Copula-based dynamic models for multivariate time series

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.

ObjectiveThis paper describes the potential use of multiple influenza surveillance data to forecast hospital admissions for respiratory diseases.IntroductionA sudden surge in hospital admissions in public hospital during influenza peak season has been a challenge to healthcare and manpower planning. In Hong Kong, the timing of influenza peak seasons are variable and early short-term indication of possible surge may facilitate preparedness which could be translated into strategies such as early discharge or reallocation of extra hospital beds. In this study we explore the potential use of multiple routinely collected syndromic data in the forecast of hospital admissions.MethodsA multivariate dynamic linear time series model was fitted to multiple syndromic data including influenza-like illness (ILI) rates among networks of public and private general practitioners (GP), and school absenteeism rates, plus drop-in fever count data from designated flu clinics (DFC) that were created during the pandemic. The latent process derived from the model has been used as a measure of the influenza activity [1]. We compare the cross-correlations between estimated influenza level based on multiple surveillance data and GP ILI data, versus accident and emergency hospital admissions with principal diagnoses of respiratory diseases and pneumonia & influenza (P&I).ResultsThe estimated influenza activity has higher cross-correlation with respiratory and P&I admissions (ρ=0.66 and 0.73 respectively) compared to that of GP ILI rates (Table 1). Cross correlations drop distinctly after lag 2 for both estimated influenza activity and GP ILI rates.ConclusionsThe use of a multivariate method to integrate information from multiple sources of influenza surveillance data may have the potential to improve forecasting of admission surge of respiratory diseases.

In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently a new test called \textit{gradient test} has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results.

Problem statement: This study considers the precision of the output s eries generated from aberrant input series in the context of the distribution of the dynamic estimate and also investigate relative merit of analyzing residuals with outliers for a volatility input dynamic model. Approach: The study developed a methodology for checking volatility at every time p oint and evaluates the influence of volatility and outliers on both the estimates of the fitted Dynamic Model (DM) and test criterion for model adequacy. Results: Both the analytical and empirical findings in this study rev eal that outliers affect significantly the estimate s of the dynamic model and there was a masking effect of volatility with outliers in the series and therefore j eopardizes test criterion for model adequacy because outlier s eries were embedded in its computation. Conclusion: The analysis of outlier in dynamic model specification can involve the determination of volatility, most e specially in economic series for which causal relationship can p roffer some evidence based solutions to decision ma kers on pressing economic issues. The model specified in th is study has shown the influence of outlier embedde d with volatility in empirical study on dynamic function m odelling. In the first instance, outlier significan tly affects the estimates of the model, apart from this; the model residual is affected, these have a combine effect o n the precision of output generated.

Stationarity testing for nonlinear time series models which include several smooth trend components with (possibly) unknown parameters is considered. A pseudo-Lagrange multiplier stationarity test is proposed and its asymptotic behaviour is derived. The limiting null distribution generally depends on the unknown parameters of the model. A bootstrap approach permits this problem to be circumvented and consistency of the bootstrapped test is obtained. The theoretical analysis is complemented with a simulation study which allows us to check the performance of the test in finite samples. The article ends with an empirical application.

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.

Stationarity Testing Under Endogenous Smooth Deterministic Components: Some Asymptotic Results

This paper proposes some new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey and Fuller. Some simulations are reported which provide evidence on the performance of the new tests in finite samples.

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.

On a family of test statistics for discretely observed diffusion processes

This chapter introduces two distinct solutions to the problem of capturing the dynamics of multiple time series and the extraction of useful knowledge over time. As these dynamics would change in a nonstationary environment, the key characteristic of the methods is the ability to evolve their structure continuously over time. In addition, reviews of existing methods of dynamic single time series analysis and modeling such as the dynamic neuro-fuzzy inference system and the neuro-fuzzy inference method for transductive reasoning, which inspired the proposed methods, are presented. This chapter also presents a comprehensive evaluation of the performance of the proposed methods on a real-world problem, which consists of predicting movement of global stock market indexes over time.

We construct a new measure of the aggressiveness of COVID-19 policies in 75 Canadian and American cities and estimate the effect of these policies on mobility patterns in each city. Using a new dataset of five municipal COVID-19 policy indicators for each of our 75 cities, combined with 11 provincial/state policy indicators, we estimate a daily measure of the “aggressiveness” of the provincial/state and municipal COVID-19 policy mix in each city. We then estimate the effects of these policies on subsequent mobility behaviour using dynamic time series models. We find strong evidence of policy effects on subsequent mobility behaviour, but few overall differences between Canadian and American cities. We discuss the significance of our findings both for COVID-19 policy research and for other comparative urban policy research in multilevel policy environments.

The optimal perturbations (singular vectors) of a dynamical coupled model, a hybrid coupled model, and a linear inverse model of ENSO are compared. The hybrid coupled model consists of a dynamical ocean model and a statistical atmospheric model. The dynamical ocean model is identical to that used in the dynamical coupled model, and the atmospheric model is a statistical model derived from long time series of the dynamical coupled model. The linear inverse model was also derived from long time series from the dynamical coupled model. Thus all three coupled models are very closely related and all produce similar ENSO oscillations. The dynamical model and hybrid model also possess similar levels of hindcast skill. However, the optimal perturbations of the tangent linear versions of each model are not the same. The hybrid and linear inverse models are unable to recover the SST structure of the optimal perturbations of the dynamical model. The SST structure of the dynamical coupled model is a result of nonnormality introduced by latent heating of the atmosphere by deep convection over the west Pacific warm pool. It is demonstrated that standard statistical techniques remove the effects of the latent heating on the nonnormality of the hybrid and linear inverse models essentially rendering them more normal than their dynamical model counterpart. When the statistical components of the hybrid coupled model and the linear inverse models were recomputed using SST anomalies that are appropriately scaled by the standard deviation of SST variability, nonnormality was reintroduced into these models and they recovered the optimal perturbation structure of the dynamical model. Even though the hybrid and linear inverse model with scaled SSTs can recover the large-scale features of the correct optimal structure, state space truncation means that the dynamics of the resulting optimal perturbations is not the same as that governing optimal perturbation growth in the dynamical model. The consequences of these results for observed estimates of optimal perturbations for ENSO are discussed.

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

A methodology is introduced for identifying dynamic regression or distributed lag models relating two time series. First, specification of a bivariate time-series model is discussed, and its relationship to the usual dynamic regression model is indicated. Then, a two-stage identification procedure is presented which involves fitting univariate time-series models to each series, and identifying a dynamic shock model relating the two univariate model innovation series. The models obtained at these two stages are combined to identify a dynamic regression model, which may then be fitted in the usual ways. Two systems of economic time series illustrate the methodology.