Diagnostic checking of multivariate nonlinear time series models with martingale difference errors

Pipe material and labor costs constitute about 70% of pipeline construction costs. Pipe and labor costs are subject to considerable fluctuations over time. These fluctuations are problematic for cost estimation and bid preparation in pipeline projects, which are mostly large and long-term projects. The accurate prediction of pipe and labor costs is invaluable for cost estimators to prepare accurate bids and manage the cost contingencies. However, the existing literature does not take advantage of the leading indicators of pipeline construction cost time series to accurately forecast cost fluctuations in pipeline projects. The objective of this research is to identify the leading indicators of pipeline construction costs and develop multivariate time series models for forecasting cost fluctuations in pipeline projects. Nineteen potential leading indicators of pipe and labor costs were initially selected based on a comprehensive review of construction cost forecasting literature. The leading indicators were identified from this pool of potential leading indicators based on unit root tests and Granger causality tests. Multivariate time series models were developed based on the results of cointegration tests. Vector error correction (VEC) models were developed for the cointegrated variables, while vector autoregressive (VAR) models were developed for the non-cointegrated variables. Since multivariate time series models include information from the identified leading indicators, multivariate time series models are often expected to deliver more accurate forecasts than univariate time series models. The forecasting accuracies of multivariate time series models were compared with those of univariate time series models based on three common error measures: mean absolute prediction error (MAPE), root-mean-squared error (RMSE), and mean average error (MAE). The results show that multivariate time series models outperform univariate models for forecasting cost fluctuations in pipeline projects. The findings of this research contribute to the state of knowledge by identifying leading indicators of pipe and labor costs and developing multivariate time series models to forecast them. The multivariate time series models with leading indicators are more accurate than univariate models for forecasting cost fluctuations in pipeline projects. It is expected that the proposed multivariate time series forecasting models contribute to the enhancement of the theory and practice of pipeline construction cost forecasting and help cost engineers and investment planners to prepare more accurate bids, cost estimates, and budgets for pipeline projects.

Multivariate analysis helps to understand the relationships between dependent variables; this methodology has great potential in several areas of knowledge. The aim of this study was to adjust and compare the univariate and multivariate Gompertz and Logistic nonlinear models to describe the productive traits of sunn hemp (Crotalaria juncea L.). Two uniformity trials were performed, and the following productive traits were analyzed in 376 sunn hemp plants along 94 days of observations (four plants per day): the fresh mass of leaves (FML), the fresh mass of stem (FMS), and the fresh mass of the aerial parts (FMAP). The Gompertz and Logistic univariate models were adjusted for each productive trait. To adjust the multivariate models, the errors covariance matrix was calculated. The matrix (Cholesky factor) was obtained for each trait, and the multivariate Gompertz (GG) and Logistic (LL) nonlinear models were generated, together with the combination of both models (GL and LG). To define the best model, the residual standard deviation (RSD), the determination coefficient (R2), the Akaike information criterion (AIC), the mean absolute deviation (MAD), and the measures of intrinsic nonlinearity (INL) and parametric nonlinearity (PNL) were calculated. The nonlinear multivariate model LL was adequate and achieved satisfactory results to describe the productive traits of sunn hemp.

Verifying the existence of a relationship between two multivariate time series represents an important consideration. In this article, the procedure developed by Cheung and Ng [A causality-in-variance test and its application to financial market prices, J. Econom. 72 (1996), pp. 33–48] designed to test causality in variance for univariate time series is generalized in several directions. A first approach proposes test statistics based on residual cross-covariance matrices of squared (standardized) residuals and cross products of (standardized) residuals. In a second approach, transformed residuals are defined for each residual vector time series, and test statistics are constructed based on the cross-correlations of these transformed residuals. Test statistics at individual lags and portmanteau-type test statistics are developed. Conditions are given under which the new test statistics converge in distribution towards chi-square distributions. The proposed methodology can be used to determine the directions of causality in variance, and appropriate test statistics are presented. Monte Carlo simulation results show that the new test statistics offer satisfactory empirical properties. An application with two bivariate financial time series illustrates the methods.

In real-world scenarios, partial information losses of multivariate time series degrade the time series analysis. Hence, the time series imputation technique has been adopted to compensate for the missing values. Existing methods focus on investigating temporal correlations, cross-variable correlations, and bidirectional dynamics of time series, and most of these methods rely on recurrent neural networks (RNNs) to capture temporal dependency. However, the RNN-based models suffer from the common problems of slow speed and high complexity when dealing with long-term dependency. While some self-attention-based models without any recurrent structures can tackle long-term dependency with parallel computing, they do not fully learn and utilize correlations across the temporal and cross-variable dimensions. To address the limitations of existing methods, we propose a novel so-called dual-branch cross-dimensional self-attention-based imputation (DCSAI) model for multivariate time series, which is capable of performing global and auxiliary cross-dimensional analyses when imputing the missing values. In particular, this model contains masked multi-head self-attention-based encoders aligned with auxiliary generators to obtain global and auxiliary correlations in two dimensions, and these correlations are then combined into one final representation through three weighted combinations. Extensive experiments are presented to show that our model performs better than other state-of-the-art benchmarkers on three real-world public datasets under various missing rates. Furthermore, ablation study results demonstrate the efficacy of each component of the model.

Empirical likelihood inference for partial linear models under martingale difference sequence

In earlier chapters we have considered only univariate models; we now proceed to examine multi-series extensions and to compare the multi-series innovations models with other multi-series schemes. We shall refer to our approach as the vector exponential smoothing (VES) framework. The innovations framework is similar to the structural time series models advocated by Harvey (1989) in that both rely upon unobserved components, but there is a fundamental difference: in keeping with the earlier developments in this book, each time series has only one source of error. The VES models are introduced in Sect. 17.1; special cases of the general model are then discussed in Sect. 17.2. An inferential framework is then developed in Sect. 17.3 for the VES models, building upon our earlier results for the univariate schemes. The most commonly used multivariate time series models are those defined within the ARIMA framework. Interestingly, this approach also has only one source of randomness for each time series. Thus, the vector versions of the ARIMA framework (VARIMA), and special cases such as vector autoregression (VAR) and vector moving average (VMA), may be classified as innovations approaches to time series analysis (Lutkepohl 2005).We compare the VES frameworkwith existing approaches in Sect. 17.4. As in Chap. 11, when we consider equivalences between vector innovations models and the VARIMA forms, we will make the infinite start-up assumption. Finally we compare the performance of VES models to VAR and other existing state space alternatives, first in an empirical study of exchange rates (Sect. 17.5), and then across a range of different time series taken froma large macroeconomic database, in Sect. 17.6.

In China in particular, large, planned special events (e.g., the Olympic Games, etc.) are viewed as great opportunities for economic development. Large numbers of visitors from other countries and provinces may be expected to attend such events, bringing in significant tourism dollars. However, as a direct result of such events, the transportation system is likely to face great challenges as travel demand increases beyond its original design capacity. Special events in central business districts (CBD) in particular will further exacerbate traffic congestion on surrounding freeway segments near event locations. To manage the transportation system, it is necessary to plan and prepare for such special events, which requires prediction of traffic conditions during the events. This dissertation presents a set of novel prototype models to forecast traffic volumes along freeway segments during special events. Almost all research to date has focused solely on traffic management techniques under special event conditions. These studies, at most, provided a qualitative analysis and there was a lack of an easy-to-implement method for quantitative analyses. This dissertation presents a systematic approach, based separately on univariate time series model with intervention analysis and multivariate time series model with intervention analysis for forecasting traffic volumes on freeway segments near an event location. A case study was carried out, which involved analyzing and modelling the historical time series data collected from loop-detector traffic monitoring stations on the Second and Third Ring Roads near Beijing Workers Stadium. The proposed time series models, with expected intervention, are found to provide reasonably accurate forecasts of traffic pattern changes efficiently. They may be used to support transportation planning and management for special events.

Energy is one of the most important factors in a country growth, both in the industrial and household fields. Among these fields, the industrial sector that needs the most in supporting the development of a company, energy saving is an important target for every company. Therefore, an accurate prediction is needed to determine future energy consumption. Many researchers have proposed research on the prediction of energy consumption using either machine learning or deep learning. One of the challenging factors in predicting energy consumption is data using a multivariate time series model with several uses in the area. In this project, researchers will conduct research on energy consumption predictions in manufacturing companies engaged in the food sector. This company has several areas as well as several predictable energies such as electricity, water, and diesel fuel, the data studied are multivariate time series modeled data. For the case of a data model like this, we use two algorithms, namely prophet and LSTM, because this algorithm can predict time series data. From the results of our research, it shows that Prophet Facebook which has the best results in predicting the energy consumption of electricity, water, and diesel fuel, a very significant difference in error rate is obtained by the LSTM algorithm for predicting time series models.

The need to establish a relation between Gross Domestic Product and Communication sector was the major focus of this research. This research work investigated the contribution of Communication sector to the Gross Domestic product of Nigeria Economy. With the aid of ACF and PACF, ARIMA (1 1 1) was suggested for both variables. Alternative multivariate time series models used for the analysis were ARIMAV, MARDL and MARDL-MA models. The research has established interaction and interdependence between the two macroeconomic variables, and has also revealed that each of the variable has contributed significantly to each other at first time lag. The error variances of the bivariate time series model were derived for GDP and Communication sector. When comparing the three models for the two economic variables, ARIMAV model for Gross Domestic Product has the least error variance of 0.2183 making it the best model, while MARDL model for communication sector produced the least error variance of 0.0723, thereby indicating that MARDL model outperformed ARIMAV and MARDL-MA models for communication sector. Hence, this research has brought to focus the fact that performance of a model over another is predicated upon the nature of the economic data. That means there is no fixed multivariate time series model for a given macroeconomic data due to the dynamic nature of the time series.

The portfolio of the Japanese Government Pension Investment Fund (GPIF) consists of a linear combination of five benchmarks of financial assets. Some of these exhibit long-memory and nonlinear behavior. Their analysis therefore requires multivariate nonlinear and long-memory time series models. Moreover, the assumption that the innovation densities underlying those models are known seems quite unrealistic. If those densities remain unspecified, the model becomes a semiparametric one, and rank-based inference methods naturally come into the picture. Rank-based inference methods under very general conditions are known to achieve the semiparametric efficiency bounds. Defining ranks in the context of multivariate time series models, however, is not obvious. We propose two distinct definitions. The first one relies on the assumption that the innovation density is some unspecified elliptical density. The second one relies on the assumption that the innovation process is described by some unspecified independent component analysis model. Applications to portfolio management problems are discussed.

Multivariate time series forecasting has very great practical significance for a long time, and it has been attracting the attention of researchers from a diverse range of fields. However, it is difficult to analyze the relationship and transformation law among multivariate data. Further, it is hard to obtain a relatively accurate prediction. In recent years, long short-term memory (LSTM) has shown high capability in dealing with nonlinearity and long memory of time series data. Although LSTM can also process multivariate data, it is insufficient to pay various degrees of attention to multivariate data. To address this issue, a multivariate time series prediction model based on multilayer perceptron (MLP), feedforward attention mechanism, and LSTM is proposed in this paper. Firstly, the simulation process utilizes the MLP module to map the multivariate initial sequences into another latent dimensional space, thereby obtaining easily captured mapping features. Then, these features are adaptively assigned attention weights through the feed-forward attention mechanism. Finally, the LSTM module uses these feature sequences with attention weights to make final predictions. The experimental results show that the method that combines the MLP layer with the feed-forward attention layer is effective in extracting multivariate features. Also, the empirical results indicate that our proposed framework (a combined model of MLP-Feedforward attention-LSTM) can achieve better performance than baselines.

This article is intended to complement previous research (Sivo, 1997; Sivo & Willson, 1998, in press) by discussing the propriety and practical advantages of specifying multivariate time series models in the context of structural equation modeling for time series and longitudinal panel data. Three practical considerations motivated this article. Unlike Marsh (1993), Sivo and Willson (2000) did not offer multiple indicator (latent order) equivalents to their autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Moreover, such models have yet to be discussed, despite Marsh's (1993) advocacy for multiple indicator models in general. Further motivating multiple indicator extensions of the AR, MA, and ARMA equivalent models is the fact that longitudinal studies often collect data on more than 1 related variable per occasion. Such multiple indicator models capitalize on 1 of the chief analytical advantages of structural equation modeling in that measurement error may be estimated directly.

This paper introduces a novel test designed to assess the validity of time-varying smooth transition conditional covariance models. We develop a model driven by five scalar parameters in order to build the Lagrange Multiplier test within the framework of multivariate conditional heteroskedastic time series models with smooth transition functions. We detail the development of these tests, emphasizing their applicability. The methodology is scrutinized through Monte Carlo simulations, providing insights into its finite sample properties. Additionally, empirical illustrations underscore the practical relevance of the proposed tests, demonstrating their efficiency in capturing time-varying smooth transitions within financial datasets.

Multivariate time series anomaly detection is a crucial data mining technique with a wide range of applications in areas such as IT applications. Currently, the majority of anomaly detection methods for time series data rely on unsupervised approaches due to the rarity of anomaly labels. However, in real-world scenarios, obtaining a limited number of anomaly labels is feasible and affordable. Effective usage of these labels can offer valuable insights into the temporal characteristics of anomalies and play a pivotal role in guiding anomaly detection efforts. To improve the performance of multivariate time series anomaly detection, we proposed a novel deep learning model named EDD (Encoder-Decoder-Discriminator) that leverages limited anomaly samples. The EDD model innovatively integrates a graph attention network with long short term memory (LSTM) to extract spatial and temporal features from multivariate time series data. This integrated approach enables the model to capture complex patterns and dependencies within the data. Additionally, the model skillfully maps series data into a latent space, utilizing a carefully crafted loss function to cluster normal data tightly in the latent space while dispersing abnormal data randomly. This innovative design results in distinct probability distributions for normal and abnormal data in the latent space, enabling precise identification of anomalous data. To evaluate the performance of our EDD model, we conducted extensive experimental validation across three diverse datasets. The results demonstrate the significant superiority of our model in multivariate time series anomaly detection. Specifically, the average F1-Score of our model outperformed the second-best method by 2.7% and 73.4% in both evaluation approaches, respectively, highlighting its superior detection capabilities. These findings validate the effectiveness of our proposed EDD model in leveraging limited anomaly samples for accurate and robust anomaly detection in multivariate time series data.

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the introduction of a novel copula construction in sequential filtering of coupled sets of dynamic generalized linear models. The new copula approach is integrated into recently introduced multiscale models in which univariate time series are coupled via nonlinear forms involving dynamic latent factors representing cross-series relationships. The resulting methodology offers dramatic speed-up in online Bayesian computations for sequential filtering and forecasting in this broad, flexible class of multivariate models. Two examples in nonlinear models for very heterogeneous time series of nonnegative counts demonstrate massive computational efficiencies relative to existing, simulation-based methods, while defining similar filtering and forecasting outcomes.