Nonlinear Time Series Research Articles

LSTM-GARCH Hybrid Model for the Prediction of Volatility in Cryptocurrency Portfolios.

In the present work, the volatility of the leading cryptocurrencies is predicted through generalised autoregressive conditional heteroskedasticity (GARCH) models, multilayer perceptron(MLP), long short-term memory (LSTM), and hybrid models of the type LSTM and GARCH, where parameters of the GARCH family are included as features of LSTM models. The study period covered the scenario of the World Health Organization pandemic declaration around March 2020 at hourly frequency. We have found that the different variants of deep neural network models outperform those of the GARCH family in the sense of the hetorerocedastic error, and absolute and squared error(HSE). Under the sharpe ratio, the volatility forecasting of a uniform portfolio at long horizons systematically outperforms the stablecoin Tether, which is considered here as the risk-free asset. Also, including transaction volume helps reduce the value at risk or loss probability for the uniform portfolio. Moreover, in a minimum variance portfolio, it is observed that before the pandemic declaration, a large proportion of the capital was allocated to bitcoin(BTC). In contrast, after March 2020, the portfolio is more diversified with short positions for BTC. Moreover, the MLP models give the best predictive results, although not statistically different in accuracy compared to the LSTM and LSTM-GARCH versions under the Diebold-Mariano test. In sum, MLP models outperform most stylised financial models and are less computationally expensive than more complex neural networks. Therefore, simple learning models are suggested in highly non-linear time series volatility forecasts as it is the cryptocurrency market.

SETAR-Tree: a novel and accurate tree algorithm for global time series forecasting

Threshold Autoregressive (TAR) models have been widely used by statisticians for non-linear time series forecasting during the past few decades, due to their simplicity and mathematical properties. On the other hand, in the forecasting community, general-purpose tree-based regression algorithms (forests, gradient-boosting) have become popular recently due to their ease of use and accuracy. In this paper, we explore the close connections between TAR models and regression trees. These enable us to use the rich methodology from the literature on TAR models to define a hierarchical TAR model as a regression tree that trains globally across series, which we call SETAR-Tree. In contrast to the general-purpose tree-based models that do not primarily focus on forecasting, and calculate averages at the leaf nodes, we introduce a new forecasting-specific tree algorithm that trains global Pooled Regression (PR) models in the leaves allowing the models to learn cross-series information and also uses some time-series-specific splitting and stopping procedures. The depth of the tree is controlled by conducting a statistical linearity test commonly employed in TAR models, as well as measuring the error reduction percentage at each node split. Thus, the proposed tree model requires minimal external hyperparameter tuning and provides competitive results under its default configuration. We also use this tree algorithm to develop a forest where the forecasts provided by a collection of diverse SETAR-Trees are combined during the forecasting process. In our evaluation on eight publicly available datasets, the proposed tree and forest models are able to achieve significantly higher accuracy than a set of state-of-the-art tree-based algorithms and forecasting benchmarks across four evaluation metrics.

Challenges and perspectives in recurrence analyses of event time series

The analysis of event time series is in general challenging. Most time series analysis tools are limited for the analysis of this kind of data. Recurrence analysis, a powerful concept from nonlinear time series analysis, provides several opportunities to work with event data and even for the most challenging task of comparing event time series with continuous time series. Here, the basic concept is introduced, the challenges are discussed, and the future perspectives are summarized.

A recursive multi-head graph attention residual network for high-speed train wheelset bearing fault diagnosis

Wheelset bearings are a core component of high-speed trains, and their fault diagnosis is the key to smooth operation. Deep learning is widely used in fault diagnosis due to its powerful classification ability. To explicitly fit the features of vibration signals and further explore the relationship between the signals, the graph attention network (GAT) is becoming a focus of research. Unlike traditional graph neural networks, GATs can focus on edges with stronger correlations with vertices, making the model more powerful when fitting graph samples in non-Euclidean space. However, existing GATs have two limitations. Firstly, most graph construction methods do not consider the characteristics of vibration signals, so the graph interpretation is not good. Secondly, the existing methods of graph attention coefficient cannot effectively reflect the importance of edges. To address these issues, a recursive multi-head graph attention residual network (RMHGARN) is proposed. In RMHGARN, vibration signals are transformed into recurrence graphs due to the recursive nature of nonlinear time series. A multi-kernel Gaussian symmetric graph attention mechanism is proposed to obtain the Hilbert spatial distribution between neighboring vertices. In addition, a graph encoding module is proposed to improve the feature representation of input samples. The effectiveness and superiority of RMHGARN under strong noise samples are verified using three wheelset bearing datasets.

Modeling hydrological non-stationarity to analyze environmental impacts on drought propagation

Climate variation and anthropic activities are two key driving forces that impact the hydrologic cycle as well as the relationships between different drought types. Thus, it is essential to evaluate the impacts of environmental variations on the relationship between meteorological and hydrological droughts. In this study, abrupt changes in the yearly hydrological time series (streamflow) of the Han River Basin (HRB) were detected using a non-linearity-based empirical segmentation approach. The Standardized Precipitation Evapotranspiration Index (SPEI) was employed to model meteorological drought, while the Generalized Additive Model for Location, Scale and Shape (GAMLSS) algorithm was adopted to model the non-linear hydrological time series to obtain the non-stationarity based Standardized Runoff Index (SRINS). Correlation analyses were conducted on meteorological droughts (as presented by SPEI) and the hydrological drought data (as presented by the SRINS). A Bayesian network model (BNM) was employed to calculate the propagation likelihood of different categories of meteorological droughts resulting in hydrological droughts. Change points in the hydrological regime were identified based on the empirical segmentation analysis after the 1990s. Significant increasing trends in urbanization, gross domestic product, and population were observed after the change points. The correlation analysis showed that the seasonal (3-month) timescale of SPEI corresponded best to the three-month SRINS. The BNM revealed that the average propagation likelihoods of severe and extreme categories of meteorological drought resulting in severe and extreme categories of hydrological drought were 23.6% and 18.2%, respectively, due to the influence of climate change. These probabilities were increased by 53.9% and 70.8%, respectively, in the human impacted era due to high pressure on water resources caused by increased population, industrialization, water extraction, etc. In conclusion, the likelihood of extreme conditions of meteorological drought resulting in extreme hydrological drought was increased significantly after the change points.

A Bayesian Optimization-Based LSTM Model for Wind Power Forecasting in the Adama District, Ethiopia

Renewable energies, such as solar and wind power, have become promising sources of energy to address the increase in greenhouse gases caused by the use of fossil fuels and to resolve the current energy crisis. Integrating wind energy into a large-scale electric grid presents a significant challenge due to the high intermittency and nonlinear behavior of wind power. Accurate wind power forecasting is essential for safe and efficient integration into the grid system. Many prediction models have been developed to predict the uncertain and nonlinear time series of wind power, but most neglect the use of Bayesian optimization to optimize the hyperparameters while training deep learning algorithms. The efficiency of grid search strategies decreases as the number of hyperparameters increases, and computation time complexity becomes an issue. This paper presents a robust and optimized long-short term memory network for forecasting wind power generation in the day ahead in the context of Ethiopia’s renewable energy sector. The proposal uses Bayesian optimization to find the best hyperparameter combination in a reasonable computation time. The results indicate that tuning hyperparameters using this metaheuristic prior to building deep learning models significantly improves the predictive performances of the models. The proposed models were evaluated using MAE, RMSE, and MAPE metrics, and outperformed both the baseline models and the optimized gated recurrent unit architecture.

Weighted dynamic transfer network and spectral entropy for weak nonlinear time series detection

Weighted dynamic transfer network and spectral entropy for weak nonlinear time series detection

Graph Deep Factors for Probabilistic Time-series Forecasting

Effective time-series forecasting methods are of significant importance to solve a broad spectrum of research problems. Deep probabilistic forecasting techniques have recently been proposed for modeling large collections of time-series. However, these techniques explicitly assume either complete independence (local model) or complete dependence (global model) between time-series in the collection. This corresponds to the two extreme cases where every time-series is disconnected from every other time-series in the collection or likewise, that every time-series is related to every other time-series resulting in a completely connected graph. In this work, we propose a deep hybrid probabilistic graph-based forecasting framework called Graph Deep Factors (GraphDF) that goes beyond these two extremes by allowing nodes and their time-series to be connected to others in an arbitrary fashion. GraphDF is a hybrid forecasting framework that consists of a relational global and relational local model. In particular, a relational global model learns complex non-linear time-series patterns globally using the structure of the graph to improve both forecasting accuracy and computational efficiency. Similarly, instead of modeling every time-series independently, a relational local model not only considers its individual time-series but also the time-series of nodes that are connected in the graph. The experiments demonstrate the effectiveness of the proposed deep hybrid graph-based forecasting model compared to the state-of-the-art methods in terms of its forecasting accuracy, runtime, and scalability. Our case study reveals that GraphDF can successfully generate cloud usage forecasts and opportunistically schedule workloads to increase cloud cluster utilization by 47.5% on average. Furthermore, we target addressing the common nature of many time-series forecasting applications where time-series are provided in a streaming version; however, most methods fail to leverage the newly incoming time-series values and result in worse performance over time. In this article, we propose an online incremental learning framework for probabilistic forecasting. The framework is theoretically proven to have lower time and space complexity. The framework can be universally applied to many other machine learning-based methods.

A Mixture Autoregressive Model Based on an Asymmetric Exponential Power Distribution

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. This paper proposes a mixture autoregressive model via an asymmetric exponential power distribution, which includes normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. Therefore, the proposed method can be seen as a generalization of some existing model, which can adapt to unknown error structures to improve prediction accuracy, even in the case of fat tail and asymmetry. In addition, an expectation-maximization algorithm is applied to implement the proposed optimization problem. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze the daily return series of the Hong Kong Hang Seng Index. The results indicate that the proposed method is more robust and adaptive to the error distributions than other existing methods.

Nonlinear prediction of functional time series

AbstractWe propose a nonlinear prediction (NOP) method for functional time series. Conventional methods for functional time series are mainly based on functional principal component analysis or functional regression models. These approaches rely on the stationary or linear assumption of the functional time series. However, real data sets are often nonstationary, and the temporal dependence between trajectories cannot be captured by linear models. Conventional methods are also hard to analyze multivariate functional time series. To tackle these challenges, the NOP method employs a nonlinear mapping for functional data that can be directly applied to multivariate functions without any preprocessing step. The NOP method constructs feature space with forecast information, hence it provides a better ground for predicting future trajectories. The NOP method avoids calculating covariance functions and enables online estimation and prediction. We examine the finite sample performance of the NOP method with simulation studies that consider linear, nonlinear and nonstationary functional time series. The NOP method shows superior prediction performances in comparison with the conventional methods. Three real applications demonstrate the advantages of the NOP method model in predicting air quality, electricity price and mortality rate.

A novel PRFB decomposition for non-stationary time-series and image analysis

This work presents a novel perfect reconstruction filterbank decomposition (PRFBD) method for nonlinear and non-stationary time-series and image data representation and analysis. The Fourier decomposition method (FDM), an adaptive approach based on Fourier representation (FR), is shown to be a special case of the proposed PRFBD. In addition, adaptive Fourier–Gauss decomposition (FGD) based on FR and Gaussian filters, and adaptive Fourier–Butterworth decomposition (FBD) based on Butterworth filters are developed as the other special cases of the proposed PRFBD method. The proposed theory of PRFBD can decompose any signal (time-series, image, or other data) into a set of desired number of Fourier intrinsic band functions (FIBFs) that follow the amplitude-modulation and frequency-modulation (AM-FM) representations. A generic filterbank representation, where perfect reconstruction can be ensured for any given set of lowpass or highpass filters, is also presented. We performed an extensive analysis on both simulated and real-life data (COVID-19 pandemic, Earthquake and Gravitational waves) to demonstrate the efficacy of the proposed method. The resolution results in the time-frequency representation demonstrate that the proposed method is more promising than the state-of-the-art approaches.

Interval type-2 fuzzy neural networks with asymmetric MFs based on the twice optimization algorithm for nonlinear system identification

This paper proposes a novel algorithm twice optimization for interval type-2 fuzzy neural networks with asymmetric membership functions (TOIT2FNN-AMF), for nonlinear system identification problems. The proposed TOIT2FNN-AMF uses an asymmetric Gaussian interval type-2 membership function to enhance the network’s ability to describe and solve nonlinear and uncertain problems. The twice optimization algorithm consists of structure learning and parameter learning. Firstly, this paper proposes a multi-strategy adaptive differential evolution (MSADE) algorithm as the first optimization algorithm, which is used to determine the structure and the initial values of the parameters of the TOIT2FNN-AMF. It applies the root mean square error (RMSE) of the TOIT2FNN-AMF as the fitness function to determine the structure (number of rules) and initial parameters of the IT2FNN by searching for the RMSE values under different structures. When the fitness value reaches the minimum, that is, the RMSE value of the TOIT2FNN-AMF, the corresponding number will become the optimal one of fuzzy rules of the TOIT2FNN-AMF. Then, the second optimization algorithm of the TOIT2FNN-AMF turns into a hybrid optimization algorithm composed of an adaptive moment estimation (Adam) algorithm and recursive least squares (RLS) algorithm. Adam is used to optimize the antecedent parameters of TOIT2FNN-AMF rules, so as to maintain rapid convergence without generating oscillation during the training process; RLS is used to optimize the consequent parameters of TOIT2FNN-AMF rules, so that the network parameters can be optimized rapidly. In this way, the problems of excessive parameters to be adjusted and excessive slow convergence of the network can be solved. Finally, this paper evaluates the proposed TOIT2FNN-AMF by testing on problems of nonlinear system identification and chaotic time-series prediction. The simulation results are compared with those of similar methods in the existing literatures, which demonstrates that the proposed TOIT2FNN-AMF model yields a lower RMSE value and a simpler network structure than the other type-2 fuzzy neural networks (T2FNNs).

Pakistan CO2 Emission Modelling and Forecasting: A Linear and Nonlinear Time Series Approach.

Pakistan is considered among the top five countries with the highest CO2 emissions globally. This calls for pragmatic policy implementation by all stakeholders to bring finality to this alarming situation since it contributes greatly to global warming, thereby leading to climate change. This study is an attempt to make a comparative analysis of the linear time series models with nonlinear time series models to study CO2 emission data in Pakistan. These linear and nonlinear time series models were used to model and forecast future values of CO2 emissions for a short period. To assess and select the best model among these linear and nonlinear time series models, we used the root mean square error (RMSE) and the mean absolute error (MAE) as performance indicators. The outputs showed that the nonlinear machine learning models are the best among all other models, having the lowest RMSE and MAE values. Based on the forecasted value of the nonlinear machine learning neural network autoregressive model, Pakistan's CO2 emissions will be 1.048 metric tons per capita by 2028. The increasing trend in emissions is a frightening and clear warning, suggesting that innovative policies must be initiated to reduce the trend. We encourage the Pakistan government to price CO2 emissions by companies and entities per ton, adapt electricity production from hydro, wind, and different sources with no emissions of CO2, initiate rigorous planting of more trees in the populated areas of Pakistan as forest covers, provide incentives to companies, organisations, institutions, and households to come out with clean technologies or use technologies with no CO2 emissions or those with lower ones, and fund more studies to develop clean and innovative technologies with less or no CO2 emissions.

Deep Featured Adaptive Dense Net Convolutional Neural Network Based Cardiac Risk Prediction in Big Data Healthcare Environment

In recent days, cardiac vascular disease has been one of the deadliest health-affecting factors causing sudden death. So, the importance of early risk prediction through feature analysis has become a big problem in data analysis because more nonlinear time series data increase the feature dimension. Irrelevant feature dimension scaling affects the prediction accuracy and leads to classification inaccuracy. To resolve this problem, we propose an Enhanced Healthcare data analysis model for cardiac data prediction using an adaptive Deep Featured Adaptive Convolution Neural Network for early risk identification. Initially, the preprocessing was augmented to formalize the time series data collected from the CVD-DS dataset. Then the feature evaluation was carried out with the Relative Subset Clustering (RSC) approach. The Cardiac Deficiency Prediction rate (CDPr) was estimated to identify the relational feature to subset margins. Based on the CDPr weight the feature is extracted using Cross-Over Mutual Scaling Feature Selection Model (CMSFS). The selected features get with a deep neural classifier based on logical neurons. They are then constructed into a Dense Net Convolution Neural Network (DN-CNN) classifier to feed forward the feature values and predict the Disease Affection Rate (DAR) by class category. The proposed system produces high prediction accuracy in classification, precision, and recall rate to support premature treatment for early cardiac disease risk prediction..

Medium-long-term prediction of water level based on an improved spatio-temporal attention mechanism for long short-term memory networks

River water level usually given by nonlinear and nonstationary time series and affected by numerous complex spatial and temporal factors. But not all input factors are positively correlated with flood forecasting, and uncorrelated inputs tend to bring a lot of noise, resulting in lower prediction accuracy. Attention mechanism is an effective solution to feature filter. This study presents a spatio-temporal attention LSTM (STA-LSTM). Meanwhile, attention visualization makes models interpretation providing the basis. In this work, the attention-weight matrix is generated independently by the spatial attention module and the temporal attention module to focus on the more valuable feature factors in time and space, respectively. Spatio-temporal attention is a combination of spatial attention and temporal attention to assign scores to input sequences. Forecasting the water level of Hanchuan in the next 6 h based on the observations in the past 6 h in the middle and lower reaches of the Hanjiang River, China. The experimental results indicate that the mean absolute error (MAE) of STA-LSTM is 0.74835, root mean square error (RMSE) is 0.90197, mean absolute percent error (MAPE) is 3.29924, and coefficient of determination (R2) is 0.94138. This study improves the accuracy of the water level prediction method, which makes it easier for decision-makers to plan evacuations in advance.

Prediction of Complex Stock Market Data Using an Improved Hybrid EMD-LSTM Model

Because of the complexity, nonlinearity, and volatility, stock market forecasting is either highly difficult or yields very unsatisfactory outcomes when utilizing traditional time series or machine learning techniques. To cope with this problem and improve the complex stock market’s prediction accuracy, we propose a new hybrid novel method that is based on a new version of EMD and a deep learning technique known as long-short memory (LSTM) network. The forecasting precision of the proposed hybrid ensemble method is evaluated using the KSE-100 index of the Pakistan Stock Exchange. Using a new version of EMD that uses the Akima spline interpolation technique instead of cubic spline interpolation, the noisy stock data are first divided into multiple components technically known as intrinsic mode functions (IMFs) varying from high to low frequency and a single monotone residue. The highly correlated sub-components are then used to build the LSTM network. By comparing the proposed hybrid model with a single LSTM and other ensemble models such as the support vector machine (SVM), Random Forest, and Decision Tree, its prediction performance is thoroughly evaluated. Three alternative statistical metrics, namely root means square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), are used to compare the aforementioned techniques. The empirical results show that the suggested hybrid Akima-EMD-LSTM model beats all other models taken into consideration for this study and is therefore recommended as an effective model for the prediction of non-stationary and nonlinear complex financial time series data.

Effects of ambient temperature on mortality among elderly residents of Chengdu city in Southwest China, 2016–2020: a distributed-lag non-linear time series analysis

BackgroundWith complex changes in the global climate, it is critical to understand how ambient temperature affects health, especially in China. We aimed to assess the effects of temperature on daily mortality, including total non-accidental, cardiovascular disease (CVD), respiratory disease, cerebrovascular disease, and ischemic heart disease (IHD) mortality between 2016 and 2020 in Chengdu, China.MethodsWe obtained daily temperature and mortality data for the period 2016–2020. A Poisson regression model combined with a distributed-lag nonlinear model was used to examine the association between temperature and daily mortality. We investigated the effects of individual characteristics by sex, age, education level, and marital status.ResultsWe found significant non-linear effects of temperature on total non-accidental, CVD, respiratory, cerebrovascular, and IHD mortality. Heat effects were immediate and lasted for 0–3 days, whereas cold effects persisted for 7–10 days. The relative risks associated with extreme high temperatures (99th percentile of temperature, 28 °C) over lags of 0–3 days were 1.22 (95% confidence interval [CI]: 1.17, 1.28) for total non-accidental mortality, 1.40 (95% CI: 1.30, 1.50) for CVD morality, 1.34 (95% CI: 1.24, 1.46) for respiratory morality, 1.33 (95% CI: 1.20, 1.47) for cerebrovascular mortality, and 1.38 (95% CI: 1.20, 1.58) for IHD mortality. The relative risks associated with extreme cold temperature (1st percentile of temperature, 3.0 °C) over lags of 0–14 days were 1.32 (95% CI: 1.19, 1.46) for total mortality, 1.45 (95% CI: 1.24, 1.68) for CVD morality, 1.28 (95% CI: 1.09, 1.50) for respiratory morality, 1.36 (95% CI: 1.09, 1.70) for cerebrovascular mortality, and 1.26 (95% CI: 0.95, 1.68) for IHD morality. We found that hot and cold affects were greater in those over 85 years of age, and that women, individuals with low education levels, and those who were widowed, divorced, or never married, were more vulnerable.ConclusionsThis study showed that exposure to hot and cold temperatures in Chengdu was associated with increased mortality, with people over 85 years old, women, those with low education levels, and unmarried individuals being more affected by hot and cold temperatures.

Multi-Reservoir Echo State Networks with Hodrick–Prescott Filter for nonlinear time-series prediction

The Echo State Network (ESN) is a representative model for reservoir computing, which is capable of high-speed model training for machine learning tasks with time series data. Extended models of the ESN, such as Multi-Reservoir ESNs (MRESNs), have been intensively studied for performance improvement in recent years. In this study, we propose a new model called an HP-MRESN by combining an MRESN with the Hodrick–Prescott (HP) filter for nonlinear time series prediction. The proposed HP-MRESN comprises three basic components: a time series decomposer, a reservoir state extractor, and an ensemble decoder. In the time series decomposer, we recursively leverage the HP filter to decompose original time-series data into multiple trend and cycle components. In the reservoir state extractor, each time series component is fed into a corresponding reservoir-state encoder for generating a reservoir state which is extracted as it is or through the principal component analysis. In the ensemble decoder, the states of multiple reservoirs are collected and processed to produce model outputs. Moreover, we propose a greedy algorithm to automatically find the best model architectures under designated hyperparameters for different prediction tasks. Experimental results on a total of 24 nonlinear time-series prediction tasks with 6 real-world datasets demonstrate that our proposed HP-MRESN not only can outperform some existing representative MRESN models and fully-trained RNN models but also can have relatively low training time. In addition, performance comparisons between the HP-MRESN and related MRESN models with other prepossessing methods show the benefit of time series decompositions using the HP filter. The codes of the proposed method are publicly available on https://github.com/Ziqiang-IRCN/HP-MRESN.

Forecasting Carbon Price Using Double Shrinkage Methods.

It is commonly recognized that setting a reasonable carbon price can promote the healthy development of a carbon trading market, so it is especially important to improve the accuracy of carbon price forecasting. In this paper, we propose and evaluate a hybrid carbon price prediction model based on so-called double shrinkage methods, which combines factor screening, dimensionality reduction, and model prediction. In order to verify the effectiveness and superiority of the proposed model, this paper takes data from the Guangdong carbon trading market for empirical analysis. The sample interval is from 5 August 2013 to 25 March 2022. Based on the results of the empirical analysis, several main findings can be summarized. First, the double shrinkage methods proposed in this paper yield more accurate prediction results than various alternative models based on the direct application of factor screening methods or dimensionality reduction methods, when comparing R2, root-mean-square error (RMSE), and root absolute error (RAE). Second, LSTM-based double shrinkage methods have superior prediction performance compared to LR-based double shrinkage methods. Third, these findings are robust with the use of normalized data, different data frequencies, different carbon trading markets, and different dataset divisions. This study provides new ideas for carbon price prediction, which might have a theoretical and practical contributions to complex and non-linear time series analysis.

On portmanteau-type tests for nonlinear multivariate time series

A general framework to devise portmanteau-type test statistics for a general class of multivariate nonlinear time series models with vector martingale difference errors is formulated. Based on this framework a suite of individual and mixed multivariate test statistics is considered. Two applications are developed: single- and multiple-lag test statistics. In each case, the resulting portmanteau test statistic is based on multivariate residuals and multivariate squared residuals. Moreover, single- and multiple-lag mixed multivariate portmanteau-type tests are introduced. These test statistics are designed to detect different forms of inadequacies in the model residuals jointly. All proposed tests take uncertainty due to model estimation properly into account. The asymptotic null distribution of each test statistic follows from the asymptotic distribution of the general portmanteau-type test statistic in a natural way. Some considerations are given to the empirical size and power of six test statistics via a simulation study. All tests have satisfactory size and power properties in finite samples. To demonstrate their practical use, the proposed test statistics are applied to the residuals of a vector bivariate nonlinear threshold model fitted to U.S. interest rates.