1.57) for a 10 unit increase at a lag of 23 days. (4) Conclusions: In our study, SSHL was confirmed to be associated with air pollution exposure with a lag effect. We discussed possible mechanisms to explore possible biological hypotheses and support further research. Large-scale studies including participants with other ethnicities and causal relationships are needed to confirm our findings.

SOME REGIME-SWITCHING MODELS FOR ECONOMIC TIME SERIES: A COMPARATIVE STUDY

This paper mainly discusses some regime-switching models and explore their usefulness in modeling the economic time series. In recent years, several time series models have been proposed which shape the idea of the existence of different regimes produced by a stochastic process. Especially, nonlinear time series models have gained more attention because linear time series models faced various limitations. The purpose of this study is to establish the methodology of the Self-Exciting Threshold Autoregressive (SETAR) model, Smooth Transition Autoregressive (STAR) model and Markov-Switching (MSW) model from parametric nonlinear time series models in the mean and to compare these models with each other through two financial data sets. For this purpose, some theoretical information on the subject models are given without going into too much detail. In the light of the obtained theoretical information, all models are modeled by using two financial data sets. The obtained models are compared with the help of some performance criteria, measurement of relative efficiency and graph showing the relation of the actual-fitted values of the models.

Statistical Causality for Multivariate Nonlinear Time Series via Gaussian Process Models

The ability to test for statistical causality in linear and nonlinear contexts, in stationary or non-stationary settings, and to identify whether statistical causality influences trend of volatility forms a particularly important class of problems to explore in multi-modal and multivariate processes. In this paper, we develop novel testing frameworks for statistical causality in general classes of multivariate nonlinear time series models. Our framework accommodates flexible features where causality may be present in either: trend, volatility or both structural components of the general multivariate Markov processes under study. In addition, we accommodate the added possibilities of flexible structural features such as long memory and persistence in the multivariate processes when applying our semi-parametric approach to causality detection. We design a calibration procedure and formal testing procedure to detect these relationships through classes of Gaussian process models. We provide a generic framework which can be applied to a wide range of problems, including partially observed generalised diffusions or general multivariate linear or nonlinear time series models. We demonstrate several illustrative examples of features that are easily testable under our framework to study the properties of the inference procedure developed including the power of the test, sensitivity and robustness. We then illustrate our method on an interesting real data example from commodity modelling.

On the semi-varying coefficient dynamic panel data model with autocorrelated errors

In nonlinear time series modeling, autocorrelation of the random errors may cause critical problems in estimation and inference. The situation becomes even worse for panel data with dynamic structure. However, most of the existing literature has not taken into account this problem. The challenge comes from the fact that the expectation of random errors conditional on lag variables is hardly to be zero. Based on the extension of Whittle likelihood, a semi-parametric dynamic model with ARMA errors for panel data is proposed. Asymptotic normality for the estimators of finite parameters and varying coefficients have been established respectively. Statistical simulations show that the proposed method can efficiently remove the bias of estimation. In real data analysis, it demonstrates that the proposed method can improve prediction when errors are autocorrelated.

Threshold Autoregressive Nearest-Neighbour Models for Claims Reserving

Motivated by claims reserving in run-off triangles, a class of threshold autoregressive nearest-neighbour (TAR-NN) models extending a major class of parametric nonlinear time series models, namely threshold autoregressive (TAR) models, is introduced. The proposed class of models also introduces a flexible regime-switching mechanism to nearest-neighbour models. Attention is given to a sub-class of TAR-NN models, namely self-exciting threshold autoregressive nearest-neighbour models (SETAR-NN), for uses in claims reserving. The (strict) stationarity and geometric ergodicity of the SETAR-NN model, and more generally, a two-dimensional nonlinear autoregressive random field, are discussed. The conditional least-square (CLS) method is used to estimate the SETAR-NN model and some of its nested models. Simulation studies on the parameter estimates from the CLS method are conducted. Using real insurance claims data and stochastic simulations, the applications of the SETAR-NN model and the nested models for projecting future claims liabilities are discussed. Comparisons of those models with the Bootstrap-Chain-Ladder (BCL) model for claims reserving are provided.

Bayesian Computation in Dynamic Latent Factor Models

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the introduction of a novel copula construction in sequential filtering of coupled sets of dynamic generalized linear models. The new copula approach is integrated into recently introduced multiscale models in which univariate time series are coupled via nonlinear forms involving dynamic latent factors representing cross-series relationships. The resulting methodology offers dramatic speed-up in online Bayesian computations for sequential filtering and forecasting in this broad, flexible class of multivariate models. Two examples in nonlinear models for very heterogeneous time series of nonnegative counts demonstrate massive computational efficiencies relative to existing, simulation-based methods, while defining similar filtering and forecasting outcomes.