Analysis and Predictions of Seasonal Affected Weather Variables of Bangladesh : SARIMA Models vs . Traditional Models

Bangladesh is a semi-tropical country, categorized by widespread seasonal disparities in rainfall, temperature, and humidity. Seasonality has been an input aspect of time series modeling when taking into account weather variables. In terms of multiple features of the weather variables i.e. randomness, cyclical variation and trend, time series methods etc. ARIMA can be a superior preference but, weather variables are affected by seasonality. Thinking about the grimy meadow, this paper presents Seasonal Auto-regressive Moving Average (SARIMA) model that takes seasonal and cyclical variation over the years. This study also aims to compare traditional methods like Single Exponential Method, Double Exponential Method, and Holt Winter Method with the SARIMA model. Time series plots, month plots, and B-B plots are used for identifying seasonal effect clearly. For seasonal stationary checking, Canova Hansen Stationary test has been utilized. Then, the order of the variables is identified, ACF and PACF have been checked and estimated preeminent order for these variables by AIC and Log-likelihood. Finally, Single Exponential Method, Double Exponential Method, and Holt Winter Method are introduced for comparing and forecasting. The proposed models SARIMA(0,0,0)(1,0,3)12, SARIMA(0,0,0)(1,0,1)12, SARIMA(0,0,0)(1,0,2)12 and SARIMA(0,0,0)(1,0,1)12 for maximum and minimum temperature, rainfall and humidity on the basis of Akaike Information Criteria and Log likelihood have been captured most seasonality of the data. Comparing them with traditional methods, traditional methods give a better result than the acquired model based on error measurement. So, traditional methods give a better estimate than the SARIMA models for selected weather variables, with lower mean square error, RMSE, MAE and MASE.


Introduction
Forecasting is a procedure in managing to support decision making as well as the process of estimation in unidentified future situations (Khan, Islam, Kabir, & Ali, 2016).Bangladesh, extremely vulnerable to natural adversities because of its terrestrial position, evenly and low-lying land, densely populated, poverty, high illiteracy, deficiency of institutional set up etc., is one of the leading deltas in the world.Also, Bangladesh is typically one of the most susceptible countries to natural calamities around the globe (Chatfield, 2003).The area of Bangladesh is consisting of 147570 sq.km that are typically floodplains (nearly 80%) leaving the majority of the country inclined to flood throughout the rainy season.Furthermore, climate alteration of the country mainly depends on high temperature, rising sea level, cyclones, and storm flow, salinity interruption, deep monsoon downpours etc. that affect the total financial condition (Chatfield, 2003).So, the climate can be categorized by three seasonal variations like burning summer, shrinking winter and average to intense rains in rainy time in Bangladesh.Even with the latest strides towards attaining sustainable development, Bangladesh's potential to sustain its development is faced with noteworthy challenges posed by climate alteration (Ahmed, & Haque, 2002).That is why utmost weights are specified for variation to climate shift by identifying its susceptibility in terms of population and sectors at risk and it is potential.For this reason, Bangladesh Government has taken streamline actions towards helping to rework climate alteration and has set up the climate change cell under the guidance of the environment and forest ministry through the eye on crucial points of climate alteration problems.Moreover, Comprehensive Disaster Management and the UNDP supervised the activities of CCC activities.The climate change cell has made an excellent effort to the make readers aware about the dynamics of climate change and feebleness in Bangladesh by accessible on climate change documents to assess and produce the current knowledge.Also, a project was specially made on which the authors planned a study to combine all the pertinent findings accessible in the presently existing literature, so it helps in perceptive of climate change and classifies paths of action by various factors involved in the national expansion progressions (Ahmed, 2006).
Since Bangladesh is a climate exaggerated state, the authorities of the country must take a right decision about the future.Forecasting techniques akin to BJ method can facilitate us to predict the prospect climate change to assist the Bangladesh authorities.The BJ model has urged ARIMA model for forecasting among other methods (Wilks, 1938).Formally, Klein et al. (1970), Glahn & Lowry (1972) and Pankratz (1983) applied simple quantitative precipitation forecasting methods where they used changing patterns and variability in rainfall that may be associated with global warming due lost their edge [26,18,23].Borlando (1996) exploited ARIMA models to forecast the amounts gained and hourly precipitation in the time of their fall to evaluate the rain data (Kibunja, Kihoro, Orwa, & Yodah, 2014).Yusof and Kane (2012) examined seasonality of rainfall prediction using the SARIMA model for Golastan province (Wilks, 1938).Permanasari (2013) introduced SARIMA for forecasting number of complaint incidence in human (Ahmed, & Haque, 2002).Also, the ARIMA proffer an excellent process for producing the magnitude of any variables (Manoj Kumar, 2009).Lloret (2000) pioneered in fishery ARIMA models to forecast fishery landing in the Hellenic sea waters when lacking organized biological time series datasets from advisory erratic (Josep Lloret, 2000).Fang (1998) combined two methods, time-series and fuzzy regression in financial forecasting, to extend the fuzzy ARIMA model pedestal upon the works (Tseng, Tzeng, Yu, & Yuan, 1998).Ediger ( 2007) forecasted preliminary energy claim on fossil fuel using ARIMA and SARIMA model (Volkan & Ediger, 2007).Wood (1996) utilized ARIMA and Neural Network to project United Stated America Capital Market Index (Douglas Wood, 1996).The foremost aims of this study are: firstly, to analyze the special distinctiveness of the time series model all the way through diverse tests.Secondly, to build up a pertinent time series models for forecasting of the selected weather variables.Thirdly, to compare forecasting accuracy in different forecasting models through accuracy measurements.Finally, to recognize weather patterns in Bangladesh.

Data Collection and Computation
In this paper, secondary data are used for investigation and ultimate encroachment.Selected components of weather data such as maximum temperature, minimum temperature, rainfall and humidity, have been collected from the websites of Bangladesh Bureau of Statistics and Bangladesh Metrological Department (Bangladesh Bureau of Statistics, 2014).Analytical solutions are perpetrated through R-3.3.2 and Minitab-15.

Graphical Analysis of Time Series Data
The primary important thing is the exploration and visualization the data through graphs.Basic features, patterns and unusual observations of the data are most easily seen through graphs.Graphs also suggest possible explanations for some of the changes in the data.The initial footstep of any time series is to figure out the data that evidence the possible nature of the time series or express trend, seasonal or cyclical variations etc (Makridakis, Wheelwright, & Hyndman, 1998).This suggests whether the time series is nonstationary or not (Fomby, 2008).

Monthly Plot of Time Series
Seasonal subseries designs are a diagrammed tool to imaging and identifying seasonality in a time series by removing the seasons from a time series into a subseries by monthlies (Cleveland, 1995;Maindonald, & Braun, 2010).A seasonal subseries plot allows to see clearly the seasonal shape and shows the fluctuations in seasonality over time to allow detecting changes between different seasons, changes within a specific season over time.However, this plot is the only useful tool in many cases when the period of the seasonality is already identified (Glahn, & Lowry, 1972).

Buys Ballot Plot of Time Series
Diagnosing the presence or absence of seasonal effects in time series, Buys Ballot plots play so useful contributions."the Seasons-By Year" plot, "the Seasonal Trends" plot and "the Seasonal Averages" plot is of them.Separately, these plots are observed and compare with non-seasonal time series.The plots and have found to be so

The Methods for Prediction
Very often, management makes a plan for decision making and planning to help the administration in order to take the precise accurate decision.So, forecasting accuracy is very much required in the decision-making process.In some cases, the prediction may be peripheral to the decision being made and so a low-level accuracy may be adequate even though the decision may be an important one.So, determine in progress the least level of forecasting accuracy will be satisfactory in any situation (Wichern, & Hanke, 2014).

Seasonal Autoregressive Integrated Moving Average (SARIMA)
SARIMA has built as the non-seasonal fragment, AR factor, MA factor, and/or order of difference.Abundant of lags such as the number of periods in a season occurs in the seasonal portion of the model and all these factors operate across these multiples of lag s.A SARIMA model is categorized as an (, , )(, , ) m model, Where, P is the quantity of SAR terms, D is the number of periodic differences, and Q is the quantity of SMA terms.If the seasonal pattern is both strong and stable over time, then one can probably use a seasonal difference regardless of whether he/she uses a non-seasonal difference, since it will avoid from dying out in the enduring estimates.Also,  is the quantity of periods per season (Chatfield, 2003).

Single Exponential Smoothing Method
Single exponential smoothing usages an exponentially weighted average of entire past values of the series to analyze the smoothed value at the individual era.The furthermost observation takes the largest weight α (where 0 < α < ), the following latest observation obtains small weight ( ) α α − 1 , the observation two-time periods in the former even less weight, α (1-α ) 2 and so forth (Newbold, Carlson, & Thorne,   2012).

Double Exponential Smoothing
Double exponential smoothing works a level factor and trend element for each period.It practices two weight, or smoothing parameters, to reform the components at apiece.The double exponential smoothing equalities are:

(
)( ) and where,  is the time  at level L, α is the weight for the level,  is the time t with the trend,  is the weight for the trend,  is the data value at time random,  is the fitted value (Newbold, Carlson, & Thorne, 2012).

Holt-Winters' Method
Winter's Method calculates energetic assessments for three modules: level, trend, and seasonal.While the level and seasonal components are multiplied together, Holt-Winters' model is multiplicative and when they are added tranquil, is addictive.So, two models are as below:

Figure
Figure 6.AC

Table 2 .
The model selection criterions of the selected weather variables

Table 3 .
12 to Single Exponential, Double Exponential and Holt Winters' Method via ME, RMSE, MAE and MASE.Forecasting accuracy measures under different models for different variables * Holt

Winters' Method 0.21724 70.2358 48.0516 0.6919
The table3shows that the Single Exponential model has lowest errors than other model both for the variable's maximum temperature and minimum temperature.The Holt-Winters' method for other two variables, rainfall and humidity appear deepest errors.