Comparative Analysis of Univariate SARIMA and Multivariate VAR Models for Time Series Forecasting: A Case Study of Climate Variables in Ninahvah City, Iraq
DOI:
https://doi.org/10.51408/1963-0113Keywords:
Modeling, Doers, Energizers, Classifiers, Cognizing, Fundamentals, DynamicityAbstract
This study involves a comparison between the application of the univariate SARIMA model and the utilization of VAR methods (vector autoregressive models) for multivariate time series analysis. The analysis is conducted using three-time series variables derived from data representing the monthly average of Humidity (H), Rainfall (R), and Temperature (T) in Ninahvah City, Iraq. Both univariate and multivariate time series approaches are employed to model these series. The paper also outlines the implementation of vector autoregressive, structural vector autoregressive, and structural vector error correction models using the 'vars' package. Additionally, it provides functions for diagnostic testing, estimation of constrained models, prediction, causality analysis, impulse response analysis, and forecast error variance decomposition. Furthermore, it introduces three fundamental functions, VAR, SVAR, and SVEC, for estimating these models. The comparison between the methods is based on evaluating the mean error produced by each approach. The findings of the study indicate that univariate linear stationary methods outperform multivariate models. The analysis of the data was carried out using the R software platform. The primary objective is to assess the performance of univariate and multivariate time series models in handling the given data. The research gap lies in the need for a comparative evaluation of SARIMA and VAR methods for time series analysis in the context of monthly environmental variables. These models were chosen due to their effectiveness in capturing temporal dependencies and interactions among multiple variables in time series data, providing a comprehensive analysis of climatic patterns in Ninahvah City, Iraq. The study aims to address the research gap by comparing these models and justifying their selection based on their capabilities to analyze the specified time series data.
References
C.A. Sims, "Macroeconomics and reality", Econometrica: Journal of the Econometric Society, pp. 1-48, 1980.
C.W. Granger, "Some properties of time series data and their use in econometric model specification", Journal of Econometrics, vol. 16, no. 1, pp. 121-130, 1981.
R.F. Engle, & C.W.J. Granger, "Co-integration and error correction: representation, estimation, and testing", Econometrica: Journal of the Econometric Society, pp. 251-276, 1987.
H. Lütkepohl, New Introduction to Multiple Time Series Analysis, Springer Science & Business Media, 2005.
D. F. Hendry, Dynamic econometrics, Oxford University Press, 1995.
S. Johansen, "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models", Oxford University Press, New York, 1995.
J. D. Hamilton, Time series analysis, Princeton University Press, Princeton, N.J., 1994.
A. Banerjee, J.J. Dolado, J.W. Galbraith, & D. Hendry, Co-integration, error correction, and the econometric analysis of non-stationary data, Oxford University Press, 1993.
J.M. Liu, R. Chen, L.M. Liu, & J.L. Harris, "A semi‐parametric time series approach in modeling hourly electricity loads", Journal of Forecasting, vol. 25, no. 8, pp. 537-559, 2006.
G.S. Maddala and I.M. Kim, Unit roots, cointegration, and structural change, 1998.
W.W. Wei, Multivariate time series analysis and applications, John Wiley & Sons, 2018.
R.S. Tsay, Multivariate time series analysis: with R and financial applications, John Wiley & Sons, 2013.
A.M. Sathe, & N.S. Upadhye, "Estimation of the Parameters of Vector Autoregressive (VAR) Time Series Model with Symmetric Stable Noise", arXiv preprint arXiv:2104.07262, 2021.
K. Yamaoka, T. Nakagawa, & T. Uno, "Application of Akaike's information criterion (AIC) in the evaluation of linear pharmacokinetic equations", Journal of Pharmacokinetics and Biopharmaceutics, vol. 6, no. 2, pp. 165-175, 1978.
H. Akaikei, "Information theory and an extension of maximum likelihood principle", In Proc. 2nd Int. Symp. on Information Theory, pp. 267-281, 1973.
E.J. Hannan, & B.G. Quinn, "The determination of the order of an autoregression", Journal of the Royal Statistical Society: Series B (Methodological), vol. 41, no. 2, pp. 190-195, 1979.
G. Schwarz, "Estimating the dimension of a model," The Annals of Statistics, vol. 6, no. 2, pp. 461-464, 1978.
S. Johansen, "Statistical analysis of cointegration vectors", Journal of Economic Dynamics and Control, vol. 12, no. 2-3, pp. 231-254, 1988.
G.S. Maddala and I.M. Kim, Unit roots, cointegration, and structural change, 1998.
V. Patilea, & H. Raïssi, "Corrected portmanteau tests for VAR models with time-varying variance", Journal of Multivariate Analysis, vol. 116, pp. 190-207, 2013.
H. Bouakez, & M. Normandin, "Fluctuations in the foreign exchange market: How important are monetary policy shocks?", Journal of International Economics, vol. 81, no. 1, pp. 139-153, 2010.
O.C. Onifade, & S.O. Olanrewaju, "Investigating performances of some statistical tests for heteroscedasticity assumption in generalized linear model: A Monte Carlo simulations study", Open Journal of Statistics, vol. 10, no. 3, pp. 453-493, 2020.
H. Lütkepohl, "Structural vector autoregressive analysis for cointegrated variables", Allgemeines Statistisches Archiv, vol. 90, pp. 75-88, 2006.
C.M. Jarque, & A.K. Bera, "A test for normality of observations and regression residuals", International Statistical Review/Revue Internationale de Statistique, pp. 163-172, 1987.
H. Herwartz, "Hodges–Lehmann detection of structural shocks–an analysis of macroeconomic dynamics in the euro area", Oxford Bulletin of Economics and Statistics, vol. 80, no. 4, pp. 736-754, 2018.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Sameera A. Othman, Hasan H. Jameel and Sadeq T. Abdulazeez
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
