Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series

Chepngetich Mercy; John Kihoro

doi:doi:10.11648/j.sjams.20150303.15

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Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series

Chepngetich Mercy, John Kihoro

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 3)

Received: 5 March 2015 Accepted: 20 March 2015 Published: 18 May 2015

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Abstract

Seasonal Autoregressive Integrated Moving Averages (SARIMA) model has been applied in most research work to forecast seasonal univariate data. Less has been done on Vector Autoregressive (VAR) process. In this research project, seasonal univariate time series data has been used to estimate a VAR model for a reshaped seasonal univariate time series for forecasting. This was done by modeling a reshaped seasonal univariate time series data using VAR. The quarterly data is reshaped to vector form and analyzed to vector form and analyzed using VAR for the year 1959 and 1997 to fit the model and the prediction for the year 1998 is used to evaluate the prediction performance. The performance measures used include; mean square error (MSE), root mean square error (RMSE), mean percentage error (MPE), mean absolute percentage error (MAPE) and Theil’s U statistic. Forecasting future values from the fitted models in both SARIMA and VAR using Box Jenkins procedures, (Box and Jenkins; 1976) was done. The results showed that both models are appropriate in forecasting but VAR is more appropriate model than SARIMA model since its predictive performance was shown to be the best. Other data sets were also used for analysis and comparison purpose.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 3)
DOI	10.11648/j.sjams.20150303.15
Page(s)	124-135
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Vector Autoregressive Process, Seasonal Autoregressive Integrated Moving Average Process, Vector Error Correction Model, Akaike Information Criterion

References

[1]	Mei, q., liu, y. & jing, x. (2011).Forecast the gdp of shanghai based on the multi-factors VAR model. Journal of Hubei University of Technology, 26(3).
[2]	Box, g.e.p., Jenkins, g.ma.1976 .Time series analysis Forecasting and control, 2nd ed. Holden-Day.San.
[3]	Box, g. E. P. & pierce. D. A. 1970. Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American statistical association, 65(332), 1509–1526
[4]	Sims, c.a. 1980. Macroeconomics and reality. Econometrica, 48, 1-48
[5]	Zivot, e. And J.wang (2006). Modeling Financial Time series with Splus, 2nd Edition.Springer, p.p. 385-386.
[6]	Clarida, r. H. & Friedman, b. M. (1984). The behavior of u.s. Short-term interest rates since October 1979. The Journal of finance, 39(3), 671-682.
[7]	Mills, T.C. (1999). The Econometric modeling of financial time series, second edition. Cambridge university press, Cambridge
[8]	Xiao Han Cai (2008). Time series analysis of air pollution co in California south coast area, with seasonal ARIMA model and VAR model. University of California, Los Angeles.
[9]	Zivot, E. and J.Wang (2006), Modeling Financial Time Series with SPlus, Springer.
[10]	Pfa, Bernhard (July 2008), ‘Var, svar and svec models: Implementation within r package vars’,Journal of Statistical software published by the Statistical Association.
[11]	Aidoo, E (2010), ‘Modelling and forecasting inflation rates in ghana: An application of sarima models’, Hogskolan Dalarna.
[12]	Diebold, F. X. & Mariano, R. S. (1995), ‘Comparing predictive accuracy’, Journal of Business and Statistics .
[13]	Halim, S. and I.N. Bisono (2008), ‘Automatic seasonal autoregressive moving average models and unit root test detection’, International Journal of Management Science and Engineering Management.
[14]	J.D., Cryer and K.S Chan (2008), Time Series Analysis with Applications in R., Springer Science +Business Media.

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APA Style

Chepngetich Mercy, John Kihoro. (2015). Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series. Science Journal of Applied Mathematics and Statistics, 3(3), 124-135. https://doi.org/10.11648/j.sjams.20150303.15

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ACS Style

Chepngetich Mercy; John Kihoro. Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series. Sci. J. Appl. Math. Stat. 2015, 3(3), 124-135. doi: 10.11648/j.sjams.20150303.15

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AMA Style

Chepngetich Mercy, John Kihoro. Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series. Sci J Appl Math Stat. 2015;3(3):124-135. doi: 10.11648/j.sjams.20150303.15

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@article{10.11648/j.sjams.20150303.15,
  author = {Chepngetich Mercy and John Kihoro},
  title = {Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {3},
  pages = {124-135},
  doi = {10.11648/j.sjams.20150303.15},
  url = {https://doi.org/10.11648/j.sjams.20150303.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150303.15},
  abstract = {Seasonal Autoregressive Integrated Moving Averages (SARIMA) model has been applied in most research work to forecast seasonal univariate data. Less has been done on Vector Autoregressive (VAR) process. In this research project, seasonal univariate time series data has been used to estimate a VAR model for a reshaped seasonal univariate time series for forecasting. This was done by modeling a reshaped seasonal univariate time series data using VAR. The quarterly data is reshaped to vector form and analyzed to vector form and analyzed using VAR for the year 1959 and 1997 to fit the model and the prediction for the year 1998 is used to evaluate the prediction performance. The performance measures used include; mean square error (MSE), root mean square error (RMSE), mean percentage error (MPE), mean absolute percentage error (MAPE) and Theil’s U statistic. Forecasting future values from the fitted models in both SARIMA and VAR using Box Jenkins procedures, (Box and Jenkins; 1976) was done. The results showed that both models are appropriate in forecasting but VAR is more appropriate model than SARIMA model since its predictive performance was shown to be the best. Other data sets were also used for analysis and comparison purpose.},
 year = {2015}
}

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TY  - JOUR
T1  - Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series
AU  - Chepngetich Mercy
AU  - John Kihoro
Y1  - 2015/05/18
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150303.15
DO  - 10.11648/j.sjams.20150303.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 124
EP  - 135
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150303.15
AB  - Seasonal Autoregressive Integrated Moving Averages (SARIMA) model has been applied in most research work to forecast seasonal univariate data. Less has been done on Vector Autoregressive (VAR) process. In this research project, seasonal univariate time series data has been used to estimate a VAR model for a reshaped seasonal univariate time series for forecasting. This was done by modeling a reshaped seasonal univariate time series data using VAR. The quarterly data is reshaped to vector form and analyzed to vector form and analyzed using VAR for the year 1959 and 1997 to fit the model and the prediction for the year 1998 is used to evaluate the prediction performance. The performance measures used include; mean square error (MSE), root mean square error (RMSE), mean percentage error (MPE), mean absolute percentage error (MAPE) and Theil’s U statistic. Forecasting future values from the fitted models in both SARIMA and VAR using Box Jenkins procedures, (Box and Jenkins; 1976) was done. The results showed that both models are appropriate in forecasting but VAR is more appropriate model than SARIMA model since its predictive performance was shown to be the best. Other data sets were also used for analysis and comparison purpose.
VL  - 3
IS  - 3
ER  -

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Author Information

Chepngetich Mercy

Jomo Kenyatta University of Agriculture and Technology, School of Mathematical Sciences, Nairobi, Kenya
John Kihoro

Cooperative University College of Kenya, Department of Computing and e-learning, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Chepngetich Mercy, John Kihoro. (2015). Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series. Science Journal of Applied Mathematics and Statistics, 3(3), 124-135. https://doi.org/10.11648/j.sjams.20150303.15

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ACS Style

Chepngetich Mercy; John Kihoro. Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series. Sci. J. Appl. Math. Stat. 2015, 3(3), 124-135. doi: 10.11648/j.sjams.20150303.15

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AMA Style

Chepngetich Mercy, John Kihoro. Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series. Sci J Appl Math Stat. 2015;3(3):124-135. doi: 10.11648/j.sjams.20150303.15

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@article{10.11648/j.sjams.20150303.15,
  author = {Chepngetich Mercy and John Kihoro},
  title = {Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {3},
  pages = {124-135},
  doi = {10.11648/j.sjams.20150303.15},
  url = {https://doi.org/10.11648/j.sjams.20150303.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150303.15},
  abstract = {Seasonal Autoregressive Integrated Moving Averages (SARIMA) model has been applied in most research work to forecast seasonal univariate data. Less has been done on Vector Autoregressive (VAR) process. In this research project, seasonal univariate time series data has been used to estimate a VAR model for a reshaped seasonal univariate time series for forecasting. This was done by modeling a reshaped seasonal univariate time series data using VAR. The quarterly data is reshaped to vector form and analyzed to vector form and analyzed using VAR for the year 1959 and 1997 to fit the model and the prediction for the year 1998 is used to evaluate the prediction performance. The performance measures used include; mean square error (MSE), root mean square error (RMSE), mean percentage error (MPE), mean absolute percentage error (MAPE) and Theil’s U statistic. Forecasting future values from the fitted models in both SARIMA and VAR using Box Jenkins procedures, (Box and Jenkins; 1976) was done. The results showed that both models are appropriate in forecasting but VAR is more appropriate model than SARIMA model since its predictive performance was shown to be the best. Other data sets were also used for analysis and comparison purpose.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series
AU  - Chepngetich Mercy
AU  - John Kihoro
Y1  - 2015/05/18
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150303.15
DO  - 10.11648/j.sjams.20150303.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 124
EP  - 135
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150303.15
AB  - Seasonal Autoregressive Integrated Moving Averages (SARIMA) model has been applied in most research work to forecast seasonal univariate data. Less has been done on Vector Autoregressive (VAR) process. In this research project, seasonal univariate time series data has been used to estimate a VAR model for a reshaped seasonal univariate time series for forecasting. This was done by modeling a reshaped seasonal univariate time series data using VAR. The quarterly data is reshaped to vector form and analyzed to vector form and analyzed using VAR for the year 1959 and 1997 to fit the model and the prediction for the year 1998 is used to evaluate the prediction performance. The performance measures used include; mean square error (MSE), root mean square error (RMSE), mean percentage error (MPE), mean absolute percentage error (MAPE) and Theil’s U statistic. Forecasting future values from the fitted models in both SARIMA and VAR using Box Jenkins procedures, (Box and Jenkins; 1976) was done. The results showed that both models are appropriate in forecasting but VAR is more appropriate model than SARIMA model since its predictive performance was shown to be the best. Other data sets were also used for analysis and comparison purpose.
VL  - 3
IS  - 3
ER  -

Copy | Download