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Application of Arima Model for Rainfall Forecasting in Rajshahi

Md. Syful Islam*
nstitute of Environmental Science, University of Rajshahi, Rajshahi-6205, Bangladesh

Md. Jahanur Rahman
Department of Statistics, University of Rajshahi, Rajshahi-6205, Bangladesh

Abstract/ Executive Summary:

Forecasting of monthly rainfall is not only challenging but also significantly important in drought forecasting in agriculture, irrigation schedule, water resources management and crop pattern design. The goal of this study is to focus on development of a reliable forecasting of rainfall using stochastic methods. In this paper, Box-Jenkins time series seasonal ARIMA (Autoregressive Integrated Moving Average) approach has been used to develop monthly forecasting models for rainfall prediction using monthly rainfall data of Rajshahi, Bangladesh. Seasonal ARIMA model (0, 0, 0) (1, 1, 1) for rainfall was identified as the best model to forecast rainfall for next four years. It is expected that this prediction will help decision makers in efficient scheduling of flood prediction, urban planning, rainwater harvesting and crop management.

Keywords: Rainfall, Stationary, Seasonal ARIMA, Forecasting.

Location: Rajshahi

Start Date:

End Date:

Program Area: Resource Development and Management

Non-commodity: Rainfall, Modeling

Objectives:

Urban Rajshahi and some other regions including Padma river basin are facing rapid ground water depletion. Besides, excessive iron and arsenic contamination has an adverse impact in drinking water supply. To pursue a sustainable alternative source of water supply, uses of rainwater has become a suitable option in many parts of the region. Therefore the aim of this study is to focus on development of a reliable forecasting of rainfall over Rajshahi to manage water resources.

Methodology:

2.1. Study Area: The study area, Rajshahi is situated within Barind Tract, 23 m (75 ft.) above sea level and lies at 24°22′26″N 88°36′04″E. The city is located on the alluvial plans of the Padma River which runs through southern side of the city. The climate of Rajshahi district is tropical wet and dry. The climate of Rajshahi is generally marked with monsoons, high temperature, considerable humidity and moderate rainfall. The highest rainfall is observed during the months of monsoon. The annual rainfall of the district is about 1448 mm (57.0 inches) but the variation from year to year is appreciable.

2.3. Software Used The various kinds of software that used during the process include Microsoft Excel (MS-Excel) and Eviews 8.

2.4. Methodology In time series analysis, the Box-Jenkins methodology applies Autoregressive Moving Average (ARMA), Autoregressive Integrated Moving Average (ARIMA) or Seasonal Autoregressive Moving Average (SARIMA) models to establish the best fit of time series to make forecasts. The order of ARIMA model p,d,q present the order of the auto regressive (AR) part; degree of differencing involved and order of the moving average (MA) part respectively.

The Box-Jenkins methodology consists of four steps: (i) Model identification, (ii) Estimation of the model parameters (iii) Diagnostic checking of the model adequacy and (iv) Forecasting. The first step involves testing whether the time series is stationary and if there is significant seasonality that needs to be modeled. The auto correlation function (ACF) and the partial auto correlation (PACF) are the most important tools for choosing the orders of the ARIMA model. The ACF quantifies the extent of linear dependence between time series observations separated by a lag k which provide information regarding stationarity of the series. The ACF and PACF help to determine how many moving average and autoregressive terms are necessary to reveal one or more of the following characteristics: time lags where high correlations appears seasonality of the series and the trend either in the means or variances of the series.

The stationary of data can also be identified by using a number of unit root tests. Moreover, we have applied some formal unit root tests for checking the stationary of the series. Unfortunately, it is well known that unit-root tests have low power and that results can vary with the types of test used and the number of lags included in the test equations. For this reason, it becomes a strategy among there searchers to examine the results of several test procedures in order to draw conclusions on stationary. With this in mind, three unit root tests are performed: (i) most widely used Augmented Dicky-Fuller (ADF) test of Dicky and Fuller (1979, 1981) (ii) the asymptotically most powerful DF-GLS test of Elliott et al., 1996 and (iii) the Kwiatkowski et al., 1992, LM test (KPSS). The null hypothesis of ADF and DF-GLS tests is that a time series variable has a unit root while KPSS test is that a variable is stationary. A common strategy is to present results of both ADF/DF-GLS and KPSS tests, and show that the results are consistent (e.g., that the former reject the null while the later fail to do so and vice-versa). The lag length is selected by using the Akaike Information Criteria (AIC), setting the maximum lag at 12.

Source of Information: Rajshahi University Journal of Environmental Science, 6, 47-54, 2017

Article Link (Online Journal):

Funding Source:

Budget:

Total Budget (Tk.) :

Achievement/Findings:

Time-series analysis is an important tool in modeling and forecasting rainfall. The Box-Jenkins seasonal ARIMA models are applied to forecast monthly rainfall of Rajshahi. Rainfall pattern of Rajshahi shows significant changes over time. Seasonality has significant effects on general pattern of the rainfall series. After having examined we conclude that seasonal ARIMA (0,0,0) (1,1,1) model is the best fit and reliable for forecasting the total recorded monthly rainfall data of Rajshahi in which constant trend can also be noticed.

Knowledge Management: Journal