Self-exciting Threshold Autoregressive Research Articles

Asymmetry in the prices of crude oil and diesel and gasoline prices in Brazil

PurposeThe aim of this study was to determine if there are asymmetries in the pass-through of West Texas Intermediate (WTI) crude oil prices to its derivatives (diesel and gasoline) in the Brazilian market.Design/methodology/approachInitially, the future WTI oil price series was analyzed using the self-exciting threshold autoregressive (SETAR) and logistic smooth transition autoregressive (LSTAR) non-linear models. Subsequently, the threshold autoregressive error-correction model (TAR-ECM) and Markov-switching model were used.FindingsThe findings indicated high prices throughout 2008 due to the subprime crisis. The findings indicated high prices throughout 2008 due to the subprime crisis. The results indicated that there is long-term pass-through of oil prices in both methods, suggesting an equilibrium adjustment in the prices of diesel and gasoline in the analyzed period. Regarding the short term, the variations in contemporary crude oil prices have positive effects on the variations in fuel prices. Lastly, this behavior can partly be explained by the internal price management structure adopted during almost all of the analyzed period.Originality/valueThis paper contributes to the literature at some points. The first contribution is the modeling of the oil price series through non-linear models, further enriching the literature on the recent behavior of this time series. The second is the simultaneous use of the TAR-ECM and Markov-switching model to capture possible short- and long-term asymmetries in the pass-through of prices, as few studies have applied these methods to the future price of oil. The third and main contribution is the investigation of whether there are asymmetries in the transfer of oil prices to the price of derivatives in Brazil. So far, no work has investigated this issue, which is very relevant to the country.

The “real” exchange rate regime in China since 2015′s exchange rate reform

Moving away from a fixed exchange rate in 2005, China has gradually enlarged the band of fluctuations of Renminbi (RMB) and implemented various reforms on its central parity to have a more flexible exchange rate regime. This paper studies the nature of the exchange rate regime in China since the exchange regime reform of August 2015. Relying on the self-exciting threshold autoregressive (SETAR) model, it identifies endogenously the band of inaction beyond which the People's bank of China (China's central bank) starts to intervene in the foreign exchange market to restrict further fluctuations. Based on the comparison of the estimated threshold with the official band, this paper shows that the RMB/USD exchange rate followed an intermediate regime similar to the crawling band but with only one single threshold of intervention which is much lower than the upper boundary of the announced band.

Self-exciting Threshold Autoregressive Model with Application to Crude Oil Production in Nigeria

In the last two years the price of oil and its fluctuations have reached levels never recorded in the history of international oil markets. The determinants of past, current, and future levels of the price of oil and its fluctuations have been the subject of analysis by academics and energy experts, given the relevance of crude oil in the worldwide economy. The paper, therefore, model and forecast crude oil production (2002-2022) sourced from Central Bank of Nigeria website. The successive least squares estimation and model diagnostics are applied. The results affirmed that the self-exciting threshold autoregressive (SETAR(2,2,1)) model outperformed autoregressive integrated moving average (ARIMA(3,1,3)) model for crude oil production fluctuations based on our diagnostics (AIC, SC, SSR and log-likelihood ratio). The results obtained will greatly assist the government and policy makers in planning for economic development since the long-run success of any country is closely related to how well management is able to foresee the future and develop appropriate strategies.

GTAR: a new ensemble evolutionary autoregressive approach to model dissolved organic carbon

AbstractThis article explores the forecasting capabilities of three classic linear and nonlinear autoregressive modeling techniques and proposes a new ensemble evolutionary time series approach to model and forecast daily dynamics in stream dissolved organic carbon (DOC). The model used data from the Oulankajoki River basin, a boreal catchment in Northern Finland. The models that were evolved used both accuracy and parsimony measures including autoregressive (AR), vector autoregressive (VAR), and self-exciting threshold autoregressive (SETAR). The new method, called genetic-based SETAR (GTAR), evolved through the integration of state-of-the-art genetic programming with SETAR. To develop the models, high-resolution DOC concentration and daily streamflow (as the external input for VAR) were measured at the same gauging station throughout the ice free season. The results showed that all the models characterize the DOC dynamics with an acceptable 1-day-ahead forecasting accuracy. Use of the streamflow time series as an exogenous variable did not increase the predictive accuracy of AR models. Moreover, the hybrid GTAR provided the best accuracy for the holdout testing data and proved to be a suitable approach for predicting DOC in boreal conditions.

An Analysis of the Pass-Through of Exchange Rates in Forest Product Markets

This paper assesses the exchange rate pass-through (ERPT) for forest product prices (i.e., sawnwood, logs) by applying a two-regime Self-Exciting Threshold Autoregressive (SETAR) model. We incorporate autoregressive second-order dynamics in the regime equations. This leads to better forecasts, as integrating more lags helps capture the cumulative effects of the price dynamics. We examine sawnwood and log products traded in the United States, Malaysia (Southeast Asia) and Cameroon (West Africa). Our results illustrate the importance of applying the two-regime SETAR-type models to analyze the non-linear exchange rate pass-through for forest product markets. The impulse response analysis of each price pair supports the changing behavior of price ratios in various regimes. This may be regarded as another justification to apply models accounting for structural changes to investigate the exchange rate pass-through in a non-linear fashion. The aftershock adjustment process is similar, but the amplitude of the impact differs among markets. The results reveal potential arbitrage opportunities in the forestry industry.

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

This paper focuses on estimating the Self-Exciting Threshold Autoregressive (SETAR) type time-series model under right-censored data. As is known, the SETAR model is used when the underlying function of the relation-ship between the time-series itself (Yt), and its p delays $$({Y_{t - j}})_{j = 1}^p$$ violates the lin-earity assumption and this function is formed by multiple behaviors that called regime. This paper addresses the right-censored dependent time-series problem which has a serious negative effect on the estimation performance. Right-censored time series cause biased coefficient estimates and unqualified predictions. The main contribution of this paper is solving the censorship problem for the SETAR by three different techniques that are kNN imputation which represents the imputation techniques, Kaplan-Meier weights that is applied based on the weighted least squares, synthetic data transformation which adds the effect of censorship to the modeling process by manipulating dataset. Then, these solutions are combined by the SETAR-type model estimation process. To observe the behavior of the nonlinear estimators in practice, a simulation study and a real data example are carried out. The Covid-19 dataset collected in China is used as real data. Results prove that although the three estimators show satisfying performance, the quality of the estimate SETAR model based on the kNN imputation technique dominates the other two estimators.

Does Economic Growth Have a Nonlinear Relationship with Unemployment in Türkiye? Evidence From Self-Exciting Threshold Autoregressive Model

Economic growth and employment have long been a source of concern for economists and policymakers. Okun, an American economist, was the first to examine the relationship between economic growth and unemployment. Okun’s law states that a 3% increase in output results in a 1% drop in unemployment. The main objective of this paper is to examine this hypothesis for Turkish economy by using quarterly data from 2001 to 2023. The relationship between the unemployment and economic growth has been analyzed by employing Granger causality test and self-exciting threshold autoregressive (SETAR) model. According to SETAR findings, there exists a threshold value binding in describing the relationship between unemployment and economic growth. As a result, Okun's Law is applicable to Türkiye.

Information quantity evaluation of nonlinear time series processes and applications

Among several models proposed in the time series literature, the Self-Exciting Threshold Autoregressive (SETAR) model is non-linear and considers threshold values to model time series affected by regimes. Beyond the linear models, the computation of information and dependence metrics in non-linear time series is of great interest to compare processes and test non-linearity. This paper considers the stationary marginal density of a SETAR(2;1,1) process to compute explicit differential entropy and Kullback–Leibler and Jeffrey’s divergences. In addition, an asymptotic homogeneity test for statistical significance of the disparity between two SETAR(2;1,1) processes was built. Numerical illustrations and applications to fish condition factor and Chilean economic perception time series are presented to illustrate the proposed methodology. Besides, a numerical algorithm based on Riemann–Stieltjes integral definition is implemented to calculate information measures based on stationary cumulative density functions of other types of nonlinear stationary stochastic processes, such as the first-order double autoregressive bilinear threshold moving average and threshold autoregressive moving average processes.

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.

Estimation of Wind Speed Data with Setar Model

The threshold model allows expression with different Autoregressive Moving Average (ARMA) models sorted according to the threshold value of the observations. In this study, nineteen years of observed wind speed data have been modeled with the Self Exciting Threshold Autoregressive (SETAR) model. Two different Autoregressive (AR(3)) models have been obtained for the situation where the wind speed was below and above 2.5 m / s of the previous observation in the time series. In addition, in the SETAR (1,3,3) model, it has been determined that the residual terms have the effect of GARCH (1,1) and a range has been estimated for model predictions.

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.

How is price explosivity triggered in the cryptocurrency markets?

We shed light on how the price explosivity characterising Bitcoin and other major cryptocurrencies is triggered, by employing the Quantile Self-Exciting Threshold Autoregressive (QSETAR) model. Our results for Bitcoin, Ripple, and Stellar reveal that the explosive behaviour originates from the extreme upper tails of the return distributions following a price increase in the preceding day. We do not find evidence of explositivity in the price of Litecoin.

Income thresholds in the remittances-growth association? a case study of Fiji

ABSTRACT Research indicates that remittances have mixed effects on growth. In this study, we investigate the role of income thresholds in this association for Fiji. Income thresholds are measured by thresholds in per-worker real GDP and are identified using the self-exciting threshold autoregression model over the period 1980 to 2017. A threshold autoregressive distributed lag model is subsequently developed. A single threshold in per-worker real GDP is estimated at US$5891. Remittances promote growth if income exceeds the threshold but is negative otherwise. Hence, remittances support growth-enhancing activities at high-income levels but may finance imports at the expense of domestic production at lower income levels.

Comparative Analysis of Different Univariate Forecasting Methods in Modelling and Predicting the Romanian Unemployment Rate for the Period 2021-2022.

Unemployment has risen as the economy has shrunk. The coronavirus crisis has affected many sectors in Romania, some companies diminishing or even ceasing their activity. Making forecasts of the unemployment rate has a fundamental impact and importance on future social policy strategies. The aim of the paper is to comparatively analyze the forecast performances of different univariate time series methods with the purpose of providing future predictions of unemployment rate. In order to do that, several forecasting models (seasonal model autoregressive integrated moving average (SARIMA), self-exciting threshold autoregressive (SETAR), Holt–Winters, ETS (error, trend, seasonal), and NNAR (neural network autoregression)) have been applied, and their forecast performances have been evaluated on both the in-sample data covering the period January 2000–December 2017 used for the model identification and estimation and the out-of-sample data covering the last three years, 2018–2020. The forecast of unemployment rate relies on the next two years, 2021–2022. Based on the in-sample forecast assessment of different methods, the forecast measures root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE) suggested that the multiplicative Holt–Winters model outperforms the other models. For the out-of-sample forecasting performance of models, RMSE and MAE values revealed that the NNAR model has better forecasting performance, while according to MAPE, the SARIMA model registers higher forecast accuracy. The empirical results of the Diebold–Mariano test at one forecast horizon for out-of-sample methods revealed differences in the forecasting performance between SARIMA and NNAR, of which the best model of modeling and forecasting unemployment rate was considered to be the NNAR model.

IDENTIFIKASI MODEL SELF-EXCITING THRESHOLD AUTOREGRESSIVE DENGAN SWITCHING TWO REGIME (KASUS PADA DATA EKSPOR AGRIKULTUR DI INDONESIA)


 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%.

Bitcoin option pricing with a SETAR-GARCH model

This paper aims to study the pricing of Bitcoin options with a view to incorporating both conditional heteroscedasticity and regime switching in Bitcoin returns. Specifically, a nonlinear time series model combining both the self-exciting threshold autoregressive (SETAR) model and the generalized autoregressive conditional heteroscedastic (GARCH) model is adopted for modeling Bitcoin return dynamics. Specifically, the SETAR model is used to model regime switching and the Heston-Nandi GARCH model is adopted to model conditional heteroscedasticity. Both the conditional Esscher transform and the variance-dependent pricing kernel are used to specify pricing kernels. Numerical studies on the Bitcoin option prices using real bitcoins data are presented.

Frequent or systematic changes? discussion on “Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection.”

We discuss Fryzlewicz’s paper that proposes WBS2.SDLL approach to detect possibly frequent changes in mean of a series. Our focus is on the potential issues related to the model misspecification. We present some numerical examples such as the self-exciting threshold autoregression and the unit root process, that can be confused as a frequent change-points model.

Time series analysis of temporal trends in hemorrhagic fever with renal syndrome morbidity rate in China from 2005 to 2019

Hemorrhagic fever with renal syndrome (HFRS) is seriously endemic in China with 70%~90% of the notified cases worldwide and showing an epidemic tendency of upturn in recent years. Early detection for its future epidemic trends plays a pivotal role in combating this threat. In this scenario, our study investigates the suitability for application in analyzing and forecasting the epidemic tendencies based on the monthly HFRS morbidity data from 2005 through 2019 using the nonlinear model-based self-exciting threshold autoregressive (SETAR) and logistic smooth transition autoregressive (LSTAR) methods. The experimental results manifested that the SETAR and LSTAR approaches presented smaller values among the performance measures in both two forecasting subsamples, when compared with the most extensively used seasonal autoregressive integrated moving average (SARIMA) method, and the former slightly outperformed the latter. Descriptive statistics showed an epidemic tendency of downturn with average annual percent change (AAPC) of −5.640% in overall HFRS, however, an upward trend with an AAPC = 1.213% was observed since 2016 and according to the forecasts using the SETAR, it would seemingly experience an outbreak of HFRS in China in December 2019. Remarkably, there were dual-peak patterns in HFRS incidence with a strong one occurring in November until January of the following year, additionally, a weak one in May and June annually. Therefore, the SETAR and LSTAR approaches may be a potential useful tool in analyzing the temporal behaviors of HFRS in China.

Forecasting performance of nonlinear time-series models: an application to weather variable

Modelling the dynamic dependent data by the linear approach is the most popular among the researchers because of its simplicity in calculation and approximation, however, in real-world phenomena, most of the time-dependent data follow the nonlinearity. Moreover, most of the nonlinear modelling of time-dependent data have found in the financial applications. Besides this sector, the authors of this paper found the presence of nonlinearity in meteorological data with the help of four popular nonlinearity tests. Furthermore, there is a scarcity of the application of regime-switching threshold autoregressive nonlinear time-series model in forecasting the weather variables like temperature. Thus, this paper aims to compare the forecasting accuracy of the linear autoregressive (linear AR), self-exciting threshold autoregression (SETAR), logistic smooth transition autoregressive model (LSTAR), and feed-forward neural network (ANNs) and fitted with the determination of regime and hyperparameters. After fitting the models, twenty steps ahead forecast considered for the comparison along with the selected model selection criteria; and results depict that the LSTAR models are selected as the most appropriate fitted models for forecasting the daily Average, Maximum and Minimum temperature. Finally, it has observed that the average, as well as maximum temperature of Dhaka, Bangladesh, have an increasing trend and minimum temperature having a decreasing trend.

On temporal aggregation of some nonlinear time-series models

Recently, economic globalisation and advances in computer technologies have accelerated the development of ‘big data’ analysis. Time-series data are routinely collected from the Internet and machine transactions at mixed frequencies. The problem of temporal aggregation arises when time-series data are observed at a lower frequency than the data generation frequency of the underlying basic model. The resulting aggregated series, which contains less information, may lead to an erroneous view of the true model and flawed decisions. Therefore, it is important to study the effects of temporal aggregation to avoid making possibly improper decisions based on distorted information from the aggregated data. Temporal aggregation of linear time-series processes has been widely studied. The effects of temporal aggregation on the first two moments of some nonlinear time-series models are assessed. More specifically, four types of nonlinear time-series models are studied: the Markov switching autoregressive (MSAR) model, the bilinear (BL) model, the mixture autoregressive (MAR) model, and the self-exciting threshold autoregressive (SETAR) model.