Estimation of Right-censored SETAR-type Nonlinear Time-series Model

The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study's findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.

This study examines two long-term time series of nitrate-nitrogen concentrations from the River Ouse and Stour situated in the Eastern England. The time series of monthly averages were decomposed into trend, seasonal and cyclical components and residuals to create a simple additive model. Residuals were then modelled by linear time series models represented by models of the ARMA (autoregressive moving average) class and nonlinear time series models with multiple regimes represented by SETAR (self-exciting threshold autoregressive) and MSW (Markov switching) models. The analysis showed that, based on the minimal value of residual sum of squares (RSS) of one-step ahead forecast in both datasets, SETAR and MSW models described the time series better than models ARMA. However, the relative improvement of SETAR models against ARMA models was low ranging between 1% and 4% with the exception of the three-regime model for the River Stour where the improvement was 48.9%. In comparison, the relative improvement of MSW models was between 44.6% and 52.5 for two-regime and from 60.4% to 75% for three-regime models. However, the visual assessment of models plotted against original datasets showed that despite a high value of RSS, some ARMA models could describe the analyzed time series better than AR (autoregressive), MA (moving average) and SETAR models with lower values of RSS. In both datasets MSW models provided a very good visual fit describing most of the extreme values. The results of this work could be used as a base for construction of other time series models used to describe or predict nitratenitrogen concentrations.

In economies that are open to foreign markets the numerical value of the currencies as a macroeconomic variable is of great importance especially when the mutual dependency among the economies is concerned. When it is considered in terms of political economy, the targeted level of the currencies have vital importance especially in economies that have the characteristics of export-driven growth and in economies that struggle not to disrupt the picture in macroeconomic design. When it is considered that each time series has a structure that is sensitive to its own internal dynamics (sometimes these dynamics are expressed as the time series components), these dynamics provide us with coordinates for estimations and may eliminate the compulsory dependency on the outsourced variables at a serious level. This is exactly what has been done in this study. First of all, the non-linear time series analyses are examined in terms of linearity tests, and the linearity tests are applied for all parties and for different time periods. Then, the SETAR Modelling, which is the title of the study, has been applied in order to explain the non-linear pattern in detail. The SETAR Modelling process and other definitions statistical analyses of this model have been applied in relevant parities for separate time periods. The SETAR model, which is one of the TAR Group modeling, shows a better performance than many other linear and non-linear modeling. In this study, the secondary purpose is to express that the SETAR model performance is superior to the other models by considering the observation values of the parities.

This study estimates the Self Exciting Threshold Autoregressive (SETAR) and Smooth Transition Autoregressive (STAR) models and examines the nonlinear and regime switching dynamics of economic growth for a set of 10 OECD countries. The null of linearity in SETAR model is tested using the recursive polynomial F test of Tsay and the bootstrap based supremum, average and exponential average Lagrange Multiplier (LM) tests of Hansen. The F test of Tsay rejects the null of linearity for all the countries, except Spain and Switzerland. The SETAR model of Hansen reinforces the evidence and suggests the rejection of linear model. The STAR model rejects the null of linearity against STAR nonlinearity for all the countries, except Denmark and Switzerland. The sequential F tests for the conditional nulls suggest the LSTAR nonlinearity for Australia, Belgium, France, Sweden and UK, and the ESTAR nonlinearity for Canada, Spain and the USA.

Palm oil is an agricultural commodity that has an important role in the global economy. Palm oil is obtained from the fruit of the oil palm tree (Elaeis guineensis) which grows in tropical regions, especially in countries such as Indonesia, Malaysia, Thailand and several West African countries. Palm oil has a variety of uses in the food, cosmetics and fuel industries, making it one of the most traded commodities in the world. Palm oil price fluctuations have a significant influence on the economy in producing and consuming countries. Therefore, a time series analysis is needed that can predict fluctuations caused by certain conditions. This analysis is carrying out nonlinear analysis using the SETAR (Self Exciting Threshold Autoregressive) method on palm oil prices to obtain a prediction model and prediction results for palm oil prices. The SETAR model is a special case part of the Threshold Autoregressive (TAR) model. The SETAR model threshold is a lag value of the series itself or the endogenous variable. Analysis carried out using the SETAR method produces a SETAR (3,1,1) model with threshold (r) = 0.01626070 where the fit value approaches the actual data value and the predicted value follows the actual data pattern

Modeling streamflow time series using nonlinear SETAR-GARCH models


 A time series model that explain the structural changes associated with data in a certain time period is the Threshold Autoregressive (TAR) model. The basic of the TAR model there are some different usage regimes in autoregressive analysis. One model based on TAR is a self-exciting threshold autoregressive (SETAR) model with the same delay parameters for each regimen. The SETAR model has a linear nature in each regime but being nonlinear if the models of each regime are combined. In addition, this model can improve jump data that cannot be captured by linear time series models. This means that the SETAR model has high-level parameters through an appropriate switching regime that is applied to agricultural export data in Indonesia. The purpose of this reseach is to test the estimated SETAR parameter model and apply it to Indonesian agricultural export data. There are three methods that can be done for estimating of parameter of SETAR model, namely the conditional quadratic sequential method, ordinary least square (OLS) and nonlinear least square (NLS). In this research, the two stage parameter estimation method is used with OLS and the second stage parameter estimation is used to optimisze the parameter values ​​that are not significant in the model. In its application, the SETAR model (2,1,1) was obtained to model agricultural export data in Indonesia and the MAPE value was 25%.

Forecasting tourist arrivals is an essential feature in tourism demand prediction. This paper applies Self Exciting Threshold Autoregressive (SETAR) models. The SETAR takes into account of possible structural changes leading to a better prediction of western tourist arrivals to Thailand. The finding reveals that although the forecasting method such as SARIMA GARCH is the state of art model in econometrics, forecasting tourism demand for some specific destinations without consideration of the potential structural changes means ignoring the long persistence of some shocks to volatility and the conditional mean values leading to less efficient forecast results than SETAR model. The findings show that SETAR model outperforms SARIMA GARCH model. Then this study based on the SETAR model uses the Bayesian analysis of Threshold Autoregressive (BAYSTAR) method to make one step ahead forecasting. This study contributes that SETAR overtakes SARIMA GARCH as it takes into account of the nonlinear features of the data via structural changes resulting in the better forecasting of Western Countries tourism demand for Thailand.

This paper develops a valuation model for options under the class of self-exciting threshold autoregressive (SETAR) models and their variants for the price dynamics of the underlying asset using the self-exciting threshold autoregressive Esscher transform (SETARET). In particular, we focus on the first generation SETAR models first proposed by Tong (1977, 1978) and later developed in Tong (1980, 1983) and Tong and Lim (1980), and the second generation models, including the SETAR-GARCH model proposed in Tong (1990) and the double-threshold autoregressive heteroskedastic time series model (DTARCH) proposed by Li and Li (1996). The class of SETAR-GARCH models has the advantage of modelling the non-linearity of the conditional first moment and the varying conditional second moment of the financial time series. We adopt the SETARET to identify an equivalent martingale measure for option valuation in the incomplete market described by the discrete-time SETAR models. We are able to justify our choice of probability measure by the SETARET by considering the self-exciting threshold dynamic utility maximization. Simulation studies will be conducted to investigate the impacts of the threshold effect in the conditional mean described by the first generation model and that in the conditional variance described by the second generation model on the qualitative behaviors of the option prices as the strike price varies.

The performance of alternative forecasting methods for SETAR models

This paper deals with the problem of joint determination of the delay parameter and autoregressive orders of the Self-Exciting Threshold Autoregressive (SETAR) models. More specifically, we propose a variant of the Predictive Density Criterion (PDC) for the purpose of SETAR model selection. The performance of this variant is evaluated by means of Monte Carlo experiments. Our results indicate that PDC serves as an effective tool for jointly selecting the correct order and delay.

The main objective of this study is to evaluate some alternatives to estimate tourism arrivals under the presence of structural changes in the sample size. Several specification of Self-exciting threshold autoregressive (SETAR) model and Smooth transition autoregressive (STAR) model, especially Logistic STAR (LSTAR) are estimated. Once the parameters are estimated, a one period out of sample forecasting is performed to evaluate the forecasting efficiency of the best specifications. The finding from the study is that the STAR model beats SETAR model slightly, and these two groups of models have forecast proficiency at least in the tourism field.

Hybrid artificial intelligence-time series models for monthly streamflow modeling

Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data.

This paper examines Jensen's [J. Finance, 1968, 23, 389–416] alphas and the time-varying return premia unexplained by standard risk factors in Japan and presents several new findings. First, in contrast to the US experience, positive alphas remain after Fama and French's three factors are applied to excess stock returns in Japan. Second, positive alphas remain in Japan, even if the Fama–French three factors combined with momentum and reversal factors are applied to excess stock returns. Third, the positive return premia unexplained by these five factors bear little relation to the dynamics of the Japanese macroeconomy. Fourth, the time series evolution of the positive return premia indicates autonomous dynamics with at least three regimes. Fifth, we can predict or time the acquisition of the positive return premia for small-size portfolios in Japan by observing the direction and effect of the return premia of large-size portfolios and high-book equity to market equity (BE/ME) portfolios. Finally, application of the self-exciting threshold autoregressive (SETAR) model shows that the size effects are stronger than the BE/ME effects in Japan, given that the return premia from small-size portfolios in the SETAR model are bounded by positive thresholds, while the return premia from high-BE/ME portfolios are bounded by negative thresholds.