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The output gap, the difference between potential and actual output, has a direct impact on policy decisions, e.g., monetary policy. Estimating this gap and its further analysis remain the subject of controversial debates due to methodological problems. We propose a local polynomial regression combined with a Self-Exciting Threshold AutoRegressive (SETAR) model and its forecasting extension for a systematic output gap estimation. Furthermore, local polynomial regression is proposed for the (multivariate) OECD production function approach and its reliability is demonstrated in forecasting output growth. A comparison of the proposed gap to the Hodrick–Prescott filter as well as to estimations by experts from the FED and OECD shows a higher correlation of our output gap with those from those economic institutions. Furthermore, sometimes gaps with different magnitude and different positions above or below the trend are observed between different methods. This may cause competing policy implications which can be improved with our results.

In this paper, we look at the instability of a self-exciting regime-switching autoregressive model, specifically regime-switching models that are locally stable in each of their regimes. It turns out that the local stability of each regime is insufficient to ensure the overall stability of the model. The instability’s mechanism is described, and a sufficient condition for the instability is provided.

The aim of the paper is to compare the forecasting performance of a class of statedependent autoregressive (SDAR) models for univariate time series with two alternative families of nonlinear models, such as the SETAR and the GARCH models. The study is conducted on US GDP growth rate using quarterly data. Two methods of forecast comparison are employed. The first method consists in evaluation the average performance by using two measures such as the root mean square error (RMSE) and the mean absolute error (MAE) over different forecast horizons, while the second method make use of one of the most used statistical test to compare the accuracy of two forecast methods such as the Diebold-Mariano test. JEL classification numbers: C22, E37, F47. Keywords: Nonlinear models for time series, GDP growth rate, Forecasting accuracy.

Evaporation is a key element for water resource management, hydrological modelling, and irrigation system designing. Monthly evaporation (Ep) was projected by deploying three machine learning (ML) models included Extreme Gradient Boosting, ElasticNet Linear Regression, and Long Short-Term Memory; and two empirical techniques namely Stephens-Stewart and Thornthwaite. The aim of this study is to develop a reliable generalised model to predict evaporation throughout Malaysia. In this context, monthly meteorological statistics from two weather stations in Malaysia were utilised for training and testing the models on the basis of climatic aspects such as maximum temperature, mean temperature, minimum temperature, wind speed, relative humidity, and solar radiation for the period of 2000–2019. For every approach, multiple models were formulated by utilising various combinations of input parameters and other model factors. The performance of models was assessed by utilising standard statistical measures. The outcomes indicated that the three machine learning models formulated outclassed empirical models and could considerably enhance the precision of monthly Ep estimate even with the same combinations of inputs. In addition, the performance assessment showed that Long Short-Term Memory Neural Network (LSTM) offered the most precise monthly Ep estimations from all the studied models for both stations. The LSTM-10 model performance measures were (R2 = 0.970, MAE = 0.135, MSE = 0.027, RMSE = 0.166, RAE = 0.173, RSE = 0.029) for Alor Setar and (R2 = 0.986, MAE = 0.058, MSE = 0.005, RMSE = 0.074, RAE = 0.120, RSE = 0.013) for Kota Bharu.

This paper evaluates the forecasting performance of linear and non-linear time series models of some macroeconomic variables viz a viz the forecasts outlook of these variables generated by professionals in international economic organizations i.e. the International Monetary Fund (IMF) and the Organization of Economic Cooperation and Development (OECD). Many time series and econometrics models are used to forecast financial and macroeconomic variables. The accuracy of such forecasts depends crucially on careful handling of nonlinearity present in the time series. The debate of forecasting ability of linear vs nonlinear models is far from settled. These models use the past patterns of the economic time series to infer the parameters of the underlying stochastic process and use them to make forecasts. In doing so these models use only the information contained in the past data. However the economists working in professional international economic organizations not only look at the past trends but use the condition of local and global economy prevailing at the time and expected future path of economies as well as their professional expertise and judgment to arrive at forecasts of macroeconomic variables. However the specific underlying models and methodology used by the economists generating these forecast is usually not communicated to the public. In comparison to the forecasts of these organizations the time series models are well developed and accessible to researchers working anywhere around the globe. Thus it is an interesting task to compare the foresting ability of linear and nonlinear time series models. This paper aims at comparing the forecasts from these models to assess how well they compete with forecasts generated from the professional economists employed by international economic organizations. The nonlinear models employed in this study are quite well known namely the Self Exciting Threshold Autoregressive (SETAR) model and the Markov Switching Autoregressive (MSAR) model. The linear models employed are the AR and ARMA models. The paper have used annual data of three macroeconomic time series variables GDP growth, consumer price inflation and exchange rate of G7 countries i.e. Canada, France, Germany, Italy, Japan, United Kingdom (UK) and United States of America (USA) as well as an emerging south Asian economy namely Pakistan. Three forecast accuracy criteria i.e. Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) are employed and the statistical significance of difference in forecasts is assessed using the Diebold-Mariono test. The results show that the forecasting ability of nonlinear Regime Switching models SETAR and MSAR is superior to the linear models. Further, although the point forecasts of linear and nonlinear models are not superior to that of economic organizations but in more than 60 percent of the cases considered the forecasting accuracy of two sets of forecast is not statistically significantly different.

There are two types of hospital in general, which are government and private hospitals. This study will help us to understand the customer perception, satisfaction and behavioural intention of hospital meal services in both government and private hospitals in Alor Setar, Kedah. Private and government hospitals differ in their style of food offering and service system. From this, customer perception, satisfaction, and behavioural intentions were investigated using a questionnaire survey with 150 respondents using descriptive and inferential analysis. The study shows that between government and private hospitals in Alor Setar, Kedah, the respondents show a positive perception of hospital meal services in Alor Setar in both government and private hospitals. In terms of customer satisfaction, both types of hospital show high satisfaction from all respondents. However, private hospital scores a bit higher in terms of satisfaction since the services and facilities are more upgraded than those of the government hospital of which respondents did not have such a high expectation for satisfaction since the fee is much lower than the private hospital. In the comparison of hospital meal services in terms of socio-demographic profile, there is no significant difference in gender and education level in both types of hospital. However, age and income level show a significant level of p=0.011 in age for a government hospital and p=0.018 and p=0.020 in monthly income for a private hospital. For the relationship of all variables (customer perception, satisfaction and behavioural intention), all of those show a robust, lively and direct relationship with each other. Hence, this study can help public and private hospitals improve their meal services and image to attract more customers.

In this paper, the tendency properties of Turkish real effective exchange rate with an inaction band are examined in nonlinear nature. The general SETAR (3) model is used. This is a convenient way of presenting the inactivity band caused by the transfer costs and other factors. In this modelling, the stationarity is defined globally which is allow to unit root in the corridor regime but the outers regimes must be a mean reverting process. The data are used de-meaned and de-trended form. For de-meaned data, we execute both the linearity and the stationarity tests. For de-trended data, only the linearity test is executed. According to our empirical results, the statistical evidence is poor for the validity of PPP in even nonlinear nature. The null of unit root is not rejected for the CPI based reel effective exchange rate and it is rejected only 5% significance level for PPI based one. However, take into account possibility of the existence of trend component, Turkish real effective exchange rates are well characterized by nonlinear process with inactivity band and a tendency property. While these findings support the transaction costs hypothesis, they do not strongly support the validity of the PPP hypothesis.

The prediction of rainfall on monthly and seasonal time scales is not only scientifically challenging but is also important for planning and devising agricultural strategies. In this paper, the study is conducted to examine the pattern of monthly rainfall in Alor Setar, Kedah within ten years which is from 2008 to 2018. This paper considered a model based on real data that obtained from Department of Meteorology Malaysia. This study indicates that the monthly rainfall in Alor Setar has a seasonal and trend pattern based on yt vs t plotting, autocorrelation function and Kruskal Wallis Test for seasonality. The examined rainfall time-series modelling approaches include Naïve Model, Decomposition Method, Holt-Winter’s and Box-Jenkins ARIMA. Multiplicative Decomposition Method was identified as the best model to forecast rainfall for the year of 2019 by analysing the previous ten-year’s data (2008-2018). As a result from the forecast of 2019, October is the wettest month with highest forecasted rainfall of 276.15mm while the driest month is in February with lowest forecasted rainfall of 50.55mm. The model is therefore adequate and appropriate to forecast future monthly rainfall values in the catchment which can help farmers to plan their farming activities ahead of time.

With the development of new maintenance techniques based on condition monitoring, diagnostic and prognostic methods are also being extended. In the process of estimating the remaining useful life (RUL) using the data-driven approach, it is difficult to determine the degradation state of the equipment with several sources of information and to predict the remaining useful life with non-smooth data that have sudden changes inherent in the monitoring data. In this paper, a procedure is presented to address these two issues in which the degradation state of the equipment is determined in the presence of several information sources using a combination of the fuzzy c-means clustering and the combination rules of the Dempster-Shafer theory, and the prediction of the data for the estimation of the remaining useful life is carried out using an autoregressive Markov regime-switching (ARMRS) model that is capable of dealing with sudden changes in condition monitoring data. To evaluate the proposed model, the bearing dataset of the FEMTO-ST Institute is used. The experimental results show the high competitiveness of the proposed procedure compared to similar methods.

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.

PurposeThis study analyses agricultural land price dynamics in order to better understand price development and to improve forecast accuracy. Understanding the evolution of agricultural land prices is important when considering sound investment decisions.Design/methodology/approachThis study applies threshold autoregression to model agricultural land prices. The data includes quarterly observations on Finnish agricultural land prices.FindingsThe study shows that Finnish agricultural land prices exhibit regime-switching behaviour when using past changes in prices as a threshold variable. The threshold autoregressive model not only fits the data better but also improves the accuracy of price forecasts compared to the linear autoregressive model.Originality/valueThe results show that a sharp fall in agricultural land prices temporarily changes the regular development of prices. This information significantly improves the accuracy of price predictions.

Modelling the dynamic dependent data by the linear approach is the most popular among the researchers because of its simplicity in calculation and approximation, however, in real-world phenomena, most of the time-dependent data follow the nonlinearity. Moreover, most of the nonlinear modelling of time-dependent data have found in the financial applications. Besides this sector, the authors of this paper found the presence of nonlinearity in meteorological data with the help of four popular nonlinearity tests. Furthermore, there is a scarcity of the application of regime-switching threshold autoregressive nonlinear time-series model in forecasting the weather variables like temperature. Thus, this paper aims to compare the forecasting accuracy of the linear autoregressive (linear AR), self-exciting threshold autoregression (SETAR), logistic smooth transition autoregressive model (LSTAR), and feed-forward neural network (ANNs) and fitted with the determination of regime and hyperparameters. After fitting the models, twenty steps ahead forecast considered for the comparison along with the selected model selection criteria; and results depict that the LSTAR models are selected as the most appropriate fitted models for forecasting the daily Average, Maximum and Minimum temperature. Finally, it has observed that the average, as well as maximum temperature of Dhaka, Bangladesh, have an increasing trend and minimum temperature having a decreasing trend.

This study revisits the relationship between energy and electricity consumption with economic activity for India applying threshold vector error correction model and non-linear ARDL methods to expl...

This paper has two aims. First, we measure the asymmetric effect of crude oil prices on stock returns under a regime switching framework in the context of major oil exporting countries namely: the United Arab Emirates (UAE), Qatar, Saudi Arabia, Russia, Venezuela and Kuwait. The key results from our baseline model suggest that stock returns in all the markets exhibit regime switching behaviour with the bull market regime dominating most of the period except for Russia. Also, we found strong linkages among the bear market periods with Qatar and Saudi Arabia exhibiting the strongest negative linkage. The UAE and Saudi Arabia are more likely to experience bearish market conditions at same period whereas Russia is segmented from other markets except Saudi Arabia. Results from our augmented model suggest that the effect of crude oil price varies across regimes, impacting more strongly on stock returns during recession than during periods of expansion especially in Venezuela and Saudi Arabia. Secondly, we examine volatility spillover from crude oil prices to stock returns and found a substantial cyclical volatility spillover from crude oil to returns especially in the UAE, Russia and Qatar and that the evolution of spillover follows key developments in the market for crude oil, geopolitical risks and then, global economic conditions. Our results hold profound implications for risk management and portfolio diversification strategy in oil exporting region.

To introduce more flexibility in process‐parameters through a regime‐switching behavior, the classical autoregressive (AR) processes have been extended to self‐exciting threshold autoregressive (SETAR) processes. However, the stationary marginal distributions of SETAR processes are usually difficult to obtain in explicit forms and, therefore, they lack appropriate characterizations. The stationary marginal distribution of a multivariate (d‐dimensional) SETAR process of order one MSETARd(1) with multivariate normal innovations is shown to belong to the unified skew‐normal (𝒮𝒰𝒩) family and characterized under a fairly broad condition. This article also characterizes the stationary marginal distributions of a subclass of the MSETARd(1) processes with symmetric multivariate stable innovations. To characterize the stationary marginal distributions of these processes, the authors show that they belong to specific skew‐distribution families, and for a given skew‐distribution from the corresponding family, an MSETARd(1) process, with stationary marginal distribution identical to the given skew‐distribution, can be associated. Furthermore, this article illustrates a diagnostic of an MSETAR2(1) model using the corresponding stationary marginal density.

This paper treats estimation in a class of new nonlinear threshold autoregressive models with both a stationary and a unit root regime. Existing literature on nonstationary threshold models have basically focused on models where the nonstationarity can be removed by differencing and/or where the threshold variable is stationary. This is not the case for the process we consider, and nonstandard estimation problems are the result. This paper proposes a parameter estimation method for such nonlinear threshold autoregressive models using the theory of null recurrent Markov chains. Under certain assumptions, we show that the ordinary least squares (OLS) estimators of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary regime can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary regime has a nonstandard asymptotic distribution. In the limit, the rate of convergence in the stationary regime is asymptotically proportional to n-1/4, whereas it is n-1 in the nonstationary regime. The proposed theory and estimation method are illustrated by both simulated data and a real data example.

Volatility is the degree of variation in the stock price over time. The stock price is volatile due to many factors, such as demand, supply, economic policy, and company earnings. Investing in a volatile market is riskier for stock traders. Most of the existing work considered Generalized Auto-regressive Conditional Heteroskedasticity (GARCH) models to capture volatility, but this model fails to capture when the volatility is very high. This paper aims to estimate the stock price volatility using the Markov regime-switching GARCH (MSGARCH) and SETAR model. The model selection was carried out using the Akaike-Informations-Criteria (AIC) and Bayesian-Information Criteria (BIC) metric. The performance of the model is evaluated using the Root mean square error (RMSE) and mean absolute percentage error (MAPE) metric. We have found that volatility estimation using the MSGARCH model performed better than the SETAR model. The experiments considered the Indian stock market data.

International audience; 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.

The unquenchable thirst of several sectors to crude oil in the recent years makes a common belief regarding its key role towards the acceleration of the recent economic recession and financial instability. This paper aims to examine the nonlinear impact of oil shocks on the sovereign credit risk for a sample of 38 worldwide oil-producing and oil-consuming countries, over a period ranging from January 2006 to March 2017. In contrast to the existing literature, CDS volatility is employed as a measure for the creditworthiness level, rather than the commonly used CDS spreads first-order moment. The methodological framework used in this paper goes beyond previous studies and takes into account more financial data features (long memory behavior, asymmetric effects and nonlinearities) according to a self-exciting regime switching model. Results reveal some dissimilarities in the explanatory power of the exogenous variables between regimes and across countries. Particularly, restricted evidences of the impact of oil shocks on sovereign CDS volatility are detected during the stable regime, whilst during the risky regime credit volatility becomes more sensitive to oil market conditions for most of the studied countries. Overall, the decline in oil price worsens the public finances tenability whether the country is oil-related or not.

This paper deals with the problem of joint determination of the delay parameter and autoregressive orders of the Self-Exciting Threshold Autoregressive (SETAR) models. More specifically, we propose...

Prediction of river flow as a fundamental source of hydrological information plays a crucial role in various fields of water projects. In this study, at first, the capabilities of two time series analysis approaches, namely self-exciting threshold autoregressive (SETAR) and generalized autoregressive conditional heteroscedasticity (GARCH) models, then three artificial intelligence approaches including artificial neural networks (ANN), multivariate adaptive regression splines (MARS), and random forests (RF) models were investigated to predict monthly river flow. For this purpose, monthly river flow data of Brantford and Galt stations on Grand River, Canada, for the period from October 1948 to September 2017 were used and their performances were evaluated based on various evaluation criteria. The SETAR model showed better performance than the GARCH one in prediction of river flows at the stations of study. Additionally, the stand-alone MARS and RF models performed slightly better than the ANN. Next, hybrid models were developed by coupling the used ANN, MARS, and RF models with SETAR and GARCH models as the non-linear time series models. The performance of various models presented in this study indicated that the new hybrid models demonstrated a much better performance compared with the stand-alone ones at both stations. Among the developed hybrid models, the RF-SETAR models generally had the best accuracy to improve the river flows modeling. As a result, it can be concluded that the presented methodology can be used to predict hydrological time series such as river flow with a high level of accuracy.

In recent years, many efforts have been made to develop hybrid models for hydrological time series modeling. The present study introduces novel hybrid models by hybridizing time series models with artificial intelligence (AI) methods. These hybrid models were used to model monthly streamflow time series for the Ocmulgee and Umpqua River stations, located in Georgia and Oregon, USA, respectively. AI-based approaches, including gene expression programming (GEP), multivariate adaptive regression splines (MARS), and simple multiple linear regression (MLR), were integrated with fractionally auto-regressive integrated moving average (FARIMA) and self-exciting threshold auto-regressive (SETAR) time series models. Accordingly, six novel hybrid models, namely GEP-FARIMA, MARS-FARIMA, MLR-FARIMA, GEP-SETAR, MARS-SETAR, and MLR-SETAR, were developed. The accuracy of the proposed models was then compared to the standalone GEP, MARS, MLR, FARIMA, and SETAR models. Results showed that time series models were superior to AI and MLR approaches. In addition, the hybrid models offered more accurate results than the standalone models when modeling monthly streamflow time series.

Although hydrological processes are generally nonlinear, linear time series models are commonly adopted in the field of water sciences. Nonlinear approaches such as threshold time series and conditional heteroscedasticity models are still seldom used. In this study, first, two- and three-regime Self-Exciting Threshold Autoregressive (SETAR) models are used to model the mean behavior of daily streamflows. The residual time series computed from the difference between observations and lag-one time-ahead best-estimates of the fitted models are also obtained. Second, the conditional variance behavior of the residual series obtained from the two- and three-regime SETAR models is modeled using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The GARCH model is hence used to capture the time-varying variance behavior of residuals as a nonlinear phenomenon and thus it removes the existence of autoregressive conditional heteroscedasticity so-called ARCH effect. Finally, the performance of SETAR models and their combination with the GARCH model are evaluated. Six deseasonalized daily streamflow series from upstream watershed rivers of Zarrineh Rood dam, in the southern part of Lake Urmia in Iran, are used to illustrate and test the procedure. The McLeod-Li test, a formal test for demonstrating the ARCH effect, indicates that the ARCH effect exists in all residual series, which means that the residuals of streamflow time series are nonstationary in terms of the variance. Results indicate that the hybrid SETAR-GARCH models performed better than the models without GARCH component. Results demonstrate also that the use of nonlinear SETAR and GARCH improves streamflow modeling efficiency by capturing the heteroscedasticity in the residuals of nonlinear threshold time series.

In this paper a robust approach to modeling electricity spot prices is introduced. Differently from what has been recently done in the literature on electricity price forecasting, where the attention has been mainly drawn by the prediction of spikes, the focus of this contribution is on the robust estimation of nonlinear SETARX models (Self-Exciting Threshold Auto Regressive models with eXogenous regressors). In this way, parameter estimates are not, or very lightly, influenced by the presence of extreme observations and the large majority of prices, which are not spikes, could be better forecasted. A Monte Carlo study is carried out in order to select the best weighting function for Generalized M-estimators of SETAR processes. A robust procedure to select and estimate nonlinear processes for electricity prices is introduced, including robust tests for stationarity and nonlinearity and robust information criteria. The application of the procedure to the Italian electricity market reveals the forecasting superiority of the robust GM-estimator based on the polynomial weighting function with respect to the non-robust Least Squares estimator. Finally, the introduction of generation from renewable sources in the robust estimation of SETARX processes contributes to the improvement of the forecasting ability of the model.