Self-exciting Threshold Autoregressive Model 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.

Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model

Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model

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.

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.

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.

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.

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.

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.

Does Inflation Targeting Policy Matter for Inflation Performance?

Purpose – Inflation targeting (IT) is a practice that central banks around the world began to adopt as early as 1990. Due to the high accountability and high transparency of central banks under IT policy, the practice expected that inflation targets would have better inflation performance. In this study, it is explored whether inflation targeting policy has positive effects on inflation performance, focusing on inflation persistence. Also, it is explored whether the behavior of inflation rates overshooting or undershooting a target range (or a tolerance band around a target level) is asymmetric. Design/Methodology/Approach – An autoregressive (AR) model is adapted with a self-exciting threshold autoregressive (TAR) model to study inflation persistence before and after inflation targeting was adopted, respectively. To address issues that events unrelated to inflation targeting policy could explain the findings, counterfactual exercises for non- inflation target are conducted. Findings – It was found that inflation target, particularly developed inflation target, have experienced a decrease in inflation persistence after implanting inflation targeting. Also, there is limited evidence on the asymmetrical behavior of inflation rates between overshooting and undershooting an inflation target range, or tolerance band, around a target level. Research Implications – The findings in this study support the positive effect of IT policy on inflation performance. In particular, it is stronger for developed inflation target than less developed inflation target. In addition, the findings support that most central banks do not show asymmetrical responses to inflation rates between overshooting and undershooting a target range or tolerance band around a target level.

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.

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.

On MCMC sampling in self-exciting integer-valued threshold time series models

Markov Chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches in statistics. However, due to the complex structure of the models, this method remains an open problem for threshold integer-valued time series models. This study develops Bayesian inference for a class of self-exciting integer-valued threshold autoregressive models, which is implemented by means of a new MCMC algorithm. By introducing the latent variables series, a complete data likelihood is obtained. Based on which, the full conditional distributions are easily obtained with familiar forms. Furthermore, by maximizing the complete data likelihood, the threshold parameter is also accurately estimated. Finally, the performance of the MCMC algorithm is evaluated via some simulations and a real data example.

Empirical likelihood for special self-exciting threshold autoregressive models with heavy-tailed errors

In this paper, we study the empirical likelihood method for special self-exciting threshold autoregressive models. We assume that the parameters of models depend on some positive integer n, the threshold effect diminishes to zero as n increases, and the errors have heavy-tailed distributions. After replacing the indicator function in the model with a smooth function, we obtain a self-weighted and smoothed least absolute deviation estimator for the threshold parameter and the asymptotic normality of the estimator is proved. Then, the confidence intervals for the threshold parameter can be constructed by the normal approximation method. In order to improve the coverage of confidence intervals, we further propose a profile empirical likelihood ratio, and prove that this statistic has the asymptotically standard chi-squared distribution. Therefore, the confidence interval of the threshold parameter can also be constructed by the empirical likelihood method. Simulations and empirical results demonstrate that the confidence interval constructed by empirical likelihood method is superior to that constructed by normal approximation method.

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.

Subgeometric ergodicity and β-mixing

AbstractIt is well known that stationary geometrically ergodic Markov chains are $\beta$ -mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies $\beta$ -mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies $\beta$ -mixing with subgeometrically decaying mixing coefficients. Although this result is simple, it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity cannot be established. To illustrate our results we derive new subgeometric ergodicity and $\beta$ -mixing results for the self-exciting threshold autoregressive model.

IN- AND OUT-OF-SAMPLE PERFORMANCE OF NONLINEAR MODELS IN INTERNATIONAL PRICE DIFFERENTIAL FORECASTING IN A COMMODITY COUNTRY FRAMEWORK

This paper presents an analysis of a group of small commodity-exporting countries' price differentials relative to the US dollar. Using unrestricted self-exciting threshold autoregressive models (SETAR), we evaluate the sixteen national Consumer Price Indexes (CPI) differentials relative to the US dollar CPI. Out-of-sample forecast accuracy is estimated through calculation of mean absolute errors measures based on the monthly rolling window and recursive forecasts, and this estimation is extended to three additional models, namely a logistic smooth transition regression (LSTAR), an additive nonlinear autoregressive model (AAR), and a simple neural network model (NNET). Our preliminary results confirm the presence of some form of nonlinearity in most of the analyzed countries. The parsimonious AR(1) model does not appear to perform any worse than any nonlinear model in the rolling sample exercise. However, in terms of a longrun equilibrium driven by purchasing power parity, its validity is undermined by the results of the recursive estimates and the outcome of the Diebold-Mariano type tests, which favor generally the Heckscher commodity points theory. As a policy advice to commodity-exporting countries, we find no apparent reason to suggest commodity export price pegging as a generalized foreign exchange policy.

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%.