GSA-based maximum likelihood estimation for threshold vector error correction model

In the analytical balance sheet of the base money monetary authority, Bank Indonesia explained that net foreign assets (NFA) affected the circulation of base money, including currency. This gives an assumption regarding the indication of a causal relationship between currency circulation and NFA. In addition to the causality test, the primary purpose of this study is to identify long-term equilibrium relationships between NFA and Currency Circulation. The cointegration test obtained r = 1, indicating cointegration (long-term equilibrium). Time series data plots of these two variables tend to have a trend and are not stationary. The Vector Error Correction Model (VECM) is applied as an analytical method used to correct long-term relationships between variables that are not stationary. However, in the concept of VECM deviation and short-term dynamics, the association is assumed to be linear. At the same time, in applying economics, the relationship between economic variables is not necessarily linear. The significance test for the presence of a threshold using a fixed regressor bootstrap shows a threshold effect or nonlinear VECM, so it is necessary to use an analytical method that can combine nonlinearity and cointegration through the Threshold Vector Error Correction Model (TVECM). In this study, modeling of TVECM 2 regimes and three regimes were carried out. TVECM 3 regimes obtain the best model with two threshold values ​​of -310850 and -260156.

This study analyzes threshold effects in the relationship between Foreign Direct Investment (FDI) and international trade in 50 emerging markets from 2010 to 2023 using Panel Threshold Vector Error Correction Models. It identifies an institutional quality threshold at 0.647, above which FDI and trade show stronger long-term relationships and faster adjustment speeds. Countries with higher institutional quality converge to equilibrium 2.3 times faster and have less regime persistence. These findings suggest that improvements in institutional quality above this threshold significantly enhance FDI-trade integration, offering clear targets for policy interventions in emerging markets.

This article analyzes the link between world prices and producer prices of rubber in Côte d’Ivoire. Using monthly data from 2006 to 2016, we gave special attention to structural breaks in the data and asymmetry in the transmission process. Empirical results validate the presence of two breaks in the data series, both in 2008 and 2011 corresponding to a general surge in commodity prices. A multivariate threshold vector error correction model (TVECM) allows us to test the presence of asymmetry. The results strongly support the linearity hypothesis against k-regime TVECM. From there, a linear VECM reveals that changes in rubber world prices are strongly transmitted to Ivorian producer prices. In case of a world price permanent decrease, this will be devastating for small producer incomes, since financial markets are essentially missing in those rural areas and switching costs for perennial crops are huge. Some recommendations are given to prevent such a crisis.

Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models

ABSTRACTThe most important environmental problem of our age is global warming. One of the most CO2 emitter countries is the United States. The CO2 emission and end-use sector energy consumption relationship in the United States has been investigated by using the threshold vector error correction model (VECM). According to the results which were obtained from empirical analysis, the relationships between CO2 emission and end-use sector energy consumption in the United State show different properties.

In this manuscript, an energy-efficient train operation between successive stations is studied. Cruising and coasting, two basic motion phases of train, should be taken into consideration in order to decrease energy consumption. Determining the optimal switching points from one motion phase into another is key in the energy saving. It is shown that, genetic algorithm and simulated annealing, when employed in a hybrid algorithm, complement each other in finding such switching points. For a performance verification of the hybrid optimization approach, multiple test tracks with different lengths are considered. Also certain real life constraints are taken into account such as punctuality and maximum speed limit. Obtained results are compared to the single genetic algorithm and it is shown that the hybrid algorithm built as a cascade combination of genetic algorithm and simulated annealing can reach optimum solution with better accuracy and lower time consumption.

In this paper, a single machine scheduling problem with an overtime constraint is studied. The objective is to minimise the total penalty cost defined as the sum of tardy, early, and overtime costs. Three novel hybrid algorithms that hybridise a new heuristic with genetic algorithm, tabu search, and simulated annealing, referred to as GAH, TSH, and SAH, are proposed to solve the problem. In each iteration of the proposed hybrid algorithms, a given metaheuristic is used to determine a sequence of jobs, whereas a new heuristic is used to minimise the total penalty cost of the sequence using a backward-forward scheduling technique and a penalty cost trade-off process. Exhaustive experiments are conducted to evaluate the effectiveness of the proposed hybrid algorithms. For medium-scale and large-scale problems, TSH with its best common parameter setting referred to as TSH2, clearly outperforms the exact algorithm, whereas both algorithms can obtain the optimal solution for small-scale problems. In addition, the computational time of TSH2 is in an acceptable range for the planner.

Achieving high stable Power Transfer Efficiency (PTE) in Wireless Power Transfer (WPT) systems remains challenging due to the nonlinear, multimodal nature of the optimization space. Conventional algorithms such as Genetic Algorithms (GA), Differential Evolution (DE), and Simulated Annealing (SA) often face premature convergence, sensitivity to parameter settings, and inconsistent performance across runs. To overcome these issues, this study introduces the Evolutionary-Swarm Hybrid Algorithm (ESHA), which integrates DE for directional exploration, GA crossover for population diversity, SA for adaptive convergence, and Lévy Flights for stochastic global search. ESHA was implemented on a WPT system with a fixed 20 cm transmission distance and compared with GA, DE, and SA using three performance indicators: PTE, convergence speed, and computational efficiency. Results show that ESHA achieved a maximum PTE of 97.18%, surpassing GA (96.81%), DE (96.65%), and SA (96.19%), while maintaining zero variance across independent runs. It converged in an average of 31.2 iterations, slightly faster than GA (33.15) and SA (32.1), and comparable to DE (31.3). Execution time was 0.4738 s, close to GA (0.4654 s) and only marginally higher than DE (0.4262 s) and SA (0.4329 s). Statistical validation confirmed significant improvements in PTE (p < 0.05).

ABSTRACTUrea fertilizer is widely used in the United States, however, urea is not publicly traded and formula pricing is common. This article studies spatial transmission and efficiency of urea prices in the Arkansas River‐New Orleans urea markets and the New Orleans‐Middle East urea markets. A vector error correction model (VECM) and Baulch's (1997) parity bound model (PBM) are estimated. A threshold VECM is considered, but no threshold effects are found so threshold effects are not included in the final VECM. The estimated VECM shows that violations of spatial price equilibrium are corrected faster between Arkansas River‐New Orleans prices than New Orleans‐Middle East prices. The long term adjustments to deviations from spatial equilibrium in the New Orleans‐Middle East price relationship are made through adjustments in the New Orleans price. The PBM shows that New Orleans‐Middle East price spreads are greater than transportation costs about 23% of the time. [EconLit citations: C32, Q13, R32].

ABSTRACTThis study investigates price relationships between organic and conventional carrots, tomatoes, and lettuce in the U.S. utilizing Nielsen scanner data from 2006–2015. We employ a threshold vector error correction model (TVECM), threshold vector autoregressive model (TVAR), and threshold cointegration test to test whether market integration exists between organic and conventional vegetables as well as the existence of asymmetric price transmission. The results find positive long-run relationships between organic and conventional prices of carrots and tomatoes and show the existence of asymmetric price transmission in price pairs of lettuce and tomatoes. Our findings suggest that the price relationship between organic and conventional vegetables varies by characteristics, such as shelf life, volatility in the price premium, and substitutability.

We propose a three-step procedure to estimate a regime-dependent vector error correction model (VECM). In this model, not only the short-run adjustment process towards equilibrium is non-linear, as in threshold VECM and Markov switching VECM frameworks, but the long-run equilibrium relationship itself can also display threshold-type non-linearity. The proposed approach is unique in explicitly testing the null hypothesis of linear cointegration against the alternative of threshold cointegration based on the Gonzalo AND PITARAKIS (2006) test. The model is applied to apple price data on wholesale markets in Hamburg and Munich, using the share of domestic apples in total wholesale trade as the threshold variable. We identify four price transmission regimes characterized by different equilibrium relationships and short-run adjustment processes. This proposed approach is particularly suitable for capturing irregular seasonal threshold effects in price transmission typical for fresh fruits and vegetables.

This paper examines the dynamic relationship between the consumer price index (CPI) and the producer price index (PPI) in the UK, France and Germany from 1997 to 2013. We employ the momentum-threshold autoregressive (MTAR) cointegration model for empirical analysis. The results show that the CPI and the PPI are cointegrated with bi-directional long-run Granger causality between CPI and PPI, signifying the existence of both demand-pull and the cost-push nature of inflation. The estimates of threshold vector error correction models (TVECMs) indicate asymmetric adjustments to equilibrium, where upward adjustments are statistically significant but downward adjustments are sluggish and insignificant. Moreover, we generate the unconditional half-life estimates as a measure of persistence, which reveal robust evidence of complex non-linearities in the adjustment process. Our overall results provide valuable information for policymakers to formulate inflation-control policies and optimal policy horizons under a non-linear framework.

Asymmetric Arbitrage Trading on Offshore and Onshore Renminbi Markets

Threshold vector error correction model is used to study the nonlinear relationships between market volatility expectations and ordering behavior. Futures price, market volatility expectations, and derivatives ordering behavior data are used in the study. The intraday data of the VIX index, stock index futures price, and stock index options ordering volume from the Taiwan Futures Exchange are used for the study. Research results show the existence of asymmetric impacts of lagged VIX index on futures price, lagged VIX index on put options buy order to sell order volume ratio, lagged futures price on VIX index, lagged call options buy order to sell order volume ratio on VIX index, and lagged put options buy order to sell order volume ratio on VIX index when using VIX index as threshold.

Gold-oil dynamic relationship and the asymmetric role of geopolitical risks: Evidence from Bayesian pdBEKK-GARCH with regime switching