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Forecasting of Climatic Variables in Dinajpur of Bangladesh

J.A. Syeda
Department of Statistics Hajee Mohammad Danesh Science and Technology University, Dinajpur

Abstract/ Executive Summary:

An attempt was made to forecast the 17 monthly climatic variables for 2005-2012 of Dinajpur using the univariate Box-Jenkin’s ARIMA (autoregressive integrated moving average) modeling techniques for 1948-2004. The 8 years data for 1973-1980 were missing and those data were replaced with the 4 years monthly forecasted data for 1948-1972 and 1981-2004 (reversing the years). The well fitted ARIMA (autoregressive integrated moving average) models were selected from the possible 16 ARIMA models based on the minimum root mean square forecasting errors (RMSFE) with the last 24 observations for all the cases and the residuals followed stationarity and normality. Several outliers were detected in the data which were replaced by the forecasted value. The fitted model for sunshine data (1989-2004) was found ARIMA (1, 1, 1)(1, 1, 1)12 and for evaporation data (1987-2000) was ARIMA (1, 1, 2)(1, 1, 1)12. . The findings supports that the changing term of the climatic variables may have adverse impacts on the crop production in this country.

Keywords: ARIMA, Climate, Forecasting

Location: Dinajpur

Start Date: 00-00-2005

End Date: 00-00-2012

Program Area: Risk Management in Agriculture

Non-commodity: Weather/Climate

Objectives:

In this study, it was tried to forecast 17 climatic variables using the monthly data by fitting the ARIMA model.

Methodology:

In this section, the methodologies used in the analyses have been discussed. Univariate Box-Jenkin’s ARIMA model was fitted to forecast the monthly data for January 2008-December 2012. After confirmed the stationary series, an effort was made for an ARIMA model to express each observation as a linear function of the previous value of the series (autoregressive parameter) and of the past error effect (moving average parameter). The available data were divided into training, validation and test sets. The training set was used to build the model, the validation set was used for parameter optimization and the test set was used to evaluate the model. The adequacy of the above model was checked by comparing the observed data with the forecasted results. In this study, the data for the last two years were used to compare with the fitted model forecasts for the years and the models were selected for the minimum root mean square forecasting error (MRMSFE) of the data set of those two years. The diagnostic techniques namely histogram of residuals, normal probability plot of residuals, autocorrelation function (ACF) and Partial autocorrelation (PACF) display of residuals, Time series (TS) plots for residual versus fitted values and TS plots for residual versus order of the data were used for checking residuals of ARIMA models. Box-Cox transformation was used for variance stabilization and the transformation of the data to get stationary series from non-stationary series, Pankraiz (1991). The software package Minitab 13 was used to fit the ARIMA models. A detailed description of the non-seasonal and seasonal ARIMA models. Box Jenkins modelling strategy and ARIMA model Box Jenkins (1976) formalized the ARIMA modeling framework in the three steps: (I) Identification, (II) Estimation and (III) Verification. In the identification stage, it is tried to identify that how many terms to be included is based on the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the differenced and/or transformed time series (Box Jenkins, 1976). In the estimation stage, the coefficients of the model are estimated by means of the maximum likelihood method. The verification of the model is done through diagnostic checks of the residuals (histogram or normal probability plot of residuals, standardized residuals and ACF and PACF of the residuals). The performance of the ARIMA models is often tested through comparison of prediction with observation not used in the fitted model. An appropriate ARIMA model provides minimum mean squared error forecasts among all linear univariate models with fixed coefficients. It can produce point forecasts for each time period and interval forecasts constructing a confidence interval around each point forecast. To have the 95% interval for each forecast the formulae f ± 2s is used, where f denotes a forecast and s is its standard error. The forecasts for a stationary model converge to the mean of the series and the speed of converging movement depends on the nature of the model. For non-stationary model the forecasts do not converge to the mean.

Source of Information: J. Environ. Sci. & Natural Resources, 10(2): 163–170, 2017 ISSN 1999-7361

Article Link (Online Journal):

Funding Source:

1.

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Total Budget (Tk.) :

Achievement/Findings:

The earlier presented ARIMA models for the monthly data during 1948-1972, 1981-2004 (reversing the years), 1948-2004 and 1948-2008 on the basis of minimum root mean square forecasting error. Those models were selected from the possible 16 ARIMA (autoregressive integrated moving average) models based on minimum root mean square forecasting error (RMSFE) with the last 24 observations for all the cases and all the residuals followed stationarity and normality. The 17 ARIMA models of the climatic variables (with the required transformations) during 1948-2004 were selected. These were ARIMA (1, 0, 0) (1, 1, 1) 12 for SQRT of TR; ARIMA (1, 1, 1) (0, 1, 1) 12 for TFIR; ARIMA (1, 0, 0) (1, 1, 1) 12 for SQRT of MXR ; ARIMA (1, 0, 1) (1, 1, 1) 12 for AMNT; ARIMA (1, 0, 0) (0, 1, 1) 12 for SQRT of AMXT; ARIMA (1, 0, 0) (0, 1, 1) 12 for ARNT; ARIMA (1, 1, 1) (0, 1, 1) 12 for ARH (l=3); ARIMA (1, 1, 1) (0, 1, 1) 12 for SQRT of AWS; ARIMA (0, 1, 1) (1, 0, 1) for SQRT of AMWS; ARIMA (0, 1, 1) (1, 1, 1) 12 for AC; ARIMA (0, 1, 1) (1, 0, 1) 12 for ADBT; ARIMA (1, 0, 1) (1, 1, 1) 12 for AWBT; ARIMA (1, 0, 1) (1, 0, 1) 12 for Ln of AT(D-W); ARIMA (0, 1, 1) (1, 0, 1) 12 for ASLP; ARIMA (2, 0, 0) (1, 0, 1) 12 for Ln of ARH(0-12); ARIMA (1989-04) (1, 1, 1) (1, 1, 1) 12 for ASH and ARIMA (1987-00) (1, 1, 2) (1, 1, 1) 12 for AE. The data of 1981 for AMNT, ARNT, ARH, AWS, AWBT and ARH(0-12) were detected as outliers which were replaced by the forecasted value of 1981 from the fitted ARIMA models for January 1982 December 2004 by reversing the years So, the findings pinpoints that the changing term of the climatic variables may have adverse impacts on the crop production in this country. Hence, judicious planning is very much essential to suit with the changes for sustainable development in agriculture.

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