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.

Interactional Impact of Defence Expenditure and Political Instability on Economic Growth in Nigeria: Revisited

ABSTRACT Over the last decade empirical research has increasingly recognized the significance of understanding how defence spending and political stability jointly influence economic growth in developing nations. This paper revisits the complex interplay between defence expenditure, political instability, and economic growth in the context of Nigeria, and for the period 1960-2021. Leveraging the robust Smooth Transition Autoregressive (STAR) model proposed by Granger and Terasvirta, this study aims to provide a comprehensive analysis of the dynamic relationships among these critical factors. Our investigation employs the STAR model to capture potential nonlinearities and regime shifts in these interactions (confirmed by the diagnostic tests), shedding light on how political instability may impact the effectiveness of defence spending on economic growth. The findings further reveal how military spending can influence political stability and governance, particularly in contexts where military resources wield significant power and influence. They also show that low military spending negatively impacts economic growth due to inadequate resources for security and stability maintenance. These findings hold vital implications for policymakers striving to enhance economic development amidst the backdrop of geopolitical uncertainty and security challenges.

Beyond the basics: mapping the inflation response to fiscal deficit in India with smooth transition autoregressive model

PurposeIndia’s historical fiscal performance has featured elevated deficit levels. Driven by the imperative need for fiscal stimulus measures in response to the crisis, efforts toward fiscal consolidation from 2003 to 2008 were reversed in 2008–2009 due to the financial crisis. These stimulus actions are believed to have wielded a notable influence on inflation dynamics. Presumably, a high inflation rate hinders growth and inflicts severe welfare costs. Accordingly, the principal objective of this paper is to scrutinise the threshold effects of fiscal deficit on inflation within the context of the Indian economy.Design/methodology/approachWe employed the Smooth Transition Autoregressive (STAR) Model, a robust tool for capturing non-linear relationships, to discern the specific threshold level of fiscal deficit. Our analysis encompasses annual data spanning from 1971 to 2020. Additionally, we have leveraged the Toda-Yamamoto causality test to establish the existence and direction of a causal connection between fiscal deficit and inflation in the Indian economy.FindingsOur analysis pinpointed a critical threshold level of 3.40% for fiscal deficit, a value beyond which inflation dynamics in India undergo a marked transition, signifying the presence of significant non-linear effects. Moreover, the results derived from the Toda-Yamamoto causality test offer substantiating evidence of a causal relationship originating from the fiscal deficit and leading to inflation within the Indian economic framework.Research limitations/implicationsThe findings of our study carry significant implications, particularly for the formulation and execution of both fiscal and monetary policies. Understanding the threshold effects of fiscal deficit on inflation in India provides policymakers with valuable insights into achieving a harmonious balance between these two critical economic variables.Originality/valueTo the best of our knowledge, this study is the first of its kind to empirically investigate threshold effects of fiscal deficit on inflation in India from a non-linear perspective using the Smooth Transition Autoregression (STAR) model.

Development of Digital Financial Inclusion in China's Regional Economy: Evidence from Panel Threshold Models

This study aims to investigate the effect of digital financial inclusion and air pollution on economic growth for 31 Chinese provinces between 2003 and 2022 using Panel Threshold Auto-Regressive (PTAR) and Panel Smooth Transition Auto-Regression (PSTAR) models. The results show that there is a nonlinear link between digital financial inclusion and economic growth in China. For PTAR, the LnDFII thresholds are 4.264 (i.e., DFII = 71.094), and for PSTAR are 4.563 (i.e., DFII = 95.871). Below these thresholds, digital financial inclusion significantly boosts economic growth by 0.061 and 0.063 in the PTAR and PSTAR models, respectively. However, above these thresholds, the positive impact diminishes, with coefficients dropping to 0.015 and 0.004 in the PTAR and PSTAR models, respectively. Additionally, both models indicate that digital financial inclusion positively affects reducing air pollution, thereby potentially fostering economic growth. Hence, authorities should strategically implement digital technologies and strengthen collaborative efforts at the regional level to maximize these benefits.

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.

Assessing the nonlinear impact of economic growth and renewable energy consumption on CO2 emissions in India: recent evidence from smooth transition autoregression model

Purpose The purpose of this study is to investigate the nonlinear effects of renewable energy (RE) consumption and economic growth on per capita CO2 emissions during the time span from 1980 to 2020. Design/methodology/approach The study uses the logistic smooth transition autoregression (STAR) model to decipher the nonlinear relationship between RE consumption, economic growth and CO2 emissions in the Indian economy. Findings The estimated results confirm a nonlinear relationship between India’s economic growth, RE consumption and CO2 emissions. The authors found that economic growth positively impacts CO2 emissions until it reaches a specific threshold of 1.81 (per capita growth). Beyond this point, further economic growth leads to a reduction in CO2 emissions. Similarly, RE consumption positively affects CO2 emissions until economic growth reaches the same threshold level, after which an increase in RE consumption negatively impacts CO2 emissions. Research limitations/implications The study suggests that India should optimize the balance between economic growth and RE consumption to mitigate CO2 emissions. Policymakers should prioritize the adoption of RE during the early stages of economic growth. As economic growth reaches the specific threshold of 1.81 per capita, the economy should shift to more sustainable and energy-efficient practices to limit the effect of further CO2 emissions on further economic growth. Originality/value To the best of the authors’ knowledge, this study represents the first-ever endeavor to reexamine the nonlinear relationship between RE consumption, economic growth and CO2 emissions in India, using the STAR model.

On the Impacts of Government Size on Economic Growth in India: Some Evidence from Smooth Transition Autoregression Model

This article examines the threshold effects of government size (measured as a percentage share of government final consumption expenditure in GDP) on economic growth from a non-linear perspective. We apply a smooth transition autoregression (STAR) model to estimate the threshold level of government size and its impact on economic growth in India for the period spanning from 1971 to 2019. The empirical results reveal that the relationship between government size and economic growth is non-linear. The study finds a statistically significant positive relationship between the size of the government and economic growth below the estimated threshold level of government size of 10.45 per cent. Above the 10.45 per cent threshold level, government size has a deleterious impact on economic growth. The results also reveal that the transition from one extreme economic phase to another is gradual. The findings of our study recommend that policymakers can enhance India’s economic growth by restricting government size to the estimated threshold level or by reducing the size of the government when it lies well above the threshold level. JEL Codes: JEL H00, JEL E6, JEL E62

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.

Forecast accuracy of the linear and nonlinear autoregressive models in macroeconomic modeling

AbstractMost nonlinear vector autoregressive methods in the econometric literature are based on specific functional forms, such as the smooth transition autoregressive model. This study proposes a general form of the nonlinear vector autoregressive model based on global approximators, such as neural networks, Volterra, and Weiner series. The simulation results of 20 linear and nonlinear multivariate time series processes indicate that nonlinear vector autoregressive methods, especially multi‐output neural networks, are more accurate based on the root mean square error and model confidence set criteria. Applying the global approximator approach to a small‐scale macroeconometric model reveals that the new approach can improve forecast accuracy compared to linear and other nonlinear vector error correction models. In addition, forecasting the relevant variables in a typical exchange rate and monetary policy models based on nonlinear specifications gives more successful results than in the linear case.

Dynamic effect of economic growth on the persistence of suicide rates

Positive and negative economic growth is closely related to the suicide rate. To answer the question whether economic development has a dynamic impact on this rate, we used a panel smooth transition autoregressive model to evaluate the threshold effect of economic growth rate on the persistence of suicide. The research period was from 1994 to 2020, and the results show that the suicide rate had a persistent effect, which varied over time depending on the transition variable within different threshold intervals. However, the persistent effect was manifested in different degrees with the change in the economic growth rate and as the lag period of the suicide rate increased, the effect of the influence gradually decreased. We investigated different lag periods and noted that the impact on the suicide rate was the strongest in the first year after an economic change and then reduced to be only marginal after three years. This means that the growth momentum of the suicide rate within the first two years after a change in the economic growth rate, should be included in policy considerations of how to prevent suicides.

비선형모형을 이용한 아파트매매가격 불확실성이 아파트전세가격에 미치는 영향 분석

The purpose of this study is to examine the nonlinear relationship between apartment jeonse price index and volatilities of apartment housing prices in Korea. We adopt a logistic smooth transition autoregressive(LSTAR) model and use apartment housing price volatility as a transition variable. To do this, we utilize the apartment jeonse price index and apartment housing price index, while the sample period ranges from May 1995 to March 2022. In this paper, the EGARCH model is used to estimate apartment housing prices volatility due to the asymmetry of volatility. We find from the estimation results of nonlinearity that nonlinear models are more appropriate than linear models to capture the dynamic properties of apartment jeonse price index. In addition, the empirical result of the nonlinear LSTAR model shows that the apartment jeonse prices increase in a situation where apartment housing price uncertainty is high. In addition, when we examine the effect of the changes in interest rate on the jeonse prices, we found that the effect of interest rate is statistically insignificant in the LSTAR model, while the changes in interest rate affects the jeonse prices negatively in the linear model. Overall, our result suggests that for the stability of the apartment jeonse prices, it is necessary to minimize uncertainties in apartment housing prices.

Assessing non-linear effects of government size on inflation in India: recent evidence from smooth transition autoregression model

PurposeStandard economic theory predicts that any increase in public spending is accompanied by a rise in inflation in an economy. This paper presents empirical proof that prices do not always rise with an increase in public expenditure but only up to a certain threshold level. The primary aim of this paper is to unearth the government size-inflation nexus in India for the period from 1971 to 2019.Design/methodology/approachThe logistic STAR (smooth transition autoregression) model is employed to unravel the government size-inflation nexus for the Indian economy from a non-linear perspective.FindingsThe finding of our study confirm the non-linear relationship between the size of the government and inflation in India. The estimated threshold level for government size is precisely found to be 9.27%. The size of the government exerts a negative influence on inflation until it reaches the optimal or threshold level. Any further increase in the size of government beyond this threshold level would result in a rise in inflation.Research limitations/implicationsThe findings have implications for the conduct of fiscal policy. Policymakers can increase government spending in a regime of small government size without having any inflationary impacts by generating revenues from taxes and other sources instead of relying much on the central bank. In the regime of a large-sized government, adhering strictly to the discipline in the conduct of fiscal and monetary policies would help curb inflation and enhance growth synchronously, hence alleviating any loss of welfare.Originality/valueTo the best of the authors’ knowledge, this study is an attempt to revisit the government size-inflation nexus in India from a non-linear perspective using the Smooth Transition Autoregression (STAR) model for the first time.

Comprehensively testing linearity hypothesis using the smooth transition autoregressive model

This article examines the null limit distribution of the quasi-likelihood ratio (QLR) statistic for testing linearity condition against the smooth transition autoregressive (STAR) model. We explicitly show that the QLR test statistic weakly converges to a functional of a multivariate Gaussian process under the null of linearity, which is done by resolving the issue of identification problem arises in two different ways under the null. In contrast with the Lagrange multiplier test that is widely employed for testing the linearity condition, the proposed QLR statistic has an omnibus power, and thus, it complements the existing testing procedure. We show the empirical relevance of our test by testing the neglected nonlinearity of the US fiscal multipliers and growth rates of US unemployment. These empirical examples demonstrate that the QLR test is useful for detecting the nonlinear structure among economic variables.

PERAMALAN HARGA BITCOIN DENGAN METODE SMOOTH TRANSITION AUTOREGRESSIVE (STAR)

One of the spectacular advances in technology in the economic field is the cryptocurrency it created. The fluctuating price of Bitcoin, is widely used as a means of making profit. The time series forecasting method that can be used for the case of nonlinear time series data such as Bitcoin data is the smooth transition autoregressive (STAR) model. STAR is an extension of the autoregressive model for nonlinear time data. The purpose of this study is to obtain the results of forecasting Bitcoin price data for the next 2 two months using the STAR method. The data used in this study is Bitcoin daily price data from September 2017 to April 2021. To estimate the STAR model, several things that must be determined are the autoregressive model, transition variables, and transition functions. If the STAR model has been estimated, forecasting will be carried out for the next 2 months, which results in the forecast for the highest Bitcoin price falling on June 30, 2021 and the lowest Bitcoin price falling on May 1, 2021.

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.

A comparison of multistep commodity price forecasts using direct and iterated smooth transition autoregressive methods

AbstractThe smooth transition autoregressive (STAR) modeling framework has gained popularity in commodity price analysis due to its ability to capture essential features of complex dynamics. This study addresses the questions of whether the improved in‐sample fit of STAR models results in more accurate forecasts compared to linear autoregressive models, and whether direct or iterated multistep STAR methods yield more accurate multistep forecasts. In the STAR framework, either a bootstrap simulation is necessary to numerically approximate iterated multistep forecasts, or a range of horizon‐specific STAR models needs to be estimated to generate direct multistep forecasts. The associated computational trade‐off underscores the need for a better understanding of advantages one method may have over another. Based on the analysis of 25 agricultural and nonagricultural commodity prices, this study finds that even when the STAR models appear to well approximate complex commodity price dynamics, they offer little advantage, and indeed, in most instances present as inferior alternatives to the basic autoregressive framework for multistep commodity price forecasting.

Relationship between Real Exchange Rate and Consumption in Nigeria: A Nonlinear Approach

This study analyses the relationship between real exchange rate and domestic consumption in Nigeria using the Smooth Transition Autoregressive (STAR) model from 1981Q1 to 2019Q4. Findings show that domestic consumption determines the regime shift in real exchange rate, suggesting a nonlinear linkage with clearly distinct regimes. The lagged exchange rate is shown to have a significant linear effect on the current exchange rate. On the other hand, current foreign consumption is positive but has no significant impact on the exchange rate in the linear part of the model. In the nonlinear part of the model, evidence of a significant negative relationship between real exchange rate and domestic consumption is found, thus, supporting the proposition of the standard international business cycle model. In addition, the study finds evidence of bi-directional nonlinear granger causality between real exchange rate and domestic consumption. The study concludes that the relationship between real exchange rate and domestic consumption is nonlinear and that fiscal and monetary authorities should aim at policies that would stimulate domestic consumption below the threshold level necessary to keep the exchange rate stable.

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.

Forecasting tourism growth with State-Dependent Models

We introduce two forecasting methods based on a general class of non-linear models called ‘State-Dependent Models’ (SDMs) for tourism demand forecasting. Using a Monte Carlo simulation which generated data from linear and non-linear models, we evidence how estimations from SDMs can capture the level shifts pattern and nonlinearity in data. Next, we apply two new forecasting methods based on SDMs to forecast tourism demand growth in Japan. The forecasts are compared with classical recursive SDM forecasting, Naïve forecasting, ARIMA, Exponential Smoothing, Neural Network models, Time varying parameters, Smooth Transition Autoregressive models, and with a linear regression model with two dummy variables. We find that improvements in forecasting with the proposed SDM-based forecasting methods are more pronounced in the longer-term horizons.

THE INFLUENCES OF STOCK MARKET ON EXCHANGE-TRADED FUND UNDER THE THRESHOLD EFFECT OF MONETARY POLICY IN CHINA

This paper estimates the smooth transition autoregressive model with exogenous variables to evaluate the effects of stock market returns on the exchange-traded funds’ (ETFs) returns in China with reserve requirement ratio (RRR) from monetary policy as a transition variable. The sample used in this study lasts from March 4, 2005 to June 30, 2017. The empirical result points out that there is the effect of RRR value on the relationship between stock market returns and ETF return. Moreover, these effects are variable depending on the conversion and its changes over time in different variations of threshold intervals. Lastly, the larger the change of China’s stock market variables’ lag period, the smaller the impacts on Chinese ETF return.