Logistic Smooth Transition Autoregressive Research Articles

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.

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.

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.

Forecasting Albanian Time Series with Linear and Nonlinear Univariate Models

Albanian economic time series show irregular patterns since the 1990s that may affect economic analyses with linear methods. The purpose of this study is to assess the ability of nonlinear methods in producing forecasts that could improve upon univariate linear models. The latter are represented by the classic autoregressive (AR) technique, which is regularly used as a benchmark in forecasting. The nonlinear family is represented by two methods, i) the logistic smooth transition autoregressive (LSTAR) model as a special form of the time-varying parameter method, and ii) the nonparametric artificial neural networks (ANN) that mimic the brain’s problem solving process. Our analysis focuses on four basic economic indicators – the CPI prices, GDP, the T-bill interest rate and the lek exchange rate – that are commonly used in various macroeconomic models. Comparing the forecast ability of the models in 1, 4 and 8 quarters ahead, we find that nonlinear methods rank on the top for more than 75 percent of the out-of-sample forecasts, led by the feed-forward artificial neural networks. Although the loss differential between linear and nonlinear model forecasts is often found not statistically significant by the Diebold-Mariano test, our results suggest that it can be worth trying various alternatives beyond the linear estimation framework. Received: 19 June 2021 / Accepted: 25 August 2021 / Published: 5 September 2021

Timing of tick size reduction: Threshold and smooth transition model analysis

“Tick size” is the minimum subdivision of price at which investors can buy or sell an asset in a financial market. Tick size is reduced to improve market quality and liquidity. This study analyzes the volume dimension of liquidity—specifically, trading volume—to determine the time of impact of the 2014 tick size reduction policy, implemented in two phases (P1 and P2) by the Tokyo Stock Exchange. Threshold autoregressive (TAR) and logistic smooth transition autoregressive (LSTAR) models are used to estimate this time of impact. The results show that the use of the TAR model changed the trading volumes for P1 and P2 on December 13, 2013, and June 30, 2014, respectively. With the addition of the LSTAR model, the trading volumes of P1 and P2 changed on December 16, 2013, and September 3, 2014, respectively. These results suggest that empirical studies on tick size reduction need longer interruptions.

Time series analysis of temporal trends in hemorrhagic fever with renal syndrome morbidity rate in China from 2005 to 2019

Hemorrhagic fever with renal syndrome (HFRS) is seriously endemic in China with 70%~90% of the notified cases worldwide and showing an epidemic tendency of upturn in recent years. Early detection for its future epidemic trends plays a pivotal role in combating this threat. In this scenario, our study investigates the suitability for application in analyzing and forecasting the epidemic tendencies based on the monthly HFRS morbidity data from 2005 through 2019 using the nonlinear model-based self-exciting threshold autoregressive (SETAR) and logistic smooth transition autoregressive (LSTAR) methods. The experimental results manifested that the SETAR and LSTAR approaches presented smaller values among the performance measures in both two forecasting subsamples, when compared with the most extensively used seasonal autoregressive integrated moving average (SARIMA) method, and the former slightly outperformed the latter. Descriptive statistics showed an epidemic tendency of downturn with average annual percent change (AAPC) of −5.640% in overall HFRS, however, an upward trend with an AAPC = 1.213% was observed since 2016 and according to the forecasts using the SETAR, it would seemingly experience an outbreak of HFRS in China in December 2019. Remarkably, there were dual-peak patterns in HFRS incidence with a strong one occurring in November until January of the following year, additionally, a weak one in May and June annually. Therefore, the SETAR and LSTAR approaches may be a potential useful tool in analyzing the temporal behaviors of HFRS in China.

Analyzing Crude Oil Prices under the Impact of COVID-19 by Using LSTARGARCHLSTM

Under the influence of the COVID-19 pandemic and the concurrent oil conflict between Russia and Saudi Arabia, oil prices have exhibited unusual and sudden changes. For this reason, the volatilities of the West Texas Intermediate (WTI), Brent and Dubai crude daily oil price data between 29 May 2006 and 31 March 2020 are analysed. Firstly, the presence of chaotic and nonlinear behaviour in the oil prices during the pandemic and the concurrent conflict is investigated by using the Shanon Entropy and Lyapunov exponent tests. The tests show that the oil prices exhibit chaotic behavior. Additionally, the current paper proposes a new hybrid modelling technique derived from the LSTARGARCH (Logistic Smooth Transition Autoregressive Generalised Autoregressive Conditional Heteroskedasticity) model and LSTM (long-short term memory) method to analyse the volatility of oil prices. In the proposed LSTARGARCHLSTM method, GARCH modelling is applied to the crude oil prices in two regimes, where regime transitions are governed with an LSTAR-type smooth transition in both the conditional mean and the conditional variance. Separating the data into two regimes allows the efficient LSTM forecaster to adapt to and exploit the different statistical characteristics and ARCH and GARCH effects in each of the two regimes and yield better prediction performance over the case of its application to all the data. A comparison of our proposed method with the GARCH and LSTARGARCH methods for crude oil price data reveals that our proposed method achieves improved forecasting performance over the others in terms of RMSE (Root Mean Square Error) and MAE (Mean Absolute Error) in the face of the chaotic structure of oil prices.

Does non-linearity in exchange rate hold in Nigeria evidence from smooth transition autoregressive model

This study employs smooth transition autoregressive (STAR) model to investigate the non-linearity in exchange rate process in Nigeria within the context of exchange rate parity theory (ERPT). Quarterly data from 1981Q1 to 2017Q4 is used. The outcome of the study confirms the presence of exchange rate parity in Nigeria using Augmented Dickey Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) unit root tests. The study rejects the null hypothesis of linearity in nominal exchange rate in Nigeria. Furthermore, the estimation result of non-linear least squares (NLS) regression indicates that most of the parameter estimates are statistically significant. The study reveals that non-linear models best explain exchange rate dynamics in Nigeria. Likewise, the study discovers that exchange rate process in Nigeria is best fit with smoothly asymmetric logistic smooth transition autoregressive (LSTAR). The study concludes that heterogeneous nature of participants and asymmetric information in the market cause exchange rate to adjust in non-linear version.

Bayesian Estimation and Unit Root Test for Logistic Smooth Transition Autoregressive Process

The paper considers nonlinear logistic smooth transition autoregressive (LSTAR) process and aims to detect the unit root under the null hypothesis of a random walk process against the alternative of a stationary LSTAR process and to estimate the parameters of the process in Bayesian framework using MCMC. The simulation study is carried out for investigating the performance of the Bayes estimators for parameters and Bayesian unit root test and it has been observed that the estimates of parameters of the LSTAR process are close to the true parameter values. It has been observed that the Bayesian unit root test performs well and the power of the test is high even for the boundary cases having root close to unity, at least when the sample size is large. Since the LSTAR models are widely applied for real exchange rate modeling, the theoretical results are illustrated empirically for the real exchange rates of ten OCED countries.

A remaining useful life prediction method for airborne fuel pump after maintenance

Remaining useful life prediction is the core of condition-based maintenance under the technology framework of prognostic and health management. But the remaining useful life of airborne fuel pump after maintenance is difficult to predict because of the multi-stage noise and small data size. A new method is proposed to solve the remaining useful life prediction of repaired fuel pump. Firstly, an alternative smooth transition auto-regression model logistic smooth transition auto-regression or exponential smooth transition auto-regression is proposed to reduce the multi-stage noise. Secondly, random effect Wiener process is utilized to model the de-noised degradation data, and the posterior parameters of remaining useful life prediction after maintenance are derived by the Bayesian method based on the parameters before maintenance. Finally, the method proposed above is compared with the methods which neglect the multi-stage noise and information before maintenance, comparative results show that the proposed method can improve the remaining useful life prediction accuracy significantly.

Classification of sleep stages based on LSTAR model

Sleep study is very important in the health since sleep disorders affect the productivity of individuals. One of the important topics in sleep research is the classification of sleep stages using the electroencephalogram (EEG) signal. Electrical activities of brain are measured by EEG signal in the laboratory. In real-world environments, EEG signal is also used in portable monitoring devices to analyze sleep. In this study, we propose an efficient method for classification of sleep stages. EEG signals are examined by a new model from autoregressive (AR) family, namely logistic smooth transition autoregressive (LSTAR) to study sleep process. In contrast to the AR model, LSTAR is a non-linear one; therefore, it is suitable for modeling non-linear signals such as EEG. In the current research, at first, each 30-second epoch of EEG signal is decomposed into the time-frequency sub-bands using the double-density dual-tree discrete wavelet transform (D3TDWT). In the second step, LSTAR model is used for feature extraction from each sub-band. Next, the dimension of feature vector is reduced by tensor locality preserving projection (tensor LPP) method, and then the obtained features are given to classifier to determine the stage of each epoch based on the number of considered classes. After classifying sleep stages, some misclassified epochs can be corrected according to the smoothing rule. We consider different classifiers and evaluate their performance. The results indicate the efficiency of the proposed method in comparison with the recently introduced methods in terms of accuracy and Kappa coefficient.

Asymmetric effects of monetary policy in the U.S and Brazil

We empirically test the effects of anticipated and unanticipated monetary policy shocks on the growth rate of real industrial production and explicitly test for different types of asymmetries in monetary policy implementation for two major international economies, the U.S. and Brazil. We depart from the conventional method of VAR analysis to estimate unanticipated monetary shocks, and instead, we use a combination of alternative methodologies. We first identify the Taylor rule that best describes the reaction of both central banks and then we test both forward looking linear and nonlinear models. We conclude that a Logistic Smooth Transition Autoregressive (LSTAR) forward looking model of the Taylor rule best describes the US FED Funds rate while a linear Taylor rule with the inclusion of a dummy variable best describes the reaction of the Central Bank of Brazil (BCB). We then use in-sample forecast errors in order to derive and identify the unexpected monetary policy shocks for both countries. In line with Cover (1992), we use these shocks to explore any asymmetries in the conduct of monetary policy on the growth rate of the real industrial production. We also find asymmetries between anticipated and unanticipated monetary shocks as well as between effects of positive and negative shocks.

PERAMALAN INDEKS HARGA SAHAM GABUNGAN DENGAN METODE LOGISTIC SMOOTH TRANSITION AUTOREGRESSIVE (LSTAR)

Smooth Transition Autoregressive (STAR) Model is one of time series model used in case of data that has nonlinear tendency. STAR is an expansion of Autoregressive (AR) Model and can be used if the nonlinear test is accepted. If the transition function G(st,γ,c) is logistic, the method used is Logistic Smooth Transition Autoregressive (LSTAR). Weekly IHSG data in period of 3 January 2010 until 24 December 2017 has nonlinier tend and logistic transition function so it can be modeled with LSTAR . The result of this research with significance level of 5% is the LSTAR(1,1) model. The forecast of IHSG data for the next 15 period has Mean Absolute Percentage Error (MAPE) 2,932612%. Keywords : autoregressive, LSTAR, nonlinier, time series

Nonlinear time series modeling and forecasting the seismic data of the Hindu Kush region

In this study, we extended the application of linear and nonlinear time models in the field of earthquake seismology and examined the out-of-sample forecast accuracy of linear Autoregressive (AR), Autoregressive Conditional Duration (ACD), Self-Exciting Threshold Autoregressive (SETAR), Threshold Autoregressive (TAR), Logistic Smooth Transition Autoregressive (LSTAR), Additive Autoregressive (AAR), and Artificial Neural Network (ANN) models for seismic data of the Hindu Kush region. We also extended the previous studies by using Vector Autoregressive (VAR) and Threshold Vector Autoregressive (TVAR) models and compared their forecasting accuracy with linear AR model. Unlike previous studies that typically consider the threshold model specifications by using internal threshold variable, we specified these models with external transition variables and compared their out-of-sample forecasting performance with the linear benchmark AR model. The modeling results show that time series models used in the present study are capable of capturing the dynamic structure present in the seismic data. The point forecast results indicate that the AR model generally outperforms the nonlinear models. However, in some cases, threshold models with external threshold variables specification produce more accurate forecasts, indicating that specification of threshold time series models is of crucial importance. For raw seismic data, the ACD model does not show an improved out-of-sample forecasting performance over the linear AR model. The results indicate that the AR model is the best forecasting device to model and forecast the raw seismic data of the Hindu Kush region.

Chaotic time series prediction for glucose dynamics in type 1 diabetes mellitus using regime-switching models

In patients with type 1 diabetes mellitus (T1DM), glucose dynamics are influenced by insulin reactions, diet, lifestyle, etc., and characterized by instability and nonlinearity. With the objective of a dependable decision support system for T1DM self-management, we aim to model glucose dynamics using their nonlinear chaotic properties. A group of patients was monitored via continuous glucose monitoring (CGM) sensors for several days under free-living conditions. We assessed the glycemic variability (GV) and chaotic properties of each time series. Time series were subsequently transformed into the phase-space and individual autoregressive (AR) models were applied to predict glucose values over 30-minute and 60-minute prediction horizons (PH). The logistic smooth transition AR (LSTAR) model provided the best prediction accuracy for patients with high GV. For a PH of 30 minutes, the average values of root mean squared error (RMSE) and mean absolute error (MAE) for the LSTAR model in the case of patients in the hypoglycemia range were 5.83 ( ± 1.95) mg/dL and 5.18 ( ± 1.64) mg/dL, respectively. For a PH of 60 minutes, the average values of RMSE and MAE were 7.43 ( ± 1.87) mg/dL and 6.54 ( ± 1.6) mg/dL, respectively. Without the burden of measuring exogenous information, nonlinear regime-switching AR models provided fast and accurate results for glucose prediction.

Adaptive LSTAR Model for Long-Range Variable Bit Rate Video Traffic Prediction

Static bandwidth allocation for variable bit rate (VBR) video traffic forfeits the available bandwidth. Prediction of the next frame size is thus useful in dynamic bandwidth allocation. It has been shown that VBR video traces are long-range dependent, which makes one-frame-ahead prediction insufficient for dynamic bandwidth allocation. Several studies have been conducted based on the linear autoregressive (AR) model to address VBR traffic prediction. In this paper, we propose the use of a nonlinear model from the AR family called logistic smooth transition autoregressive (LSTAR) to predict VBR video traffic. Furthermore, we introduce adaptive algorithms, including least mean square (LMS), normalized LMS (NLMS), kernel LMS (KLMS), and normalized KLMS (NKLMS), to obtain the parameters of the LSTAR model used in long-range VBR traffic prediction. In the proposed model, we do not separate traffic of different frame types and use only one predictor, which results in lower computational complexity. The performance of the proposed predictor for different prediction steps was evaluated and compared with recently introduced predictors. The results indicate that the proposed nonlinear LSTAR-based predictor yields better results than the optimum linear AR predictor, i.e., Wiener–Hopf and others.

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.

Forecasting with nonlinear time series model: A Monte-Carlo bootstrap approach

In this paper, we propose a new method of forecasting with nonlinear time series model using Monte-Carlo Bootstrap method. This new method gives better result in terms of forecast root mean squared error (RMSE) when compared with the traditional Bootstrap method and Monte-Carlo method of forecasting using a special nonlinear time series model, called logistic smooth transition autoregressive (LSTAR) model. We illustrate this new method using some simulation experiments. Keywords : Bootstrap, Forecasting, LSTAR, Monte-Carlo, Monte-Carlo Bootstrap

Femtocell base station clustering and logistic smooth transition autoregressive‐based predicted signal‐to‐interference‐plus‐noise ratio for performance improvement of two‐tier macro/femtocell networks

The aim of this study is to improve the performance of two-tier macro/femtocell networks using a power control approach. In wireless networks, power control plays an important role in improving a number of performance parameters such as co-channel interference and outage probability reduction, throughput increasing, and power saving. This study explores the evolution of centralised power control algorithm based on femtocell base station (FBS) clustering and predicted signal-to-interference-plus-noise ratio (SINR) of users. To reduce the computational complexity of centralised algorithm, dense deployed femtocells are considered in different clusters. In this case, femtocells inside one cluster make considerable interference to each other, while the interferences from femtocells of other clusters are negligible. Moreover, because of the non-linearity of SINR samples, non-linear logistic smooth transition autoregressive (LSTAR) model is used to model the SINR data, and then the next SINR samples are predicted from the previous samples. According to the clustered FBSs and predicted SINR, the proposed power control scheme is applied to femtocell network in the downlink. The results demonstrate that the introduced method improves the outage probability and throughput and outperforms previous methods significantly.