Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia)

Teshome Hailemeskel Abebe

doi:doi:10.11648/j.ijtam.20200605.13

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Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia)

Teshome Hailemeskel Abebe

Published in International Journal of Theoretical and Applied Mathematics (Volume 6, Issue 5)

Received: 27 October 2020 Accepted: 5 November 2020 Published: 11 December 2020

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Abstract

Forecasting mean temperature and rainfall is an important for planning and formulating agricultural strategies. Thus, this paper, try to analyze and forecast monthly mean temperature and rainfall in Ambo area on the data from January 2012 to March 2019. From graphical analysis on time plot and ACF, the series seems to have a seasonal component. For that purpose, a Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used to estimate and forecast the average monthly temperature and rainfall in the Ambo area, Ethiopia. Among the competitive tentative model, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 model are the best time series model for fitting and forecasting mean temperature and rainfall, respectively. Moreover, the model diagnostic test on the residuals of SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 on mean temperature and rainfall satisfies the randomness, independency, normality and constant variance (homoscedasticity) assumptions. Finally, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 were used to forecast mean of monthly temperature and rainfall from the period April 2019 to March 2023.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 6, Issue 5)
DOI	10.11648/j.ijtam.20200605.13
Page(s)	76-87
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

Temperature, Rainfall, SARIMA, Modeling, Forecasting

References

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[6]	Robinson, S., Willenbockel, D. and Strzelecki, K., (2012). A Dynamic General Equilibrium Analysis of Adaptation to Climate Change in Ethiopia. Review of Development Economics 16, 489-502.
[7]	Box GEP, Pierce, D. A. (1970). Distributions of residual autocorrelations in autoregressive integrated moving average models. J American Stat Assoc 72: 397-402.
[8]	Tektaş, M. (2010). Weather forecasting using ANFIS and ARIMA models. A case study for Istanbul. Environmental Research, Engineering and Management 51 (1): 5–10.
[9]	Ademola, A., Emmanuel, C. O., and Aderemi, K. A. (2018). Statistical Modeling of Monthly Rainfall in Selected Stations in Forest and Savannah Eco-climatic Regions of Nigeria. Journal of Climatology & Weather Forecasting. 6: S1. DOI: 10.4172/2332-2594.1000226.
[10]	BOX, G. E. P. & JENKINS, G. M. (1976). Time Series Analysis: Forecasting and Control. Revised Edition, Holden-Day: San Francisco, CA.
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[15]	Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Journal of Econometrics, Vol. 50, P 987-1007.
[16]	Chatfield, C. (2004). The analysis of time series: An introduction, 6^th ed. London, UK: Chapman & Hall/CRC.

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APA Style

Teshome Hailemeskel Abebe. (2020). Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia). International Journal of Theoretical and Applied Mathematics, 6(5), 76-87. https://doi.org/10.11648/j.ijtam.20200605.13

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ACS Style

Teshome Hailemeskel Abebe. Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia). Int. J. Theor. Appl. Math. 2020, 6(5), 76-87. doi: 10.11648/j.ijtam.20200605.13

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AMA Style

Teshome Hailemeskel Abebe. Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia). Int J Theor Appl Math. 2020;6(5):76-87. doi: 10.11648/j.ijtam.20200605.13

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@article{10.11648/j.ijtam.20200605.13,
  author = {Teshome Hailemeskel Abebe},
  title = {Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia)},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {6},
  number = {5},
  pages = {76-87},
  doi = {10.11648/j.ijtam.20200605.13},
  url = {https://doi.org/10.11648/j.ijtam.20200605.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20200605.13},
  abstract = {Forecasting mean temperature and rainfall is an important for planning and formulating agricultural strategies. Thus, this paper, try to analyze and forecast monthly mean temperature and rainfall in Ambo area on the data from January 2012 to March 2019. From graphical analysis on time plot and ACF, the series seems to have a seasonal component. For that purpose, a Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used to estimate and forecast the average monthly temperature and rainfall in the Ambo area, Ethiopia. Among the competitive tentative model, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 model are the best time series model for fitting and forecasting mean temperature and rainfall, respectively. Moreover, the model diagnostic test on the residuals of SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 on mean temperature and rainfall satisfies the randomness, independency, normality and constant variance (homoscedasticity) assumptions. Finally, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 were used to forecast mean of monthly temperature and rainfall from the period April 2019 to March 2023.},
 year = {2020}
}

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TY  - JOUR
T1  - Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia)
AU  - Teshome Hailemeskel Abebe
Y1  - 2020/12/11
PY  - 2020
N1  - https://doi.org/10.11648/j.ijtam.20200605.13
DO  - 10.11648/j.ijtam.20200605.13
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 76
EP  - 87
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20200605.13
AB  - Forecasting mean temperature and rainfall is an important for planning and formulating agricultural strategies. Thus, this paper, try to analyze and forecast monthly mean temperature and rainfall in Ambo area on the data from January 2012 to March 2019. From graphical analysis on time plot and ACF, the series seems to have a seasonal component. For that purpose, a Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used to estimate and forecast the average monthly temperature and rainfall in the Ambo area, Ethiopia. Among the competitive tentative model, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 model are the best time series model for fitting and forecasting mean temperature and rainfall, respectively. Moreover, the model diagnostic test on the residuals of SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 on mean temperature and rainfall satisfies the randomness, independency, normality and constant variance (homoscedasticity) assumptions. Finally, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 were used to forecast mean of monthly temperature and rainfall from the period April 2019 to March 2023.
VL  - 6
IS  - 5
ER  -

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Author Information

Teshome Hailemeskel Abebe

Department of Economics, Ambo University, Ambo, Ethiopia

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Plain Text BibTeX RIS

APA Style

Teshome Hailemeskel Abebe. (2020). Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia). International Journal of Theoretical and Applied Mathematics, 6(5), 76-87. https://doi.org/10.11648/j.ijtam.20200605.13

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ACS Style

Teshome Hailemeskel Abebe. Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia). Int. J. Theor. Appl. Math. 2020, 6(5), 76-87. doi: 10.11648/j.ijtam.20200605.13

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AMA Style

Teshome Hailemeskel Abebe. Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia). Int J Theor Appl Math. 2020;6(5):76-87. doi: 10.11648/j.ijtam.20200605.13

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@article{10.11648/j.ijtam.20200605.13,
  author = {Teshome Hailemeskel Abebe},
  title = {Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia)},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {6},
  number = {5},
  pages = {76-87},
  doi = {10.11648/j.ijtam.20200605.13},
  url = {https://doi.org/10.11648/j.ijtam.20200605.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20200605.13},
  abstract = {Forecasting mean temperature and rainfall is an important for planning and formulating agricultural strategies. Thus, this paper, try to analyze and forecast monthly mean temperature and rainfall in Ambo area on the data from January 2012 to March 2019. From graphical analysis on time plot and ACF, the series seems to have a seasonal component. For that purpose, a Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used to estimate and forecast the average monthly temperature and rainfall in the Ambo area, Ethiopia. Among the competitive tentative model, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 model are the best time series model for fitting and forecasting mean temperature and rainfall, respectively. Moreover, the model diagnostic test on the residuals of SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 on mean temperature and rainfall satisfies the randomness, independency, normality and constant variance (homoscedasticity) assumptions. Finally, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 were used to forecast mean of monthly temperature and rainfall from the period April 2019 to March 2023.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia)
AU  - Teshome Hailemeskel Abebe
Y1  - 2020/12/11
PY  - 2020
N1  - https://doi.org/10.11648/j.ijtam.20200605.13
DO  - 10.11648/j.ijtam.20200605.13
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 76
EP  - 87
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20200605.13
AB  - Forecasting mean temperature and rainfall is an important for planning and formulating agricultural strategies. Thus, this paper, try to analyze and forecast monthly mean temperature and rainfall in Ambo area on the data from January 2012 to March 2019. From graphical analysis on time plot and ACF, the series seems to have a seasonal component. For that purpose, a Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used to estimate and forecast the average monthly temperature and rainfall in the Ambo area, Ethiopia. Among the competitive tentative model, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 model are the best time series model for fitting and forecasting mean temperature and rainfall, respectively. Moreover, the model diagnostic test on the residuals of SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 on mean temperature and rainfall satisfies the randomness, independency, normality and constant variance (homoscedasticity) assumptions. Finally, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 were used to forecast mean of monthly temperature and rainfall from the period April 2019 to March 2023.
VL  - 6
IS  - 5
ER  -

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