Abstract
Prior uncertain autoregressive (UAR) model research has focused principally on a univariate time series. However, different variables tend to influence each other in reality. In order to fill this gap, this paper explores the interrelationships among different variables and proposes an exposition of uncertain vector autoregressive (UVAR) model. Furthermore, we choose the least squares principle to estimate the unknown parameters in the UVAR model and analyze the residual of disturbance term. Then, we present the point estimation and confidence interval of the variables in the next period. Finally, the empirical results show that essential improvements in forecasting can be obtained by adding relative variables.
Similar content being viewed by others
References
Chen D (2020) Tukey’s Biweight estimation for uncertain regression model with imprecise observations. Tech Rep. https://doi.org/10.1007/s00500-020-04973-x
Chen X, Ralescu DA (2012) B-spline method of uncertain statistics with application to estimating travel distance. J Uncertain Syst 6(4):256–262
Fang L, Hong Y (2020) Uncertain revised regression analysis with responses of logarithmic, square root and reciprocal transformations. Soft Comput 24(4):2655–2670
Hu Z, Gao J (2020) Uncertain Gompertz regression model with imprecise observations. Soft Comput 24:2543–2549
Koop G, Korobilis D (2016) Model uncertainty in panel vector autoregressive models. Eur Rev Agric 81:115–131
Lewis R, Reinsel GC (1985) Prediction of multivariate time series by autoregressive model fitting. J Multivar Anal 16(3):393–411
Lütkepohl H (2013) Vector autoregressive models. Handbook of research methods and applications in empirical macroeconomics. Edward Elgar Publishing, Cheltenham
Lio W, Liu B (2018) Residual and confidence interval for uncertain regression model with imprecise observations. J Intell Fuzzy Syst 35(2):2573–2583
Lio W, Liu B (2020) Maximum likelihood estimation for uncertain regression analysis. Technical Report
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu S (2019) Leave-\(p\)-out cross-validation test for uncertain Verhulst-Pearl model with imprecise observations. IEEE Access 7:131705–131709
Liu Z, Yang Y (2020) Least absolute deviations estimation for uncertain regression with imprecise observations. Fuzzy Optim Decis Mak 19(1):33–52
Sims CA (1980) Macroeconomics and reality. Econometrica 48(1):1–48
Song Y, Fu Z (2018) Uncertain multivariable regression model. Soft Comput 22(17):5861–5866
Song Q, Chissom BS (1991) Forecasting enrollments with fuzzy time series-part I. Fuzzy Set Syst 54:1–9
Song Q, Chissom BS (1993) Fuzzy time series and its models. Fuzzy Set Syst 54(3):269–277
Song Q, Chissom BS (1994) Forecasting enrollments with fuzzy time series-part II. Fuzzy Set Syst 62(1):1–8
Tang H (2020) Uncertain threshold autoregressive model with imprecise observations. Technical Report
Wang X, Gao Z, Guo H (2012) Delphi method for estimating uncertainty distributions. Inf Int Interdiscip J 15(2):449–460
Wang X, Peng Z (2014) Method of moments for estimating uncertainty distributions. J Uncertain Anal Appl 2(1):1–10
Yao K, Liu B (2018) Uncertain regression analysis: an approach for imprecise observation. Soft Comput 22(17):5579–5582
Yang X, Liu B (2019) Uncertain time series analysis with imprecise observations. Fuzzy Optim Decis Mak 18(3):263–278
Yang X, Ni Y (2020) Least squares estimation for uncertain moving average model. Commun Stat-Theory Methods. https://doi.org/10.1080/03610926.2020.1713373
Yule GU (1927) On a method of investigating periodicities in disturbed series with special reference to Wolfer’s sunspot numbers. Philos Trans R Soc Lond 226:267–298
Acknowledgements
This work was supported by National Natural Science Foundation of China Grant No.61873329.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares that he has no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by the author.
Additional information
Communicated by V. Loia.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tang, H. Uncertain vector autoregressive model with imprecise observations. Soft Comput 24, 17001–17007 (2020). https://doi.org/10.1007/s00500-020-04991-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-020-04991-9