Threshold Autoregressive Model Research Articles

Bayesian nonlinear expectation for time series modelling and its application to Bitcoin

This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or misspecification in the conditional mean and volatility. At the first stage, a reference or approximating time series model is specified and estimated. At the second stage, Bayesian nonlinear expectations are introduced to incorporate model uncertainty or misspecification in prediction via specifying a family of alternative models. The Bayesian nonlinear expectations for prediction are constructed from closed-form Bayesian credible intervals evaluated using conjugate priors and residuals of the estimated approximating model. Using real Bitcoin data including some periods of Covid 19, applications of the proposed method to forecasting and risk evaluation of Bitcoin are discussed via three major parametric nonlinear time series models, namely the self-exciting threshold autoregressive model, the generalized autoregressive conditional heteroscedasticity model and the stochastic volatility model.

Market integration and price transmission in the regional grain markets in Ethiopia

ABSTRACT Persistent increases in basic food prices have become a critical challenge in Ethiopia since 2006. This paper assesses whether the structure of the grain market has contributed to the price increases. Traders having market power could create commodity price stickiness, implying that what goes up does not come down, leading to price increases. The study examines price linkages between principal grain markets in Ethiopia, using monthly prices from the wheat, maize, and teff markets. The Engle-Granger cointegration test is used to check for cointegration, while the Threshold Autoregressive Model is employed to investigate potential asymmetric price transmission. The findings indicate that major grain markets in Ethiopia are well integrated. Moreover, the threshold cointegration model reveals that they are characterized by symmetric adjustment. Hence, I argue that there is insufficient evidence to support the claim that market structure contributes to the price increase in Ethiopian grain markets.

Linear approximation of the Threshold AutoRegressive model: an application to order estimation

This paper proposes a linear approximation of the nonlinear Threshold AutoRegressive model. It is shown that there is a relation between the autoregressive order of the threshold model and the order of its autoregressive moving average approximation. The main advantage of this approximation can be found in the extension of some theoretical results developed in the linear setting to the nonlinear domain. Among them is proposed a new order estimation procedure for threshold models whose performance is compared, through a Monte Carlo study, to other criteria largely employed in the nonlinear threshold context.

Does Inflation Targeting Policy Matter for Inflation Performance?

Purpose – Inflation targeting (IT) is a practice that central banks around the world began to adopt as early as 1990. Due to the high accountability and high transparency of central banks under IT policy, the practice expected that inflation targets would have better inflation performance. In this study, it is explored whether inflation targeting policy has positive effects on inflation performance, focusing on inflation persistence. Also, it is explored whether the behavior of inflation rates overshooting or undershooting a target range (or a tolerance band around a target level) is asymmetric. Design/Methodology/Approach – An autoregressive (AR) model is adapted with a self-exciting threshold autoregressive (TAR) model to study inflation persistence before and after inflation targeting was adopted, respectively. To address issues that events unrelated to inflation targeting policy could explain the findings, counterfactual exercises for non- inflation target are conducted. Findings – It was found that inflation target, particularly developed inflation target, have experienced a decrease in inflation persistence after implanting inflation targeting. Also, there is limited evidence on the asymmetrical behavior of inflation rates between overshooting and undershooting an inflation target range, or tolerance band, around a target level. Research Implications – The findings in this study support the positive effect of IT policy on inflation performance. In particular, it is stronger for developed inflation target than less developed inflation target. In addition, the findings support that most central banks do not show asymmetrical responses to inflation rates between overshooting and undershooting a target range or tolerance band around a target level.

The contagion effect of jump risk across Asian stock markets during the Covid-19 pandemic

This paper tests the market jump contagion hypothesis in the context of the Covid-19 pandemic. We first use a nonparametric approach to identify jumps by decomposing the realized volatility into continuous and jump components, and we use the threshold autoregressive model to describe the jump interdependency structure between different markets. We empirically investigate the contagion effect across several major Asian equity markets (Mainland China, Hong Kong, Japan, South Korea, Singapore, Thailand, and Taiwan) using the 5-minute high frequency data. Some key findings emerge: jump behaviors occur frequently and make an important contribution to the total realized volatility; jump dynamics exhibit significant nonlinearity, asymmetry, and the feature of structural breaks, which can be effectively captured by the threshold autoregressive model; jump contagion effects are obviously detected and this effect varies depending on the regime.

Asymmetry and transmission of international price shocks of cocoa and coffee in Togo

This study assesses the mechanism of the transmission of international price shocks to producer prices of coffee and cocoa in Togo. A threshold autoregressive (TAR) model was estimated using monthly series of international and producer prices of coffee and cocoa in Togo from 1994 to 2018. The results show that there is asymmetric transmission of international price shocks to producer prices. Domestic prices respond less quickly to international price increase than decreases. The asymmetric price transmission is similar in term of the speed of adjustment for the two commodities. In order to deal with this phenomenon, further investigations need to be done to detect the reasons for the asymmetry in price transmission between domestic and international coffee and cocoa markets.

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.

THE RELATIONSHIP BETWEEN ECONOMIC GROWTH AND PUBLIC DEBT: A THRESHOLD REGRESSION APPROACH IN GHANA

Purpose– Ghana’s debt stock has been a subject of debate for a very long time. This study is to estimate the debt threshold level above which it will be detrimental to economic growth. Methodology– The study used a threshold autoregressive model introduced by Tong (1978) and Hansen (1996). The study employed time-series data for thirty-one years from 1990 to 2020. Economic growth was measured by the Gross Domestic Product Per Capita (GDPPC). The study sought to answer the following question: What is Ghana's public debt threshold value? Findings– The data reveal that Ghana has a single public debt threshold value (i.e., structural breakpoint), implying that public debt and growth are not linear. The derived threshold regression model indicates a public debt threshold of 57.09 per cent, above which the growth rate of GDPPC is considerably retarded. In addition, below the threshold level, there is a statistically significant positive association between public debt and growth. Conclusion– This article concludes that low public debt is growth-enhancing, whereas public debt above the threshold value is detrimental to economic growth. Therefore, policymakers should focus on monetary policies that aid in maintaining public debt at a low level. However, this study makes the following recommendations to help sustain Ghana's expanding state debt: To begin with, the government should halt the accumulation of external debt, which incurs additional costs during periods of currency depreciation. Second, policymakers with decision-making authority should exert severe restraint on the growing cedi. Thirdly, the government should eliminate all wasteful spending. Finally, the government of Ghana should allocate its external debt appropriately for economic investment and maintain a strong debt management policy. Keywords: Ghana’s debt stock, threshold, economic growth, policymakers. JEL codes: F34, H63

Asymmetric Price Transmission: A Case of Wheat in India

In the present paper, horizontal and vertical integration was carried out on the wholesale and retail prices of wheat in the major markets of India. On confirming cointegration between the wholesale and retail prices of wheat in all needs, the vector error correction model (VECM) was applied to find the speed of adjustment in the corresponding price channel. The results revealed that price signals are transmitted across regions, indicating that price changes in one market are consistently related to price changes in markets and can influence the prices in other markets. In addition to studying cointegration, threshold autoregressive (TAR) and Momentum TAR (MTAR) models were applied to test for asymmetric cointegration. Hasen and Seo’s test was used to test for the presence of threshold cointegration. It revealed a significant presence of asymmetric and nonlinear cointegration in many markets. Accordingly, a threshold VECM (TVECM) model with two regimes was applied. The results indicate that the retail price significantly responds to the deviations from the long-run equilibrium compared to the wholesale price.

Deep learning in predicting cryptocurrency volatility

This paper focuses on the prediction of cryptocurrency volatility. The stock market volatility represents a very influential aspect that affects a wide range of decisions in business and finance. Recently, the volatility spillovers between the cryptocurrency market and other financial markets are detecting. Nevertheless, the cryptocurrency volatility forecasts underperform the market dynamics. This paper develops a suitable model to capture the cryptocurrency volatility dynamics. We base on deep learning techniques, which produce more reliable results than standard methods in finance by capturing complex data interactions. Specifically, we refer to a Jordan Neural Network, which is a parsimonious recurrent neural network showing more predictability power compared to other models designed for time series, the Self Exciting Threshold Autoregressive model models and the Non-Linear Autoregressive Neural Networks. Empirical evidence is provided using data from three different cryptocurrencies, Bitcoin, Ripple, and Ethereum.

Threshold Autoregressive Nearest-Neighbour Models for Claims Reserving

Motivated by claims reserving in run-off triangles, a class of threshold autoregressive nearest-neighbour (TAR-NN) models extending a major class of parametric nonlinear time series models, namely threshold autoregressive (TAR) models, is introduced. The proposed class of models also introduces a flexible regime-switching mechanism to nearest-neighbour models. Attention is given to a sub-class of TAR-NN models, namely self-exciting threshold autoregressive nearest-neighbour models (SETAR-NN), for uses in claims reserving. The (strict) stationarity and geometric ergodicity of the SETAR-NN model, and more generally, a two-dimensional nonlinear autoregressive random field, are discussed. The conditional least-square (CLS) method is used to estimate the SETAR-NN model and some of its nested models. Simulation studies on the parameter estimates from the CLS method are conducted. Using real insurance claims data and stochastic simulations, the applications of the SETAR-NN model and the nested models for projecting future claims liabilities are discussed. Comparisons of those models with the Bootstrap-Chain-Ladder (BCL) model for claims reserving are provided.

Prediction of Landslide Displacement Based on the Combined VMD-Stacked LSTM-TAR Model

The volatility of the cumulative displacement of landslides is related to the influence of external factors. To improve the prediction of nonlinear changes in landslide displacement caused by external influences, a new combined forecasting model of landslide displacement has been proposed. Variational modal decomposition (VMD) was used to obtain the trend and fluctuation sequences of the original sequence of landslide displacement. First, we established a stacked long short time memory (LSTM) network model and introduced rainfall and reservoir water levels as influencing factors to predict the fluctuation sequence; next, we used a threshold autoregressive (TAR) model to predict the trend sequence, following which the trend and fluctuation prediction sequence were superimposed to obtain the cumulative predicted displacement of the landslide. Finally, the VMD-stacked LSTM-TAR combination model based on the variational modal decomposition, stacked long short time memory network, and a threshold autoregressive model was built. Taking the landslide of Baishuihe in the Three Gorges Reservoir area as an example, through comparison with the prediction results of the VMD-recurrent neural network-TAR, VMD-back propagation neural network-TAR, and VMD-LSTM-TAR, the proposed combined prediction model was noted to have high accuracy, and it provided a novel approach for the prediction of volatile landslide displacement.

The Role Of Education And Health In Work Participation In Cambodia

This study's goal is to determine how the role of investment in health and education on job participation in Cambodia. This study examines investment in education, investment in health, and the number of Cambodian residents who work or are absorbed as laborers in Cambodia. This study uses secondary data from the world bank. We use behavioral data analysis with the Threshold Autoregressive model. The research period in this study is the annual period from 2000 to 2019.We found that employment in Cambodia is impacted by investments in health and education. Education is able to increase human capital so that people can find suitable and more productive jobs and jobs that require experts are increasingly filled, this increases work participation while increasing economic performance. Health itself keeps the community healthy and can still work productively so that it can increase the work participation of the Cambodian community

Statistical analysis of multi‐day solar irradiance using a threshold time series model

AbstractThe analysis of solar irradiance has important applications in predicting solar energy production from solar power plants. Although the sun provides every day more energy than we need, the variability caused by environmental conditions affects electricity production. Recently, new statistical models have been proposed to provide stochastic simulations of high‐resolution data to downscale and forecast solar irradiance measurements. Most of the existing models are linear and highly depend on normality assumptions. However, solar irradiance shows strong nonlinearity and is only measured during the day time. Thus, we propose a new multi‐day threshold autoregressive model to quantify the variability of the daily irradiance time series. We establish the sufficient conditions for our model to be stationary, and we develop an inferential procedure to estimate the model parameters. When we apply our model to study the statistical properties of observed irradiance data in Guadeloupe island group, a French overseas region located in the Southern Caribbean Sea, we are able to characterize two states of the irradiance series. These states represent the clear‐sky and non‐clear sky regimes. Using our model, we are able to simulate irradiance series that behave similarly to the real data in mean and variability, and more accurate forecasts compared to linear models.

Estimation of generalized threshold autoregressive models

In this article, the maximum likelihood estimate and Bayesian estimate for a general threshold autoregressive model are considered. It is shown that under certain regular conditions, the maximum likelihood estimator (MLE) and Bayesian estimator (BE) of the threshold parameters are super consistent with convergence rate n. And the moments of the Bayesian estimator exist when the corresponding moments of the noise are finite and its limit distribution is a functional of integrated compound Poisson processes. Furthermore, the estimators of the regression parameters are shown to be asymptotically normal with convergence rate Two simulations are conducted to compare the BE with MLE.

Penalized estimation of threshold auto-regressive models with many components and thresholds.

Thanks to their simplicity and interpretable structure, autoregressive processes are widely used to model time series data. However, many real time series data sets exhibit non-linear patterns, requiring nonlinear modeling. The threshold Auto-Regressive (TAR) process provides a family of non-linear auto-regressive time series models in which the process dynamics are specific step functions of a thresholding variable. While estimation and inference for low-dimensional TAR models have been investigated, high-dimensional TAR models have received less attention. In this article, we develop a new framework for estimating high-dimensional TAR models, and propose two different sparsity-inducing penalties. The first penalty corresponds to a natural extension of classical TAR model to high-dimensional settings, where the same threshold is enforced for all model parameters. Our second penalty develops a more flexible TAR model, where different thresholds are allowed for different auto-regressive coefficients. We show that both penalized estimation strategies can be utilized in a three-step procedure that consistently learns both the thresholds and the corresponding auto-regressive coefficients. However, our theoretical and empirical investigations show that the direct extension of the TAR model is not appropriate for high-dimensional settings and is better suited for moderate dimensions. In contrast, the more flexible extension of the TAR model leads to consistent estimation and superior empirical performance in high dimensions.

The role of transition regime models for corn prices forecasting

Abstract: Given the relevance of corn for food and fuel industries, analysts and scholars are constantly comparing the forecasting accuracy of econometric models. These exercises test not only for the use of new approaches and methods, but also for the addition of fundamental variables linked to the corn market. This paper compares the accuracy of different usual models in financial macro-econometric literature for the period between 1995 and 2017. The main contribution lies in the use of transition regime models, which accommodate structural breaks and perform better for corn price forecasting. The results point out that the best models as those which consider not only the corn market structure, or macroeconomic and financial fundamentals, but also the non-linear trend and transition regimes, such as threshold autoregressive models.

Additive Outliers in Open-Loop Threshold Autoregressive Models: A Simulation Study

The effect of additive outliers is studied on an adapted non-linearity test and a robust estimation method for autoregressive coefficients in open-loop TAR (threshold autoregressive) models. Through a Monte Carlo experiment, the power and size of the non-linearity test are studied. Regarding the estimation method, the bias and ratio of mean squared errors are compared between the robust estimator and least squares. Simulation exercises are carried out for different percentages of contamination and the proportion of observations on each model regime. Furthermore, the approximation of the univariate normal distribution to the empirical distribution of estimated coefficients is analyzed along with the coverage level of asymptotic confidence intervals for the parameters. Results show that the adapted non-linearity test does not have size distortions, and it has a superior power than its least-squares counterpart when additive outliers are present. On the other hand, the robust estimation method for the autoregressive coefficients has a better mean squared error than least-squares when this type of observations are present. Lastly, the use of the non-linearity test and the estimation method are illustrated through a real example.

On fitting and forecasting the log-returns of cryptocurrency exchange rates using a new logistic model and machine learning algorithms

<abstract><p>Cryptocurrency is a digital currency and also exists in the form of coins. It has turned out as a leading method for peer-to-peer online cash systems. Due to the importance and increasing influence of Bitcoin on business and other related sectors, it is very crucial to model or predict its behavior. Therefore, in recent, numerous researchers have attempted to understand and model the behaviors of cryptocurrency exchange rates. In the practice of actuarial and financial studies, heavy-tailed distributions play a fruitful role in modeling and describing the log returns of financial phenomena. In this paper, we propose a new family of distributions that possess heavy-tailed characteristics. Based on the proposed approach, a modified version of the logistic distribution, namely, a new modified exponential-logistic distribution is introduced. To illustrate the new modified exponential-logistic model, two financial data sets are analyzed. The first data set represents the log-returns of the Bitcoin exchange rates. Whereas, the second data set represents the log-returns of the Ethereum exchange rates. Furthermore, to forecast the high volatile behavior of the same datasets, we apply dual machine learning algorithms, namely Artificial neural network and support vector regression. The effectiveness of these models is evaluated against self exciting threshold autoregressive model.</p></abstract>

On MCMC sampling in self-exciting integer-valued threshold time series models

Markov Chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches in statistics. However, due to the complex structure of the models, this method remains an open problem for threshold integer-valued time series models. This study develops Bayesian inference for a class of self-exciting integer-valued threshold autoregressive models, which is implemented by means of a new MCMC algorithm. By introducing the latent variables series, a complete data likelihood is obtained. Based on which, the full conditional distributions are easily obtained with familiar forms. Furthermore, by maximizing the complete data likelihood, the threshold parameter is also accurately estimated. Finally, the performance of the MCMC algorithm is evaluated via some simulations and a real data example.