Exponential Smooth Transition Autoregressive Model Research Articles

Logistic Smooth Transition Autoregressive (LSTAR) and Exponential Smooth Transition Autoregressive (ESTAR) Methods in Predicting the Exchange Rate of Farmers in Lampung Province, Indonesia

There are many time series forecasting techniques, one of which is Smooth Transition Autoregressive (STAR). STAR is an extension of the autoregressive model for nonlinear time series data. The STAR model consists of the Logistic STAR (LSTAR) model and the Exponential STAR (ESTAR) model. The aim of this research is to compare which model is more suitable for predicting farmer exchange rates in Lampung Province, Indonesia. The results of this research show that the ESTAR model outperforms the LSTAR model based on a smaller AIC.

The Fourier approach and testing for cointegration in LSTAR model

This paper proposes a new logistic smooth transition autoregressive (LSTAR) cointegration test by combining the Fourier function to catch the structural changes that occur over time and the LSTAR model to consider the nonlinearity. Logistic and exponential functions are the main transition functions defining the nonlinearity in STAR models since the exponential smooth transition autoregressive (ESTAR) and LSTAR models can explain the different structures of economic variables. The Fourier approach is a simple and effective way to model the structural changes in time series as an alternative to dummy variables. The most significant advantage of the method is that it does not require prior knowledge about the date, number of breaks, or forms. Monte Carlo simulation results show that the proposed test has good size and power properties for different sample sizes and parameters. The results also revealed that the power performance of the proposed test and the Fourier ESTAR test offered by Güriş and Sedefoğlu (2022) are close to each other. The steps of the Fourier-based tests are illustrated by providing an empirical example of testing the validity of the purchasing power parity (PPP) hypothesis in Türkiye.

A proposal of nonlinear cointegration test with the flexible Fourier approach

In this study, we propose a cointegration test in which structural changes are modeled gradually through the Fourier approach and the nonlinear structure is modeled with an exponential smooth transition autoregressive (ESTAR) model. In the traditional tests, structural changes are mostly modeled by dummy variables. However, the extended literature supposes that the flexible Fourier approach is an alternative approach to dummy variables since there is no need to know the form, date, and number of breaks with the Fourier approach. The lack of a cointegration test to combine the ESTAR model and Fourier approach in the literature constitutes the motivation of this study. Monte Carlo simulation results demonstrate that the size properties are close to the nominal size and the power of the test shows good performance even in the small sample simulation experiment. Results also indicate that the proposed test shows better power performance compared to the ESTAR cointegration test ignoring breaks.

On Evaluating the Volatility of Nigerian Gross Domestic Product Using Smooth Transition Autoregressive-GARCH (STAR - GARCH) Models

STAR-GARCH models are hybrid models that combine the functional form of smooth transition autoregressive models and Generalized autoregressive conditional heteroscedasticity models. The two classes of STAR models considered in this paper are Exponential and Logistic Smooth transition autoregressive models (ESTAR and LSTAR). The functional form of each of this was combined with that of GARCH model and the resulting models becomes ESTAR-GARCH and LSTAR-GARCH models. The derived equations were applied to Nigerian gross domestic product (Real estate) for empirical illustration. Statonarity tests (Unit root test Graphical and correlogrom methods) conducted revealed that the series was stationary at Second difference. The hybrid models equations so derived were used to determine the model that performed better using the information criteria (AIC, SIC and HQIC), variances obtained from the data, performance measure indices (RMSE, MAE, MAPE THEIL U, Bias proportion, variance Bias proportion and covariance Bias proportion) analysis and in - sample forecast accuracy for the models. From all the criteria used it was observed that the duo of LSTAR-GARCH and ESTAR-GARCH models performed far better than classical GARCH model. However, LSTAR-GARCH performs slightly better than ESTAR-GARCH. From these results it is evident that volatility in Nigerian gross domestic product (Real estate) is best captured using Logistic smooth transition GARCH (LSTAR-GARCH) models, it is therefore, recommended for would be forecasters, investors and other end users to make use of LSTAR-GARCH models.

TESTING PURCHASING POWER PARITY IN SOME EMERGING ECONOMIES IN THE LONG-RUN

ABSTRACT In this paper, we examine the long-run purchasing power parity (PPP) by testing for a unit root in real exchange rates between the US and 14 emerging economies from 1st January 1990 to 31st December 2018. The main objective of this paper is to investigate the real exchange rate adjustment for these emerging economies using both standards linear and nonlinear of exponential smooth transition autoregressive (ESTAR) model. Specifically, the objective is to estimate the PPP adjustment toward long-run equilibrium. The research also aims to model long-run validity of PPP hypothesis using bivariate vector error correction models which we can do with our data. The speed of adjustment is better captured that way as it a bivariate approach. The results seem to suggest that both linear and nonlinear unit root tests fail to reject the null hypothesis of the exchange rates for these emerging economies. One key policy implementation is that the validity of using PPP to decide the equilibrium exchange rate for these 8 countries. Moreover, our vector error correction model seems to suggest that most of the countries do not support PPP. Keywords unit root test; real exchange rates; panel data; non-stationary; Johansen cointegration test, vector error correction model

The short- and long-run efficiency of energy, precious metals, and base metals markets: Evidence from the exponential smooth transition autoregressive models

The aim of this paper is to investigate the long and short-run relationship between spot and futures prices of the energy, precious metals, and base metals markets. We analyze daily data from January 1985 to February 2019. The empirical findings based on the cointegration test, which follows a nonlinear process, suggest that the spot prices of energy and metals assets have long-run relationships with their futures prices. Nonparametric Granger causality test results also indicate bi-directional causality among futures and spot prices. These findings indicate that the energy and metals markets are informationally efficient in the sense of Fama (1970).

Testing for cointegration in nonlinear asymmetric smooth transition error correction models

The present paper proposes an alternative procedure to test for cointegration in asymmetric exponential smooth transition autoregressive (AESTAR) model. The proposed new F-statistics test the null hypothesis of no cointegration against the alternative hypothesis of cointegration with asymmetric ESTAR adjustment. We derive the nonstandard limit distributions analytically via Monte Carlo simulations. We also study the finite sample properties and the power of proposed tests with Monte Carlo simulations and find that the empirical sizes of two tests are quite close to the nominal one and the proposed tests do not lead to over-rejections of the null hypothesis of no cointegration.

Do real exchange rates in small Central and Eastern European economies obey purchasing power parity

This study contributes to the purchasing power parity (PPP) literature in two ways. First, in order to circumvent the pitfalls of linear specifications in testing the behaviour of exchange rates, we apply a nonlinear unit root test based on the exponential smooth transition autoregressive model. Second, we test the PPP theory for a class of ten Central Eastern European economies comprising the period from January 2001 to December 2016. The results of unit root tests imply that the null hypothesis of non-stationarity of real exchange rates cannot be rejected for the whole period. Our fragmentary evidence on PPP is reduced to individual subsamples for a small number of Central Eastern European countries. The weak evidence on PPP, found in this study, suggests that the process of real integration of Central and Eastern European economies and the subsequent price convergence among European markets remains incomplete.

Revisiting the Effects of Free Trade Agreement (FTA) on PPP Using the ESTAR Model: Evidence From South Korea

I explore whether the Free Trade Agreement (FTA) has a positive influence on PPP between South Korea and its FTA partners in this study. There are a few studies on the effects of FTA on PPP, but they do not find positive effects of FTA on PPP even though trade barriers, especially, tariffs have decreased or eliminated after FTA. One reason for this may be that the empirical models used in earlier studies were incorrectly specified. In particular, the models are unable to assess whether trade does not occur. By using the Exponential Smooth Transition Autoregressive (ESTAR) model, which separates the case where trade does not occur from the case where trade occurs, I revisit the effects of FTA on PPP between South Korea and its FTA partners in the sample periods over January 1998 to May 2018. It was found that the speed of mean-reversion of price differential is faster after FTA for most ASEAN FTA partners, but the same thing is not observed for other FTA partners. These findings imply that the effects of FTA on PPP are different across FTA partners, which means the effects of FTA on market integration are different across FTA partners.

Simulation Study for Determining the Best Architecture of Multilayer Perceptron for Forecasting Nonlinear Seasonal Time Series

Neural network is one of flexible nonlinear models that could handle various relationship patterns on data with high accuracy. The data-driven approach is one of the advantages of neural network models in solving complex problems in forecasting. The selection of the best model becomes one of the most important problems in the application of neural network for time series forecasting, which consists of determining the input, the number of neurons in the hidden layer, the activation function, and preprocessing method. This paper focuses on the simulation study to explore how to determine the best architecture of multilayer perceptron for forecasting nonlinear seasonal time series. The data that be generated from seasonal exponential smooth transition autoregressive model are used as a case study. The results show that the inputs and the number of neurons in the hidden layer are two main factors that affect significantly the forecast accuracy. In contrary, the activation function and preprocessing method do not significantly influence the forecast accuracy.

Modelling non-linear behaviour of block price deviations when trades are executed outside the bid-ask quotes

PurposeThe purpose of this paper is to test and model non-linearities in block price deviations when they are executed outside the bid-ask quotes. The author conducts an empirical analysis on 662,312 transactions that were traded outside the bid-ask quotes in 2014 on the London Stock Exchange.Design/methodology/approachThe tests reject the linearity hypothesis and the paper shows that the exponential smooth transition autoregressive model is capable of capturing the non-linear behaviour of block price misalignments.FindingsThe findings imply that when the deviation of block prices from their quoted value is small (large), trading will occur slowly (rapidly) to restore equilibrium, suggesting that trading costs eliminate continuous trading and that the block trade market is efficient.Originality/valueThe purpose of this paper is to re-model block price deviations from the bid-ask quotes. The major contribution is that the paper presents new empirical evidence, which explicitly allows for the possibility that block price misalignments from the bid-ask quotes can be characterized by a non-linear mean reverting process. The author demonstrates that the presence of transaction costs induces non-linear adjustments of block trade prices.

Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models

Exponential smooth transition autoregressive (ESTAR) models are widely used in the international finance literature, particularly for the modelling of real exchange rates. We show that the exponential function is ill-suited as a regime weighting function because of two undesirable properties. Firstly, it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter , which governs the shape of the function, is ‘small’. This leads to an identification problem with respect to the transition function parameter and the slope vector, as both enter as a product into the conditional mean of the model. Secondly, the exponential regime weighting function can behave like an indicator function (or dummy variable) for very large values of the transition function parameter . This has the effect of ‘spuriously overfitting’ a small number of observations around the location parameter µ. We show that both of these effects lead to estimation problems in ESTAR models. We illustrate this by means of an empirical replication of a widely cited study, as well as a simulation exercise.

Unit Root Testing and Estimation in Nonlinear ESTAR Models with Normal and Non-Normal Errors.

Exponential Smooth Transition Autoregressive (ESTAR) models can capture non-linear adjustment of the deviations from equilibrium conditions which may explain the economic behavior of many variables that appear non stationary from a linear viewpoint. Many researchers employ the Kapetanios test which has a unit root as the null and a stationary nonlinear model as the alternative. However this test statistics is based on the assumption of normally distributed errors in the DGP. Cook has analyzed the size of the nonlinear unit root of this test in the presence of heavy-tailed innovation process and obtained the critical values for both finite variance and infinite variance cases. However the test statistics of Cook are oversized. It has been found by researchers that using conventional tests is dangerous though the best performance among these is a HCCME. The over sizing for LM tests can be reduced by employing fixed design wild bootstrap remedies which provide a valuable alternative to the conventional tests. In this paper the size of the Kapetanios test statistic employing hetroscedastic consistent covariance matrices has been derived and the results are reported for various sample sizes in which size distortion is reduced. The properties for estimates of ESTAR models have been investigated when errors are assumed non-normal. We compare the results obtained through the fitting of nonlinear least square with that of the quantile regression fitting in the presence of outliers and the error distribution was considered to be from t-distribution for various sample sizes.

Nonlinear dynamic of the renewable energy cycle transition in Tunisia: Evidence from smooth transition autoregressive models

In this paper, we focus on the problem of the energy transition in Tunisia were we suggest to study and modeling the nonlinear dynamic of the endogenous renewable energy cycle.As today the socioeconomic development in Tunisia is too complicated and dependent on the adopted energetic strategy. Our contribution consists on recognizing exactly the main bases of this correlative development.In this context, we try to provide some theoretical and empirical studies for renewable energy politics especially under the chaotic transition in the post revolution period in Tunisia.All this work will be based on the application of the univariate STAR (smooth transition autoregressive) method composed by two transition process types the logistic STAR model (LSTAR) and the exponential STAR model (ESTAR). As results we found that the LSTAR process is more adequate for asymmetric data for our case. In this regard, our results indicated that the renewable energy can not only work as a possible factor for energetic strategy transition in Tunisia, but also, is a promising candidate for stability and socioeconomic development.

Analysis of cyclical fish landings through ESTAR nonlinear time-series approach

Exponential smooth transition autoregressive (ESTAR) is a family of parametric nonlinear time-series models capable of capturing the non-Gaussian characteristics of the time-series along with cyclical fluctuations. The present study is based on the time-series data on oilsardine landings from Kerala during the period 1961 to 2008. The parameters of the model were estimated by genetic algorithm (GA). From the analysis of data it was concluded that ESTAR model fitted through GA has performed better than ARIMA model.

Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models

Exponential smooth transition autoregressive (ESTAR) models have been widely used in the empirical international finance literature. We show that the exponential function used in ESTAR models is ill-suited as a regime weighting function because of two undesirable properties. The first is that it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter γ, which governs the shape of the function, is ‘small’. This leads to identification issues with respect to the transition function parameter and the slope vector in ESTAR models. The second is that the exponential function becomes an indicator function over the entire range of the threshold variable, except at the point where the threshold variable is equal to the location parameter µ. This results in a high propensity to spuriously overfit a small number of observations around µ, leading to an ‘outlier fitting effect’ of the exponential function. We show the effect of both of these problems on estimation of ESTAR models by means of an empirical replication of the well known study by Taylor et al. (2001), and an extensive simulation exercise, where we vary the magnitude of the threshold parameter as well as the sample size.

Asymmetric Behaviour of Inflation around the Target in Inflation‐Targeting Countries

AbstractWe explore the asymmetric behaviour of inflation around the target level for inflation‐targeting countries. The first rationale behind this asymmetry is the asymmetric policy response of the central bank around the target. Central banks could have a stronger bias towards overshooting rather than undershooting the inflation target. Consequently, the policy response would be stronger once the inflation jumps above the target, compared to a negative deviation. Second rationale is the asymmetric inflation persistence. We suggest that recently developed Asymmetric Exponential Smooth Transition Autoregressive (AESTAR) model provides a convenient framework to capture the asymmetric behaviour of inflation driven by these two effects. We further conduct an out‐of‐sample forecasting exercise and show that the predictive power of AESTAR model for inflation is high for some countries in our sample, especially at long‐horizons.

Wild bootstrap testing for cointegration in an ESTAR error correction model

This paper proposes a bootstrap cointegration test in an exponential smooth transition autoregressive (ESTAR) error correction model (ECM). We introduce the t-type test that has a null hypothesis of no cointegration and an alternative hypothesis of the ESTAR-ECM and develop the test using a wild bootstrap. Monte Carlo simulation results show that the t-type test and conventional tests considerably overreject the null hypothesis of no cointegration in the presence of multivariate GARCH errors and multivariate stochastic volatility, whereas the proposed wild bootstrap test has correct empirical sizes, in contrast to other tests, and reasonable powers under cointegration with the ESTAR-ECM.

Wild bootstrap tests for unit root in ESTAR models

This paper introduces wild bootstrap tests for unit root in exponential smooth transition autoregressive (ESTAR) models. Asymptotic unit root tests in ESTAR models have severe size distortions in the presence of heteroskedastic variances such as generalized autoregressive conditional heteroskedasticity and stochastic volatility, and hence, to improve these distortions, we use a wild bootstrap. Monte Carlo simulations show that in asymptotic tests, severe over-rejection of the null hypothesis occurs under heteroskedastic variances, whereas the proposed wild bootstrap tests have reasonable size and power properties.

Nonlinear Exchange Rate Adjustment and the Monetary Model

AbstractAlthough the empirical literature has delivered evidence in favor of nonlinearities in nominal and real exchange rate adjustment, the corresponding mechanisms with respect to the relationship between nominal exchange rates and fundamentals in general have rarely been put under any close scrutiny. This paper extends the work of other authors, who estimate exponential smooth transition autoregressive models to deviations of the exchange rate from monetary fundamentals. Using monthly data from 1976:01 to 2010:12 for theUSA,UK, andJapan, this paper first adopts a cointegrated vector autoregression (VAR) framework to test for the multivariate validity of the monetary model by applying restrictions on the long‐run relationships. Then, nonlinear vector error correction models are estimated to tackle the question of whether the adjustment of the nominal exchange rate with respect to those relationships follows a nonlinear path.