Smooth Transition Autoregressive Research Articles

A Study on China’s Urban Electricity Productivity Convergence with Spatial Smooth Transition Effect

This paper analyzes the absolute convergence of urban electricity productivity in China during 1990–2011, applying Spatial Error Smooth Transition Auto-regression Model, and examines the spatial effect in convergence process. Then it analyzes the stage characteristics of electricity productivity convergence during the process of electricity market reformation and the conditional convergence which is affected by the urban economy. According to the results of our research, there exists significant absolute convergence of urban electricity productivity in China, and the spatial effect, especially spatial smooth transition effect, significantly enhance the convergence of urban electricity productivity. Since the electricity market reformation in 2002, significant stage characteristics exist in convergence of urban electricity productivity. The convergence rate of electricity productivity before 2002 is obviously lower than the one during the whole sample period, also the one after 2002 and the spatial nonlinear effect strengthens during the later period with marketization in electricity market and stricter regulation on energy conservation. The urban economy also affects the convergence of urban electricity productivity, while it does not promote the convergence rate because the high proportion of electricity-intensive industry in cities of western and northeastern region. At the conclusion of our paper, we put forward policy suggestions with the objective of narrowing the gap of urban electricity productivity and realizing sustainable urban development.

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.

Unemployment hysteresis and structural change in Europe

We examine the unemployment hysteresis hypothesis for 31 European countries, the USA and Japan, using alternative linear and nonlinear unit root tests, taking into account possible structural breaks. Two types of smooth transition models—Exponential Smooth Transition Autoregressive and Asymmetric Exponential Smooth Transition Autoregressive—are employed to account for the nonlinear mean-reverting behaviour in unemployment due to heterogeneity in hiring and firing costs across firms. Four main results emerge: first, the hysteresis hypothesis is rejected for 60 % of the countries in our sample. Second, nonlinear models capture the asymmetries in unemployment dynamics over the business cycle for some countries. Third, many of the series display multiple structural breaks which might point out shifts in mean level of unemployment. Fourth, forecasting powers of our nonlinear models display poor performance against the linear AR specification. The results have policy implications for the debate on the benefits of demand or supply-side policies for tackling the current unemployment problem in Europe.

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.

Time-varying persistence of inflation: evidence from a wavelet-based approach

AbstractWe propose a new stochastic long-memory model with a time-varying fractional integration parameter, evolving non-linearly according to a Logistic Smooth Transition Autoregressive (LSTAR) specification. To estimate the time-varying fractional integration parameter, we implement a method based on the wavelet approach, using the instantaneous least squares estimator (ILSE). The empirical results show the relevance of the modeling approach and provide evidence of regime change in inflation persistence that contributes to a better understanding of the inflationary process in the US. Most importantly, these empirical findings remind us that a “one-size-fits-all” monetary policy is unlikely to work in all circumstances. The empirical results are consistent with newly developed tests of wavelet-based unit root and fractional Brownian motion.

Modeling price transmission between farm and retail prices: a soft switches approach

AbstractVector error correction models (VECM) are used to model price transmission when farm and retail prices are cointegrated. To allow for nonlinearity in the cointegration process, researchers may specify thresholds to break the error correction process into regimes according to whether the retail price is above, below, or close to its equilibrium value given farm prices. However, because the coefficients in a VECM can change when there is movement from one regime to another, the model can be discontinuous. This implies sudden, “hard” regime changes. In this study, we extend the threshold VECM to include features of smooth transition autoregression (STAR) models. Our approach allows for gradual, soft regime changes. An empirical application to retail cheese and farm milk prices is presented.

Tests for Linearity in Star Models: Supwald and Lm‐Type Tests

This article investigates approximation and supremum approaches for testing linearity in smooth transition autoregressive (STAR) models. We show that since the approximation of STAR models by Taylor series expansions may not accurately describe the specific transition dynamic when the process is away from the null, LM‐type tests may fail to detect the form of nonlinearity for which they are designed for. Investigating a supremum approach, the article provides the asymptotic distribution of a SupWald test that is obtained by taking the supremum of a Wald statistic over the Cartesian product of the spaces for the transition and threshold parameters. Simulated asymptotic critical values for the resulting tests are provided for a wide range of autoregressive orders and shown to differ across exponential and logistic STAR (ESTAR and LSTAR) models. Monte Carlo experiments show that SupWald tests for ESTAR and LSTAR models outperform LM‐type tests, compares well relative to the recently developed score‐based tests and each SupWald statistic performs the best against the true alternative for which it is formed. SupWald tests also provide results that are consistent with the findings from (independently) estimating and diagnostic testing of STAR models in real exchange rate data.

Interval Forecast for Smooth Transition Autoregressive Model

In this paper, we propose a simple method for constructing interval forecast for smooth transition autoregressive (STAR) model. This interval forecast is based on bootstrapping the residual error of the estimated STAR model for each forecast horizon and computing various Akaike information criterion (AIC) function. This new interval forecast suggest definite and better coverage to the future sample path than the conventional method of using a multiple of standard error of the forecast distribution using bootstrap method. Simulation studies are used to illustrate the proposed method.Keywords: AIC; bootstrap; Interval forecast; STAR

The Analysis of Domestic Debt Asymmetry in Turkey by Regime Switching Models

Abstract Domestic debt is an important tool of government finance for the economies which are vulnerable to budget deficits arising from government expenditures exceeding revenues. This tool used for government fiscal policy is a determinant of macroeconomic stability due to the effects on growth, employment and investment variables. In this context, the analysis of domestic debt dynamics has a vital importance especially for developing economies. As a developing economy for Turkey, the deterioration of fiscal balance after 1990's has led to a consistent increase in domestic debt. Aftermath of 2001 crises, domestic debt was restrained by the fiscal discipline which came into prominence by “Transition to Strong Economic Program”. In this regard, our study examines the structure of domestic debt process in Turkish economy over the period 1998-2015. Firstly, we investigate the linearity of the domestic debt series. Following the examination of non-linearity, we analyze the transition characteristics of domestic debt series by means of STAR (Smooth Transition Autoregressive) model.

Фондовые рынки в условиях смены условий торговли

Stock indices are among the indicators of the state of the economy, that among the first to respond to both the positive and the negative economic phenomena. It makes the understanding of mechanisms influencing them very important. Structural Vector Autoregression model (SVAR) approach is widely used for this purpose. These models allow us to estimate impulse responses of indices to the impact of different economic variables. A slightly different Smooth Transition Autoregression model (STAR) approach that allows identifying differences in responses due to economic conditions is used in this paper for the estimating of responses of stock indices. More specifically we apply Smooth Transition Vector Error Correction model (STVECM) approach. We use oil prices as the characteristic of the Russian economy defining changes in economic conditions and as a proxy defining changes in terms of trade, since oil is one of the major export goods for Russia. Other macroeconomic factors used in the paper are state budget expenses, consumer price index (CPI), the exchange rate of the dollar against the ruble, ratio of the exchange rates of dollar and euro against the ruble, LIBOR interest rate, and the S&P500 index. Obtained results show that the responses differ significantly depending on the level of oil prices. These results are also useful for the design of mechanisms affecting stock market.

Time-Varying Persistence of Inflation: Evidence from a Wavelet-Based Approach

We propose a new long-memory model with a time-varying fractional integration parameter, evolving non-linearly according to a Logistic Smooth Transition Autoregressive (LSTAR) specification. To estimate the time-varying fractional integration parameter, we implement a method based on the wavelet approach, using the instantaneous least squares estimator (ILSE). The empirical results show the relevance of the modeling approach and provide evidence of regime change in inflation persistence that contributes to a better understanding of the inflationary process in the US. Most importantly, these empirical findings remind us that a one-size-fits-all monetary policy is unlikely to work in all circumstances.

Sincronización cíclica del sector manufacturero de méxico y estados unidos desde una perspectiva no lineal autorregresiva con transición suave

<span>El objetivo de este artículo es validar el modelo Autorregresivo de Transición Suave (STAR) para el análisis de la sincronización cíclica del sector manufacturero de Estados Unidos con México, a partir de la apertura comercial de este último. Para este fin se revisa la bibliografía sobre la metodología STAR y se describen los aportes teóricos y prácticos relacionados con esta. Teóricamente se concluye que debido a su estructura lineal intrínseca, los modelos STAR son capaces de guiar al investigador hacia la elección de la metodología adecuada para modelar el comportamiento real de los datos; además, gracias a su componente no lineal, poseen la capacidad de modelar comportamientos cíclicos asimétricos de las series.</span>

Understanding PPP Puzzle Using a New Dynamics and Time-Varying Equilibrium

Rogoff asked how could the slow rate of reversal towards PPP be reconciled with the high volatility of the real exchange rate. After this well-known PPP puzzle, literature focuses on econometric models either with new mechanisms of dynamics or time-varying equilibrium to find shorter half-life so that the puzzle can be partially solved. Recent researchers examine the PPP puzzle by combining the two previous approaches into a single framework. This paper follows this strategy. We find that a model with Integral Correction Mechanism (ICM) represents the real exchange rate dynamics very well, significantly better than existing alternatives, such as those based on the popular Smooth Transition Autoregression (STAR). Finally, we investigate the possible origin of the ICM effect and find it could be related to its power in explaining the spectrum and autocorrelation function of real exchange rate, which also implies a new way to understand the PPP puzzle.

Financial Sector-Output Dynamics in the Euro Area: Non-Linearities Reconsidered

We analyze the feedback mechanisms between economic downturns and financial stress for euro area countries. Our study employs newly constructed financial condition indices that incorporate extensively banking variables. We apply a nonlinear Vector Smooth Transition Autoregressive (VSTAR) model for investigating instabilities in the fi nancial sector-output linkages. The VSTAR model appears appropriate since it allows for smooth regime changes and asymmetric dynamics. We find that regime-switching takes place rather smoothly which dampens the negative output response after a shock in the financial sector in the selected euro area countries. Moreover, linearity cannot be rejected for all countries over some extensive time period questioning non-linearities in the financial sector-output nexus as unambiguous feature. In particular, we show that the negative e ffect of financial stress on output typically observed is not always present. This holds specifi cally for the time before the Lehman collapse, even if this is a model-de fined high stress regime. After the collapse, we observe strong ampli fication mechanisms. This suggests that events leading to a strong economic breakdown are rare but large events and related to financial cycles which exhibit low frequency.

Financial sector and output dynamics in the euro area: Non-linearities reconsidered

We analyze the feedback mechanisms between economic downturns and financial stress for several euro area countries. Our study employs newly constructed financial condition indices that incorporate banking variables extensively. We apply a non-linear Logistic Vector Smooth Transition Autoregressive (LVSTAR) model for investigating instabilities in the link between the financial sector and economic activity. The LVSTAR model allows for non-linear dynamics and regime changes between low and high stress regimes. It can also replicate the regime-specific amplification effects shown by our theoretical model. The amplification effects, however, change over time. Specifically after the Lehman collapse, we observe the presence of strong non-linearities and amplification mechanisms for some euro area countries. Thus, these strong amplification effects appear to be related to rare but large events, and to a low-frequency financial cycle. Prior to the financial crisis outbreak we find corridor stability even if the financial sector shock takes place in a high stress regime. More important seems to be the shock propagation over time in the economy. Only with the occurrence of rare but large events we find strong endogenous feedback loops and a loss of stability as described by the high stress regime of our theoretical model. The economy leaves the corridor of stability and is prone to adverse feedback loops.

Non-linear modelling of market cycles in South Africa

Purpose – The purpose of this paper is to expand on the sparse literature on non-linear modelling in South Africa and test for non-linearity of the market cycle on the Johannesburg Stock Exchange, with specific focus on a particular non-linear model – a Smooth Transition Auto-Regressive (STAR) model. Design/methodology/approach – Non-linear estimation methods are used to describe the market cycle, as defined by equity prices, for the period 1998-2010. Findings – In applying the STAR model to daily, weekly and monthly returns data, it was found that the fit of this family of models differs heavily based on the frequency of data used. The daily Logarithmic STAR (LSTAR) model was found to be the best fit relative to other data frequencies. Indeed, the weekly LSTAR model, while still appropriate to use, was less apt at forecasting than its daily counterpart. Monthly return data indicated that a linear AR model was more appropriate than a non-linear one. Practical implications – The results assist in understanding the cyclical nature of emerging markets as well contributing to the understanding of creating a portfolio consisting of international securities. If one can show that equity returns in a particular emerging market follow non-linear behaviour, expanding this hypothesis to other emerging markets enables a minimum variance portfolio to be constructed that is informed by returns changing over time. Originality/value – The findings can be used for further research into share price modelling, portfolio management and perhaps as an avenue into the reasoning behind the formation of market cycles.

Asia-Pacific Stock Market Integration: New Evidence by Incorporating Regime Changes

ABSTRACTThis work provides new evidence of Asia-Pacific stock market integration by incorporating the regime changes of each stock market through the smooth transition autoregressive (STAR) model. According to empirical results, most Asia-Pacific stock market returns follow STAR dynamics to a significant degree with more rapid and frequent regime changes of a shorter nature compared with G7 markets. A series of STAR-based Granger causality tests reveal evidence of stronger equity market integration compared with linear Granger causality tests. We also find that Asia-Pacific stock markets are integrated in different levels. Finally, we provide evidence that in the early twenty-first century the influence of China and the United States on Asia-Pacific stock markets has been maintained while that of Japan has been weakened.

NONLINEAR SMOOTH TRANSITION AUTOREGRESSIVE (STAR)–TYPE MODELLING AND FORECASTING ON MALAYSIA AIRLINES (MAS) STOCK RETURNS

This study aims to apply nonlinear Smooth Transition Autoregressive (STAR)-type model to the Malaysia Airlines (MAS) Stock Returns, which consists of 4450 number of observations. The data taken started from 29th August 1996 until 26th September 2014. Following the STAR strategies by Terasvirta, the diagnostic plots of linear Autoregressive (AR) model revealed that AR (3) model is adequate in modelling the MAS returns series. However, the squared residuals of Autocorrelation Function (ACF) of returns series illustrates a slight presence of correlations in the model, hence the effort to apply nonlinear model was continued. Before proceed to nonlinear STAR modelling, the identification of delay parameter in the second stage of Terasvirta need to be determined. The results of Lagrange Multiplier (LM) tests revealed that delay parameter, d=3 is the best to choose. In addition, the null hypothesis of linearity from LM test is rejected. Furthermore, from the sequence of nested hypothesis of delay parameter, d=3 indicated that LSTAR model is preferred than ESTAR model. Finally, the forecasts and comparison stages was made to compare which models are best performed in forecasting the future series of MAS returns. It proved that LSTAR model performed better in term of forecasting accuracy when compared to ESTAR and AR model.

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.

Forecasting daily river flows using nonlinear time series models

Summary In the hydrology studies, it is well known that the river flows are affected by various factors, and therefore the dynamics in their associated time series are complicated and have nonlinear behaviors. In an empirical study, we investigate the capability of five classes of nonlinear time series models, namely Threshold Autoregressive (TAR), Smooth Transition Autoregressive (STAR), Exponential Autoregressive (EXPAR), Bilinear Model (BL) and Markov Switching Autoregressive (MSAR) to capture the dynamics in the Colorado river discharge time series. Least Squares (LS) and Maximum Likelihood (ML) methods are employed to estimate parameters of the models. For model comparison three criteria, namely loglikelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC) are calculated. The results show that a self-exciting TAR (SETAR) model performs better than other four competing models. To forecast future river discharge values an iterative method is applied and forecasting confidence intervals are constructed. The out-of-sample 1-day to 5-day ahead forecasting performances of the models based on ten forecast accuracy measures are evaluated. Comparing verification metrics of all models, SETAR model presents the best forecasting performance.