Threshold Autoregressive Model Research Articles

Uncertain threshold autoregressive model with imprecise observations

Uncertain time series analysis is a methodology that deals with expert’s experimental time series data. Previous studies mainly focus on linear models such as an uncertain autoregressive (UAR) model. Nevertheless, the laws of motion in the real world are usually non linear. In order to model the observations that periodically vary over time, this article introduces an uncertain threshold autoregressive (UTAR) model. Then unknown parameters in the UTAR model can be estimated with the least squares estimation and residual analysis is presented. Furthermore, we discuss the forecast value and confidence interval for variables in the next periods. Ultimately, a numerical example is given.

Empirical likelihood inference for threshold autoregressive conditional heteroscedasticity model

This paper considers the parameter estimation problem of a first-order threshold autoregressive conditional heteroscedasticity model by using the empirical likelihood method. We obtain the empirical likelihood ratio statistic based on the estimating equation of the least squares estimation and construct the confidence region for the model parameters. Simulation studies indicate that the empirical likelihood method outperforms the normal approximation-based method in terms of coverage probability.

Revisiting the Canadian Lynx Time Series Analysis Through TARMA Models

The class of threshold autoregressive models has been proven to be a powerful and appropriate tool to describe many dynamical phenomena in different fields. In this work, we deploy the threshold autoregressive moving-average framework to revisit the analysis of the benchmark Canadian lynx time series. This data set has attracted great attention among non-linear time series analysts due to its asymmetric cycle that makes the investigation very challenging. We compare some of the best threshold autoregressive models (TAR) proposed in literature with a selection of thresholdautoregressive moving-average models (TARMA). The models are compared under different prospectives: (i) goodness-of-fit through information criteria, (ii) their ability to reproduce characteristic cycles, (iv) their capability to capture multimodality and (iii) forecasting performance. We found TARMAmodels that perform better than TAR models with respect to all these aspects.

Emerging Issues in Fiscal Sustainability in India: A Study of Central Government Finances, 1979–1980 to 2018–2019

The objective of the article is to examine the fiscal sustainability of the Indian central government’s finances in the era of rule-based fiscal policy. Asymmetric budgetary adjustment process and revenue–expenditure nexus are also analysed in this article by employing threshold autoregressive models/momentum threshold autoregressive models. Findings of the article reveal emerging issues in fiscal sustainability in India. The central government’s expenditure as a share of gross domestic product (GDP) has been falling continuously, leaving little room for further pruning. The current scenario of negative growth in central government’s revenue as a share of GDP, if not reversed, can become the Achilles heel of government finances in India. JEL Classification: E62, H600, H500, C32

ASYMMETRIC ADJUSTMENT OF THE SECTORIAL LENDINGDEPOSIT RATE SPREAD IN FIJI

This study investigates the asymmetric adjustment of the sectorial lending-deposit rate spread in Fiji’s banking industry using monthly data from January 2000 to February 2020. The study uses the threshold autoregressive and the momentum threshold autoregressive models to test for cointegration and to detect asymmetries. The analysis provides evidence of an asymmetric adjustment process in the sectorial lending deposit rate spread among Fijian commercial banks. This finding has important policy implications and provides better understanding of the asymmetric behaviour in Fiji’s banking industry.

Threshold autoregressive model blind identification based on array clustering

In this paper, we propose a new algorithm to estimate all the parameters of a Self Exited Threshold AutoRegressive (SETAR) model from an observed time series. The aim of this algorithm is to relax all the hypotheses concerning the SETAR model for instance, the knowledge (or assumption) of the number of regimes, the switching variables, as well as of the switching function. For this, we reverse the usual framework of SETAR model identification of the previous papers, by first identifying the AR models using array clustering (instead of the switching variables and function) and second the switching conditions (instead of the AR models). The proposed algorithm is a pipeline of well-known algorithms in image/data processing allowing us to deal with the statistical non-stationarity of the observed time series. We pay a special attention on the results of each step over the possible discrepancies over the following step. Since we do not assume any SETAR model property, asymptotical properties of the identification results are difficult to derive. Thus, we validate our approach on several experiment sets. In order to assess the performance of our algorithm, we introduce global metrics and ancillary metrics to validate each step of the proposed algorithm.

Impact of Exchange Rate Threshold Level on Stock Market Performance-Evidence from Ghana

Exchange rate plays a vital role in an economy and the purpose of this study is to investigate the impact of exchange rate threshold level on the capital market performance. The study employed a Threshold Autoregressive model introduced by Tong (1978) and Hansen (1996). The study used secondary quarter-time series data for thirty-years from 1990 to 2019. The capital market performance was measured by the value of shares traded; market turnover; market capitalization and all-shares index. However, the results revealed the following estimated threshold level of exchange rate for each performance indicator: 7.94%; 25.33%; 25.33% and 7.80% respectively. In all, the threshold level of the exchange rate estimated was 8 and 25 per cent. The findings suggest that low exchange rate is performance-enhancing. In addition, the exchange rate above the threshold level is detrimental to the capital market performance. The findings of this investigation might be helpful to the government of Ghana and policymakers as they settle on an exchange rate target to adopt to avoid the detrimental effects of high exchange rate while obtaining the growth benefits of the low exchange rate. It has indicated that the exchange rate impacts the economy more than inflation in the Sub Saharan Africa but, not much works in the subject area in Sub Saharan Africa. Therefore, I recommend that more threshold studies have to be carried out on the exchange rate in the other sectors of the economy to ascertain its impact on the economy.

Absence of evidence of climate-driven cycles in Carboniferous deposits of Joggins, Nova Scotia, Canada: influence of salt withdrawal tectonics on deposition and pedogenesis

ABSTRACT During the Late Paleozoic Ice Age, the fault-bounded equatorial Cumberland Basin of Nova Scotia experienced rapid subsidence, accumulating kilometer-thick fluvial sedimentary units derived from two highlands to the northwest and southeast. Major variations are recorded in the paleosols exposed at the Joggins Fossil Cliffs, ranging from oxidized and well-drained paleosols with recognizable vertic features to highly reduced organic-rich paleosols. These different soil lithologies suggest alternating conditions between well-drained floodplain environments and water saturation associated with overall poor soil development. Although halokinetic subsidence of the Cumberland Basin is known to have been operative during deposition of these units, previous research favored glacio-eustatic processes as the primary forcing mechanism of sedimentation. A total of 474 fluvial aggradational cycles were identified within a kilometer-thick interval and show a fluctuating accommodation history with a very abrupt nature. The series of fluvial aggradational cycles was used to develop threshold autoregressive models based on 1) their thickness, 2) their paleosol thickness, 3) their sandstone content, and 4) their paleosol-to-sandstone ratio. For each model, results suggest no evidence of statistically significant cyclicity, contradicting the hypothesis that fluvial sedimentation was mainly driven by glacio-eustatic cyclothems. Additionally, a total of 7 lithologies were recognized through 1,655 beds. Evaluation of 8 spherical semivariograms suggests no evidence for cyclicity in the frequency, order, or distribution of the data based on lithologies, although some covariance was found at distances between 550 and 750 m suggesting similar processes controlling sedimentation in the lower and upper Joggins Formation. The Cumberland Basin is known to have been rapidly subsiding, mainly because of ductile deformation of salt deposits in the deeper basinal units. Our results suggest that Joggins records tectonically induced ponding of a part of the sedimentary basin, allowing more extensive preservation of abundant coal and organic-rich units, as well as still-standing fossil forests exposed along the cliffs. These new results suggest that tectonic subsidence of the Cumberland Basin during the Late Paleozoic Ice Age was a more important driver of fluvial sedimentation than previously thought. This novel application of the TAR methodology provides a mathematical description of the sediment accumulation history of terrestrial basins when applied to conformable sedimentary successions, along with the means of linking paleosol development to climatic processes.

Has the Euro Shrunk the Band? Relative Purchasing Power Parity Convergence in a Currency Union*

AbstractI study the effects of entry to the European Monetary Union (EMU) on relative purchasing power parity (PPP) convergence using monthly disaggregated price indices from 32 European countries from 1999 to 2016. I examine the entry of Cyprus, Malta, Slovakia, and Slovenia to the EMU, and I estimate the bands of inaction of relative prices before and after entry using a threshold autoregressive model. I find a positive effect of the EMU on relative PPP convergence: after entry, the bands of inaction with EMU members fell by 17 percent. Cross‐sectional evidence supports the theoretical prediction that bands of inaction are related to transaction costs.

On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria

The linear time series model refers to the class of models for which fixed correlation parameters can fully explain the dependency between two random variables, but many real-life circumstances, such as monthly unemployment results, supplies and demands, interest rate, exchange rate, share prices, rainfall, etc., violate the assumption of linearity. For fitting and forecasting of nonlinear time series data, the self-exiting threshold autoregressive (SETAR) model was suggested. Using R to generate random nonlinear autoregressive data, a Monte Carlo simulation was performed, the SETAR model was fitted to the simulated data and Lafia rainfall data, Nasarawa State, Nigeria to determine the best regime orders and/or scheme number to make future forecast. Using Mean Square Error (MSE) and Akaike Information Criteria (AIC), the relative performance of models was examined. At a specific autoregressive order, regime order, sample size and step ahead, the model with minimum criteria was considered as the best. The results show that the best autoregressive and regime orders to be chosen are 3rd and 2nd [SETAR (3, 2)] respectively for fitting and forecasting nonlinear autoregressive time series data with small and moderate sample sizes. As the sample size increases, the output of the four models increases. Finally, it is shown that when sample size and number of steps forward are increased, the efficiency and forecasting capacity of the four models improves.

Conditional Threshold Autoregression (CoTAR)

We propose a new time series model where the threshold is specified as an empirical quantile of recent observations of a threshold variable. The resulting conditional threshold traces the fluctuation of the threshold variable, which can enhance the fit and interpretation of the model. In the proposed conditional threshold autoregressive (CoTAR) model, the existence of threshold effects can be tested by wild-bootstrap tests which incorporate all possible values of nuisance parameters. The estimation and hypothesis testing of the CoTAR model satisfy desired statistical properties in both large and small samples. We fit the CoTAR model to new confirmed COVID-19 cases in the U.S. and Japan. Significant conditional threshold effects are detected for both countries, and the implied persistence structures are consistent with the fact that the number of new confirmed cases in the U.S. is larger than in Japan.

IN- AND OUT-OF-SAMPLE PERFORMANCE OF NONLINEAR MODELS IN INTERNATIONAL PRICE DIFFERENTIAL FORECASTING IN A COMMODITY COUNTRY FRAMEWORK

This paper presents an analysis of a group of small commodity-exporting countries' price differentials relative to the US dollar. Using unrestricted self-exciting threshold autoregressive models (SETAR), we evaluate the sixteen national Consumer Price Indexes (CPI) differentials relative to the US dollar CPI. Out-of-sample forecast accuracy is estimated through calculation of mean absolute errors measures based on the monthly rolling window and recursive forecasts, and this estimation is extended to three additional models, namely a logistic smooth transition regression (LSTAR), an additive nonlinear autoregressive model (AAR), and a simple neural network model (NNET). Our preliminary results confirm the presence of some form of nonlinearity in most of the analyzed countries. The parsimonious AR(1) model does not appear to perform any worse than any nonlinear model in the rolling sample exercise. However, in terms of a longrun equilibrium driven by purchasing power parity, its validity is undermined by the results of the recursive estimates and the outcome of the Diebold-Mariano type tests, which favor generally the Heckscher commodity points theory. As a policy advice to commodity-exporting countries, we find no apparent reason to suggest commodity export price pegging as a generalized foreign exchange policy.

Threshold effects and unit roots of real commodity prices since the mid-nineteenth century

This paper investigates whether a unit root process and nonlinearities can characterize real commodity prices for six major primary goods. An unconstrained two-regime threshold autoregressive model is used with an autoregressive unit root. Among the main results, it is found that terms of trade for agricultural, mineral, non-tropical, and non-oil goods are nonlinear processes that are characterized by a unit root process. The finding of nonlinearities explains why the deterioration of the terms of trade has been episodic. Additionally, we found there is no statistical evidence supporting the Prebisch-Singer hypothesis for agricultural, mineral, non-tropical, and non-oil goods.

IDENTIFIKASI MODEL SELF-EXCITING THRESHOLD AUTOREGRESSIVE DENGAN SWITCHING TWO REGIME (KASUS PADA DATA EKSPOR AGRIKULTUR DI INDONESIA)


 A time series model that explain the structural changes associated with data in a certain time period is the Threshold Autoregressive (TAR) model. The basic of the TAR model there are some different usage regimes in autoregressive analysis. One model based on TAR is a self-exciting threshold autoregressive (SETAR) model with the same delay parameters for each regimen. The SETAR model has a linear nature in each regime but being nonlinear if the models of each regime are combined. In addition, this model can improve jump data that cannot be captured by linear time series models. This means that the SETAR model has high-level parameters through an appropriate switching regime that is applied to agricultural export data in Indonesia. The purpose of this reseach is to test the estimated SETAR parameter model and apply it to Indonesian agricultural export data. There are three methods that can be done for estimating of parameter of SETAR model, namely the conditional quadratic sequential method, ordinary least square (OLS) and nonlinear least square (NLS). In this research, the two stage parameter estimation method is used with OLS and the second stage parameter estimation is used to optimisze the parameter values ​​that are not significant in the model. In its application, the SETAR model (2,1,1) was obtained to model agricultural export data in Indonesia and the MAPE value was 25%.

Dissecting Tether’s Nonlinear Dynamics during Covid-19

The present study is on the five cryptocurrency daily mean return time series linearity dynamics during the Covid-19 period. These cryptocurrencies were chosen based on their influence on the market, primarily driven by its market capitalisation. Tether is included as the most important stable coin on the market, nominally pegged to the U.S. dollar (USD). The reason to investigate it is that there are some inconsistencies in its behaviour as opposed to the other four cryptocurrencies. This study found that the behaviour of Tether cryptocurrency daily average return time series pattern is highly nonlinear and chaotic in nature, whereas the other four cryptocurrencies (namely Bitcoin, Ethereum, XRP and Bitcoin Cash) daily average return time series were found to be linear in nature. To further study Tether’s nonlinear time series rich dynamics, this study deployed one category of the regime switching models popularly known as the threshold regressions. The study estimates fairly suggest that both the threshold autoregression (TAR) and smooth transition autoregressive (STAR) models with lag 1 are adequate to capture the rich nonlinear and chaotic dynamics of Tether’s daily average return time series.

Bayesian estimation for threshold autoregressive model with multiple structural breaks

This paper provides a Bayesian setup for multiple regimes threshold autoregressive model with possible break points. A full conditional posterior distribution is obtained for all model parameters with considering suitable prior information. Threshold and break point variables do not attain standard form distributions. To compute posterior distributions, we apply the Gibbs sampler with the Metropolis-Hastings algorithm. A variety of loss functions are considered for optimizing the risk associated with each parameter. For empirical evidence, simulation study and real data illustration are carried out.

Bitcoin option pricing with a SETAR-GARCH model

This paper aims to study the pricing of Bitcoin options with a view to incorporating both conditional heteroscedasticity and regime switching in Bitcoin returns. Specifically, a nonlinear time series model combining both the self-exciting threshold autoregressive (SETAR) model and the generalized autoregressive conditional heteroscedastic (GARCH) model is adopted for modeling Bitcoin return dynamics. Specifically, the SETAR model is used to model regime switching and the Heston-Nandi GARCH model is adopted to model conditional heteroscedasticity. Both the conditional Esscher transform and the variance-dependent pricing kernel are used to specify pricing kernels. Numerical studies on the Bitcoin option prices using real bitcoins data are presented.

Introduction to the Theme Issue: The Skew-Normal and Related Distributions

This theme issue on the skew-Normal and related distributions is motivated by the workshop held on November 6th, 2017 in memory of Antonella Capitanio, one year after her premature loss. The issue contains the transcript of the conversation between Angela Montanari, Adelchi Azzalini and Narayanaswamy Balakrishnan regarding their scientific collaboration with Antonella. Moreover, the last unpublished work of Antonella Capitanio on mixtures of skew normal distributions is reproduced here with the kind permission of her family. We also take the opportunity to re-present the seminal 1986 Azzalini paper, together with corrections and comments from the author. The last contribution, by Howell Tong and Dong Li, concerns the interesting relationship between skew symmetric distributions and threshold autoregressive models.

Bayesian estimation of subset threshold autoregressions: short-term forecasting of traffic occupancy

Traffic management authorities in metropolitan areas use real-time systems that analyze high-frequency measurements from fixed sensors, to perform short-term forecasting and incident detection for various locations of a road network. Published research over the last 20 years focused primarily on modeling and forecasting of traffic volumes and speeds. Traffic occupancy approximates vehicular density through the percentage of time a sensor detects a vehicle within a pre-specified time interval. It exhibits weekly periodic patterns and heteroskedasticity and has been used as a metric for characterizing traffic regimes (e.g. free flow, congestion). This article presents a Bayesian three-step model building procedure for parsimonious estimation of Threshold-Autoregressive (TAR) models, designed for location- day- and horizon-specific forecasting of traffic occupancy. In the first step, multiple regime TAR models reformulated as high-dimensional linear regressions are estimated using Bayesian horseshoe priors. Next, significant regimes are identified through a forward selection algorithm based on Kullback-Leibler (KL) distances between the posterior predictive distribution of the full reference model and TAR models with fewer regimes. Given the regimes, the forward selection algorithm can be implemented again to select significant autoregressive terms. In addition to forecasting, the proposed specification and model-building scheme, may assist in determining location-specific congestion thresholds and associations between traffic dynamics observed in different regions of a network. Empirical results applied to data from a traffic forecasting competition, illustrate the efficacy of the proposed procedures in obtaining interpretable models and in producing satisfactory point and density forecasts at multiple horizons.

On using predictive-ability tests in the selection of time-series prediction models: A Monte Carlo evaluation

To select a forecast model among competing models, researchers often use ex-ante prediction experiments over training samples. Following Diebold and Mariano (1995), forecasters routinely evaluate the relative performance of competing models with accuracy tests and may base their selection on test significance on top of comparing forecast errors. With extensive Monte Carlo analysis, we investigated whether this practice favors simpler models over more complex ones, without gains in forecast accuracy. We simulated the autoregressive moving-average model, the self-exciting threshold autoregressive model, and vector autoregression. We considered two variants of the Diebold–Mariano test, the test by Giacomini and White (2006), the F-test by Clark and McCracken (2001), the Akaike information criterion, and a pure training-sample evaluation. The findings showed some accuracy gains for small samples when applying accuracy tests, particularly for the Clark–McCracken and bootstrapped Diebold–Mariano tests. Evidence against this testing procedure dominated, however, and training-sample evaluations without accuracy tests performed best in many cases.