Bivariate Time Series Model Research Articles

A Copula Discretization of Time Series-Type Model for Examining Climate Data

The study presents a comparative analysis of climate data under two scenarios: a Gaussian copula marginal regression model for count time series data and a copula-based bivariate count time series model. These models, built after comprehensive simulations, offer adaptable autocorrelation structures considering the daily average temperature and humidity data observed at a regional airport in Mobile, AL.

Bivariate Time Series Analysis of Nigeria Gross Domestics Product and Communication Sector

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.

Bivariate INAR(1) model under negative binomial innovations with non-homogeneous over-dispersed indices and application

This paper introduces a new bivariate integer-valued autoregressive of order (1) (BINAR(1)) model with negative binomial (NB) innovations under non-stationary moments. The purpose of this time series process is mainly to model series that are affected by time-dependent covariate effects and that, in particular, exhibit different levels of over-dispersion which is a phenomenon commonly noticed in many real-life series applications. In this proposed model, the cross-correlation is induced locally by allowing the current counting series observation to relate with the previous-lagged observation of the other series or vice versa while the pair of NB innovations are assumed uncorrelated. The estimation of the regression, over-dispersion and dependence parameters is conducted using a generalized quasi-likelihood (GQL) approach since the specification of the likelihood function, under non-stationarity, is rather difficult to specify in the above situation. Monte-Carlo simulation experiments are executed to assess the quality of the GQL estimators. The model is also applied and compared with other bivariate time series models to some real-life series in Mauritius.

Monitoring parameter change for bivariate time series models of counts.

In this study, we consider an online monitoring procedure to detect a parameter change for bivariate time series of counts, following bivariate integer-valued generalized autoregressive heteroscedastic (BIGARCH) and autoregressive (BINAR) models. To handle this problem, we employ the cumulative sum (CUSUM) process constructed from the (standardized) residuals obtained from those models. To attain control limits, we develop limit theorems for the proposed monitoring process. A simulation study and real data analysis are conducted to affirm the validity of the proposed method.

Measuring systemic risk for financial time series: A dynamic bivariate Dvine model

Accurate measurements of the tail risk of financial assets are major interest in financial markets. The main objective of our paper is to measure and forecast the value-at-risk (VaR) and the conditional value-at-risk (CoVaR) of financial assets using a new bivariate time series model. The proposed model can simultaneously capture serial dependence and cross-sectional dependence that exist in bivariate time series to improve the accuracy of estimation and prediction. In the process of model inference, we provide the parameter estimators of our bivariate time series model and give the estimators of VaR and CoVaR via the plug-in principle. We also establish the asymptotic properties of the Dvine model estimators. Real applications for financial stock price show that our model performs well in risk measurement and prediction.

Bivariate Time Series Analysis of Rainfall Pattern in Selected States in Nigeria

The issues concerning global rainfall distribution and warming/climate change cannot be over emphasized since it affects virtually every part of live. The study used rainfall pattern in two states of Nigeria. Data on the monthly rainfall distribution in Imo and Rivers state, for a period of 37 years was examined. The result showed a continuous increase in the pattern of rainfall for a period of thirty seven years within the period under study. However the pattern was inconsistence for the remaining years with some kind of fluctuations. The monthly mean series plots showed a clear presence of trend with the peak period being September annually in both series with coefficient of determination- R square value of 83% and 86% for Imo and Rivers series respectively. The yearly mean series plots showed a clear irregular variation over the years in both series. The irregularity in the pattern of rainfall calls for serious commitment in joining the force for climate change abatement process. Pearson correlation coefficient between the two series is 0.80 (substantial correlation), which is the same result with cross correlation between the two rainfall series (0.79988 approx. 0.80). The series reveal the following characteristics: high correlations appear seasonality of order 12 in the monthly mean plots (every September), irregular variation and trend curve which is quadratic trend. ARIMAX model with independent variable was employed to identify the best bivariate time series model for prediction purpose. The result reveal an increase in Rivers series (Yt ) would tend to a linear combination of some increase of the preceding Imo series (It ) values which is vise visa. SARIMAX (1, 2) and SARIMAX (2, 1) models are identified as the best model with respect to Rivers on Imo series rainfall; via Imo on Rivers series rainfall.

Bivariate Discrete Time Series Model for Assessing the effects of Rainfall and Temperature on Road Accidents: The case of Morogoro and Pwani Regions in Tanzania

In this article the contributions of weather on the occurrences of road accidents in Tanzania particularly for Morogoro and Pwani Regions is discussed. The correlation between road accidents and weather variables have indirect relationship taking into consideration that the later affects other factors like humans (drivers and other road users), state of vehicles and infrastructure before contributing to the incidence of road accidents. A bivariate discrete time series BINAR(1) model is formulated, and contribution of weather variability conditions in determining and forecasting road accidents is assessed using real data from Tanzania Meteorological Authority and Tanzania Police Force. The results show that, the contribution of weather variables specifically rainfall and temperature on road accidents vary either positively or negatively depending on the particular situation. Therefore, model properties are used to obtain correlation of these factors to road accidents as well as forecasting road accidents. It is not straight forward that increase (decrease) of rainfall or temperature lead to rise (decline) of road accidents. This indicates that, there might be other factors contributing to road accidents that need to be considered for achieving minimal if not zero road accidents. Therefore, we recommend the Government of Tanzania through the Tanzania Police Force to strictly enforce road safety laws and other necessary bylaws as well as providing education about road safety regulations to all road users. This will result to road accidents to be reduced significantly during rain and dry (high temperature) seasons.

Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data

The class of bivariate integer-valued time series models, described via copula theory, is gaining popularity in the literature because of applications in health sciences, engineering, financial management and more. Each time series follows a Markov chain with the serial dependence captured using copula-based distribution functions from the Poisson and the zero-inflated Poisson margins. The copula theory is again used to capture the dependence between the two series.
 
 However, the efficiency and adaptability of the copula are being challenged because of the discrete nature of data and also in the case of zero-inflation of count time series. Likelihood-based inference is used to estimate the model parameters for simulated and real data with the bivariate integral of copula functions. While such copula functions offer great flexibility in capturing dependence, there remain challenges related to identifying the best copula type for a given application.  This paper presents a survey of the literature on bivariate copula for discrete data with an emphasis on the zero-inflated nature of the modelling. We demonstrate additional experiments on to confirm that the copula has potential as greater research area.

Single-Month Unemployment Rate Estimates for the Brazilian Labour Force Survey Using State-Space Models

AbstractThe Brazilian Labour Force Survey publishes monthly national indicators based on 3-month rolling data. This paper presents state-space models to produce state-level single-month unemployment rate estimates. The models account for sampling errors and the increased dynamics in the labour force series due to the unforeseen SARS-COV-2 pandemic. Bivariate time series models with claimant count auxiliary data and multivariate models combining survey data of several states are investigated. The results demonstrated the benefits of the univariate state-space approach to produce unemployment official statistics for Brazil. Additionally, the regional multivariate model shows promising results but requires further investigation.

Nowcasting Register Labour Force Participation Rates in Municipal Districts Using Survey Data

Abstract In the Netherlands, very precise and detailed statistical information on labour force participation is derived from registers. A drawback of this data source is that it is not timely since definitive versions typically become available with a delay of two years. More timely information on labour force participation can be derived from the Labour Force Survey (LFS). Quarterly figures, for example, become available six weeks after the calendar quarter. A well-known drawback of this data source is the uncertainty due to sampling error. In this article, a nowcast method is proposed to produce preliminary but timely nowcasts for the register labour force participation on a quarterly frequency at the level of municipalities and neighbourhoods, using the data from the LFS. As a first step, small area estimates for quarterly municipal figures on labour force participation are obtained using the LFS data and the unit-level modelling approach of Battese, Harter and Fuller (1988). Subsequently, time series of these small area estimates at the municipal level are combined with time series on register labour force participation in a bivariate structural time series model in order to nowcast the register labour force participation at the level of municipalities and neighbourhoods.

A Class of Copula-Based Bivariate Poisson Time Series Models with Applications

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was used to estimate the models’ parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized Monte Carlo methods. To evaluate the proposed class of models, a comprehensive simulated study was conducted. Then, two sets of real-life examples were analyzed assuming the Poisson and the ZIP marginals, respectively. The results showed the superiority of the proposed class of models.

A COMPARATIVE STUDY BETWEEN UNIVARIATE AND BIVARIATE TIME SERIES MODELS FOR CRUDE PALM OIL INDUSTRY IN PENINSULAR MALAYSIA

The main purpose of this study is to compare the performances of univariate and bivariate models on four time series variables of the crude palm oil industry in Peninsular Malaysia. The monthly data for the four variables, which are the crude palm oil production, price, import and export, were obtained from Malaysian Palm Oil Board (MPOB) and Malaysian Palm Oil Council (MPOC). In the first part of this study, univariate time series models, namely, the autoregressive integrated moving average (ARIMA), fractionally integrated autoregressive moving average (ARFIMA) and autoregressive autoregressive (ARAR) algorithm were used for modelling and forecasting purposes. Subsequently, the dependence between any two of the four variables were checked using the residuals’ sample cross correlation functions before modelling the bivariate time series. In order to model the bivariate time series and make prediction, the transfer function models were used. The forecast accuracy criteria used to evaluate the performances of the models were the mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). The results of the univariate time series showed that the best model for predicting the production was ARIMA while the ARAR algorithm were the best forecast models for predicting both the import and export of crude palm oil. However, ARIMA appeared to be the best forecast model for price based on the MAE and MAPE values while ARFIMA emerged the best model based on the RMSE value. When considering bivariate time series models, the production was dependent on import while the export was dependent on either price or import. The results showed that the bivariate models had better performance compared to the univariate models for production and export of crude palm oil based on the forecast accuracy criteria used.

Modeling bivariate long‐range dependence with general phase

Bivariate time series models are considered that are suitable for estimation, that have interpretable parameters and that can capture the general semi‐parametric formulation of bivariate long‐range dependence, including a general phase. The models also allow for short‐range dependence and fractional cointegration. A simulation study to test the performance of a conditional maximum likelihood estimation method is carried out, under the proposed models. Finally, an application is presented to the U.S. inflation rates in goods and services where models not allowing for general phase suffer from misspecification.

The family of the bivariate integer-valued autoregressive process (BINAR(1)) with Poisson–Lindley (PL) innovations

ABSTRACTIn the literature of discrete-valued time series modelling, various bivariate integer-valued autoregressive time series models of order 1 (BINAR(1)) have been proposed particularly based on the binomial thinning mechanism and with different innovation distributions. These BINAR(1)s are mostly suitable for modelling bivariate counting series of varied levels of overdispersion. Recently, in the context of overdispersion, the INAR(1) with Poisson–Lindley (PL) innovations have been introduced to provide superior model fitness criteria than other competing INAR(1)s. Thus, this paper proposes to develop classes of BINAR(1)PL, including BINAR(1)PL(I) and BINAR(1)PL(II), under different cross-correlation functions. The parameter estimations are conducted via the conditional maximum likelihood (CML) approach. Monte Carlo simulation experiments are implemented to assess the asymptotic properties of the CML estimators under different combinations of the cross-correlation parameters. The proposed models are also applied to the Pittsburg crimes data and compared with other competing popular overdispersed BINAR(1) models.

Reproducing the results in “Does the time-consistency problem explain the behavior of inflation in the United States?” using the Metropolis–Hastings algorithm

The study of Ireland (J Monet Econ 44:279–291, 1999) derives the restrictions imposed by Barro and Gordon’s theory of time-consistent monetary policy on a bivariate time-series model for US inflation and unemployment rate. The model is then estimated via maximum likelihood techniques using quarterly data from 1960q1 to 1997q2. In this study, we reproduce the central results of Ireland (1999) using the Metropolis–Hastings algorithm. Although we apply Bayesian instead of classical estimation, posterior parameter estimates are similar to maximum likelihood parameter estimates reported in Ireland (1999).

Modelling with Dispersed Bivariate Moving Average Processes

Abstract This paper proposes a non-stationary bivariate integer-valued moving average of order 1 (BINMA(1)) model where the respective innovations are marginal COM-Poisson and unrelated. As opposed to other such bivariate time series model, the dependence between the series in the above is constructed via the relation between the current series with survivor elements of the other series at the preceding time point. Under these assumptions, the BINMA(1) process is shown to accommodate different levels and combinations of over-, equi- and under-dispersion. Since under the non-stationary conditions, the joint likelihood function is hardly laborious to construct, a generalized quasi-likelihood (GQL) method of estimation is proposed to estimate the dynamic effects and dependence parameters. The asymptotic and consistency properties of the GQL estimators are also established. Monte-Carlo experiments and a real-life application to analyze intra-day stock transactions are presented to validate the proposed model and the estimation methodology.

Stochastic bivariate time series models of waves in the North Sea and their application in simulation-based design

In this paper, we present and evaluate three long-term wave models for application in simulation-based design of ships and marine structures. Designers and researchers often rely on historical weather data as a source for ocean area characteristics based on hindcast datasets or in-situ measurements. The limited access and size of historical datasets reduces repeatability of simulations and analyses, making it difficult to assess the sampling variability of performance and loads on marine vessels and structures. Markov, VAR and VARMA wave models, producing independent long-term time series of significant wave height (Hs) and spectral peak period (Tp), is presented as possible solutions to this problem. The models are tested and compared by addressing how the models affect interpretation of design concepts and the ability to replicate statistical and physical characteristics of the wave process. Our results show that the VAR and VARMA models perform sufficiently in describing design performance, but does not capture the physical process fully. The Markov model is found to perform worst of the tested models in the applied tests, especially for measures covering several consecutive sea states.

A Primer on a Flexible Bivariate Time Series Model for Analyzing First and Second Half Football Goal Scores: The Case of the Big 3 London Rivals in the EPL

The ranking of some English Premier League (EPL) clubs during football season is of keen interest to many stakeholders with special attention to the London rivals: Arsenal, Chelsea and Tottenham. In particular, the first (GF) and second half (GS) scores, besides being inter-related, is perceived as a convenient measure of the clubs potential. This paper studies the contributory effects of the possible factors that commonly influence the club scoring capacity in the halves along with forecasted measures diagnostics via a novel flexible bivariate time series model with COM-Poisson innovations using data from August 2014 to December 2017.

Producing the Dutch and Belgian mortality projections: a stochastic multi-population standard

The quantification of longevity risk in a systematic way requires statistically sound forecasts of mortality rates and their corresponding uncertainty. Actuarial associations have a long history and continue to play an important role in the development, application and dispersion of mortality projections for the countries they represent. This paper gives an in depth presentation and discussion of the mortality projections as published by the Dutch (in 2014) and Belgian (in 2015) actuarial associations. The goal of these institutions was to publish a stochastic mortality projection model in line with both rigorous standards of state-of-the-art academic work as well as the requirements of practical work such as robustness and transparency. Constructed by a team of authors from both academia and practice, the developed mortality projection standard is a Li and Lee type multi-population model. To project mortality, a global Western European trend and a country-specific deviation from this trend are jointly modelled with a bivariate time series model. We motivate and document all choices made in the model specification, calibration and forecasting process as well as the model selection strategy. We show the model fit and mortality projections and illustrate the use of the model in several pension-related applications.

Estimation in a bivariate integer-valued autoregressive process

ABSTRACTA bivariate integer-valued autoregressive time series model is presented. The model structure is based on binomial thinning. The unconditional and conditional first and second moments are considered. Correlation structure of marginal processes is shown to be analogous to the ARMA(2, 1) model. Some estimation methods such as the Yule–Walker and conditional least squares are considered and the asymptotic distributions of the obtained estimators are derived. Comparison between bivariate model with binomial thinning and bivariate model with negative binomial thinning is given.