Smooth Transition Autoregressive Research Articles

Correction to: A Smooth Transition Autoregressive Model for Matrix-Variate Time Series

Correction to: A Smooth Transition Autoregressive Model for Matrix-Variate Time Series

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.

Financial fragility, regime change, and monetary policy in an open economy – A model and empirical application to emerging market countries

July 20, 2023 (Revised April 15, 2024) The experiences of the 1997–98 Asian Financial Crisis and the 2008–09 Global Financial Crisis encouraged economists to develop new open-economy dynamic finance-macro models. Such models allow for nonlinearities -- to study the effects of contractionary currency devaluation -- in contrast to models of expansionary currency devaluation. The generic dynamic model of the finance-macro link in this paper includes the dynamics of the inflation rates, output gap, and financial variables (credit flows, risk premia, and exchange rates). The theoretical model with nonlinearities shows that there can be resilient or non-resilient outcomes of the dynamics. The level of resilience is however dependent on some empirical vulnerabilities. Relevant empirics show the risk premium is related not only to domestic real macro and financial variables, but also to the exchange rate and the foreign currency reserves. Econometrically, this paper explores the regime-dependent interaction of the output gap and financial variables in a two-regime non-linear Logistic Vector Smooth Transition Auto-Regressive (LVSTAR) model with a logistic-type transition function. This empirical study reveals that the financial variables of emerging economies show regime-dependent responses to external shocks. Therefore, a positive shock to the risk premia in a negative output gap regime entails an exchange rate depreciation, and accelerating contractions. Overall, however, a diversity of EM economies are examined in terms of their response to external shocks and their resilience levels. This research also has implications for international portfolio holdings.

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.

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

PurposeThe 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/approachThe 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.FindingsThe 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/implicationsThe 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/valueTo 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

Nonlinear impact of interest rates on price level (smooth transition autoregressive approach)

Economic and monetary policy-making shall benefit from the nominal interest rates and inflation causal relationship for macroeconomic issues. In this paper, by expanding Fisher’s Quantity Theory of Money, we investigate this relationship using the “Smooth Transition Autoregressive” approach for Iran's economy.The results show that when the interest rate rises (particularly when it exceeds the threshold), its positive impact on inflation will increase. Moreover, the effect of a low-interest rate increase does not have a severe effect on price change. It is concluded that interest rate is not a good policy instrument for high inflation dampening, and those policies that diminish money circulation velocity might be more effective for general price level control. Macro-economically, the results show that in the long run, interest rate yield that is paid to the factors of production is practically eliminated by reducing the purchasing power of money due to the price increase in the economy.This might be understood as one of the pearls of wisdom that Almighty God has cited in the Holy Qur'an about the prohibition of usury: "God effaces usury"5 means that Almighty God eliminates the effects of the usury yield increment in the economy.Interest rate, Price, Smooth Transfer Autoregressive Model, Quantity Theory of Money, Irving Fisher.

The role of uncertainty in forecasting volatility comovements across stock markets

Earlier studies found that uncertainty is important in forecasting the financial market covolatilities. However, it is not clear how uncertainty affects the covariance matrix dynamics across different market and economic conditions. To fill this gap, we specify the dynamic relationship between stock market covolatilities and uncertainty in a nonlinear framework, and we analyze the relevance of uncertainty measures in anticipating the transition of conditional covariances between different regimes. Specifically, we propose alternative transformations of the realized covariance matrix which we model by means of the Vector Logistic Smooth Transition Autoregressive (VLSTAR) model. Empirical results indicate that uncertainty measures used as transition variables help to detect covolatilities changes; moreover, the VLSTAR exhibits a significantly better forecast performance compared to alternative linear and multivariate GARCH models. Finally, our results show that the evidence on the role of macroeconomic and financial predictors is mixed, depending on the specification of the realized covariance dynamics.

Testing for Unit Roots in Nonlinear Dynamic Heterogeneous Panels with Logistic Smooth Breaks

In this study, we investigate the validity of the purchasing power parity (PPP) proposition for 34 European and selected global countries. For this purpose, we propose a new unit root test for cross-sectionally dependent heterogeneous panels that allows for gradual structural breaks and symmetric nonlinear adjustment toward the equilibrium level. The alternative hypothesis stationary is obtained by symmetric adjustment due to exponential smooth transition autoregression (ESTAR) around a nonlinear trend. Moreover, we provide small sample properties extensively for the newly proposed test. Hence, this alternative hypothesis has been proven to characterize real exchange rate data (REER) correctly. Thus, the newly proposed tests provide an essential basis for modeling the REER series correctly. Finally, we also derive the approximate asymptotic distribution of the proposed tests using new techniques.

Forecasting BDI Sea Freight Shipment Cost, VIX Investor Sentiment and MSCI Global Stock Market Indicator Indices: LSTAR-GARCH and LSTAR-APGARCH Models

Prediction of the economy in global markets is of crucial importance for individuals, decisionmakers, and policies. To this end, effectiveness in modeling and forecasting the directions of such leading indicators is of crucial importance. For this purpose, we analyzed the Baltic Dry Index (BDI), Investor Sentiment Index (VIX), and Global Stock Market Indicator (MSCI) for their distributional characteristics leading to proposed econometric methods. Among these, the BDI is an economic indicator based on shipment of dry cargo costs, the VIX is a measure of investor fear, and the MSCI represents an emerging and developed county stock market indicator. By utilizing daily data for a sample covering 1 November 2007–30 May 2022, the BDI, VIX, and MSCI indices are investigated with various methods for nonlinearity, chaos, and regime-switching volatility. The BDS independence test confirmed dependence and nonlinearity in all three series; Lyapunov exponent, Shannon, and Kolmogorov entropy tests suggest that series follow chaotic processes. Smooth transition autoregressive (STAR) type nonlinearity tests favored two-regime GARCH and Asymmetric Power GARCH (APGARCH) nonlinear conditional volatility models where regime changes are governed by smooth logistic transitions. Nonlinear LSTAR-GARCH and LSTAR-APGARCH models, in addition to their single-regime variants, are estimated and evaluated for in-sample and out-of-sample forecasts. The findings determined significant prediction and forecast improvement of LSTAR-APGARCH, closely followed by LSTAR-GARCH models. Overall results confirm the necessity of models integrating nonlinearity and volatility dynamics to utilize the BDI, VIX, and MSCI indices as effective leading economic indicators for investors and policymakers to predict the direction of the global economy.

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 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.

Smooth Threshold Autoregressive models and Markov process: An application to the Lebanese GDP growth rate

This paper analyzes the evolution of the Lebanese GDP growth rate over the period 1970-2018 by estimating two kinds of switching models: The Smooth Transition Autoregressive (STAR) model and the model of the Markov process. These models show, on the one hand, asymmetries in the evolution of GDP growth with an abrupt transition from a regime to another and, on the other hand, a high probability that the economy remains in the recession regime. Even though the duration of the expansion phase is longer than the duration of the recession phase, the Lebanese economy experiencing the greatest difficulties in moving from a recession regime to an expansion regime. In addition, such an evolution is explosive and volatile during the lower regime (recession phase) but stationary and damped in the upper regime (expansion phase). Finally, the paper shows that the STAR model, taking a logistic form, better fits the Lebanese GDP growth than the Markov model.