A time series is a set of numbers that measures the status of some activity over equally spaced time interval. It is the historical record of some activity, with measurements taken at equally spaced intervals with a consistency in the activity and the method of measurement.
Box and Jenkins procedure’s steps i. Preliminary analysis: create conditions such that the data at hand can be considered as the realization of a stationary stochastic process. ii. Identification: specify the orders p, d, q of the ARIMA model so that it is clear the number of parameters to estimate. Recognizing the behavior of empirical autocorrelation functions plays an extremely important role. iii. Estimate: efficient, consistent, sufficient estimate of the parameters of the ARIMA model (maximum likelihood estimator). iv. Diagnostics: check if the model is a good one using tests on the parameters and residuals of the model. Note that also when the model is rejected, still this is a very useful step to obtain information to improve the model.
5.1. Other Techniques and Tools Used in This Study • To check normality assumption “Jarque-Bera” test (Jarque & Bera, 1980) is used which is a goodness of fit measure of departure from normality, based on the sample kurtosis and skewness. • To check autocorrelation among the residuals, “Ljung-Box” (Box and Ljung, 1978) test is used under the hypothesis that there is no autocorrelation among the residuals. • Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) are used to detect the order of difference of stationarity conditions. • Akaike Information Criterion (AIC) and Baysian Information Criterion (BIC) are used as a model selection criterion.
6. Data Sources, Data Manipulation and Used Software The climatic information are available from the Bangladesh Government’s authorized websites of Bangladesh Rice Research Council (BARC) named as www.barc.gov.bd. The pulse crop datasets are also available from Bangladesh Agricultural Ministry’s website named as www.moa.gov.bd. These dataset are available from the year 1972 to 2006. Climatic information was in the original form such a way that it is arranged in the monthly average information corresponding to the years from 1972 to 2006 according to the 30 climatic stations. The name of these stations are Dinajpur, Rangpur, Rajshahi, Bogra, Mymensingh, Sylhet, Srimangal, Ishurdi, Dhaka, Comilla, Chandpur, Josser, Faridpur, Madaripur, Khulna, Satkhira, Barisal, Bhola, Feni, MaijdeeCourt, Hatiya, Sitakunda, Sandwip, Chittagong, Kutubdia, Cox's Bazar, Teknaf, Rangamati, Patuakhali, Khepupara, Tangail, and Mongla. It is taken the month October, November, December, January and February as a “dry season” and March, April, May, June, July, August, September as a “summer season” considering the weather and climatic conditions of Bangladesh. Then, finally we take average seasonal climatic information of 30 climatic station corresponding to the year from 1972 to 2006. We take the average of 30 climatic area because of focusing the overall country’s situation and overall model fitting for whole Bangladesh. This analysis has completely done by statistical programming based open source Software R for windows (version 2.15.1). The additional library packages used for analysis are forecast, TSA and tseries, etc.
7. Used Climatic Variables in This Study sun.sum = Sunshine of the Summer Season, sun.dry = Sunshine of the Dry Season , clo.sum = Cloud Coverage of the Summer Season, clo.dry = Cloud Coverage of the Dry Season, max.tem.dry = Maximum Temperature of the Dry Season, max.tem.sum = Maximum Temperature of the Summer Season, min.tem.dry = Minimum Temperature of the Dry Season, min.tem.sum = Minimum Temperature of the Summer Season, rain.dry= Ammount of Rainfall of the Dry Season, rain.sum= Amount Rainfall of the Summer Season, rh.dry = Relative Humidity of the Dry Season, rh.sum= Relative Humidity of the Summer Season, wind.dry = Wind Speed of the Dry Season and wind.sum = Wind Speed of The Summer Season.