Forecasting Temperatures in Bangladesh: An Application of SARIMA Models

Forecasting Temperatures in Bangladesh: An Application of SARIMA Models
IJSM
Forecasting Temperatures in Bangladesh: An Application
of SARIMA Models
Md. Siraj Ud Doulah
Department of Statistics, Begum Rokeya University, Rangpur, Bangladesh.
E-mail: sdoulah_brur@yahoo.com
Climate change is presently among the significant topics of discussion and temperature is one of
its main components. In this study, it is to be observed that the minimum temperature is more
fluctuating compared to the maximum temperature. Several suggested SARIMA models were
established for maximum and minimum temperature series according to the methods of the Box
Jenkin’s methodology. The best model for maximum temperature is SARIMA (1, 0, 0) (1, 1, 0)12
and for minimum temperature is SARIMA (2, 0, 1) (2, 1, 0)12 selected based on AIC. From the model
validation outcomes, the projected values are well-fitted through the original data with the lower
and upper limits holding bulks of the original data. The detected models are therefore suitable to
be used for projecting monthly maximum and minimum temperature in Bangladesh. The selected
SARIMA models give two-year predicted monthly maximum and minimum temperatures that can
help decision makers to establish priorities for preparing themselves against forthcoming
weather fluctuations. The forecasts also display that the minimum temperature of Bangladesh will
continue with the upward trend. This is a reflection of a fluctuating climate in the entire country.
Keywords: Temperature, SARIMA, Validation, Forecasting, Bangladesh
INTRODUCTION
The most influential factors in the climate are temperature
and moisture. According to a study by Oluwafemi et al.
(2010), climate change seems to be one of the most
important issues in the recent two decades and
temperature has been identified as one of the key
elements that can indicate climate change. The gradual
rise in the mean temperature of the Earth’s atmosphere
and its oceans is referred to as Global warming. It is widely
believed that the changing temperature due to global
warming is permanently changing the entire Earth’s
climate. For a long time, the biggest debate in a number of
local and international forums worldwide has been whether
global warming is real which is described in (Nigar and
Mahedi, 2015). Some people think that global warming is
not real. However, several climate scientists have carried
out researches and have come to a conclusion that the
globe is gradually warming. People perceive the impacts
of global warming differently with some taking the
necessary precautions to help reduce the rates of the
rising temperatures. Increase in temperatures are likely to
lead to a global increase in drought conditions, decreased
water supplies due to evapotranspiration and an increase
in urban and agricultural demand. Vital sectors of the
Bangladesh economy like Agriculture greatly rely on
climate. Plants can grow only within certain limits of
temperature. Each plant species has an optimal
temperature limit for its different stages of growth and
functions which are described in (Syeda, 2012). They also
have an upper and lower lethal limits between which they
can properly grow. Temperature determines which species
can survive in a particular region. Several farmers are
however unaware of the changing climate and are also
ignorant of the adverse impacts it will have on their
livelihoods. High temperatures causes prolonged
droughts, affects the amount of water in the soil, affects
rainfall patterns and reduces water catchment areas. The
increased temperatures can also cause an outbreak of
pests and diseases that affects plants, animals and
humans. Farmers who are aware of the changing climate
are also helpless and unaware of what to do. They
continue with poor agricultural practices like burning of
wastes and poor disposal of unused fertilizers that worsen
the situation by releasing greenhouse gasses to the
atmosphere. Studying temperature changes is thus vital
for the Bangladesh economy as Agriculture which is the
country’s largest source revenue is directly affected by the
rising temperatures. The Bangladesh government derives
nearly 20% of its revenue from the agricultural sector. As
the largest employer in the economy, the agricultural
sector accounts for about 50% of the country’s
International Journal of Statistics and Mathematics
Vol. 5(1), pp. 108-118, September, 2018. © www.premierpublishers.org. ISSN: 2375-0499
Research Article

Doulah 109
employment. In addition, more than 70% of Bangladesh
population living in rural areas depends on agricultural
related activities for their daily livelihoods. Climatic studies
on temperature are therefore vital for the survival of the
agricultural sector as the key source of revenue to the
government of Bangladesh.
Temperature is one of the key elements of climate and it is
important to various sectors of the economy like
Agriculture. Temperature affects water sources, pests that
attack plants, animals and human diseases. Despite the
increasing climate changes, majority of Bangladeshi
citizens are still not well informed. Analyzing and
forecasting of temperature changes will thus help various
stakeholders and government to plan in advance in order
to counter climate related disasters. The objective of this
research is to build a time series model and use this model
to analyze and forecast the variation in maximum and
minimum temperature in Bangladesh in order to inform
stakeholders who depend directly or indirectly on it to plan
in advance.
METHODOLOGY
Average Maximum and Minimum Monthly temperature
data covering Bangladesh has been collected from the
Bangladesh Meteorological Department (BMD). This data
was recorded in monthly basis covering an 18 year period
from January 2000 to December 2017 (www.data.gov.bd).
The temperatures are measured in degrees Celsius. The
temperature data is a continuous univariate time series as
it contains a single variable (temperature) which is
measured at every instant of time. However, this data was
merged into monthly intervals transforming it to a discrete
univariate time series.
The Box-Jenkins Method
This study follows the Box-Jenkins methodology for
modeling. The following conceptual framework proposed
by Box et al. (1976) is considered in this study.
Figure 1. Box- Jenkins ARIMA Model
Seasonal ARIMA (SARIMA) Model
Gurudeo and Mahbub (2010) alludes that most natural
factors like temperature have strong seasonal
Components. It is therefore necessary to use
autoregressive and moving average polynomials that
identify with the seasonal lags. One such model is the
SARIMA model. SARIMA model is an extension of ARIMA
model and it is applied when the series contains both
seasonal and non-seasonal behavior. SARIMA model is
sometimes called the multiplicative seasonal
autoregressive integrated moving average and is denoted
by SARIMA (p,d,q)(P,D,Q)S. The Seasonal AR can be
written as:
tt
s
p yB  )(
The Seasonal MA can be written as
t
s
Qt By )(
The seasonal differencing is expressed as
sttt
s
yyyB  )1(
Combining the above equations, we get SARIMA
t
s
Qqt
Dsds
pp BByBBBB  )()()1()1)(()( 0 
Where the constant equals
)]1)(1[( 110 pp   
Where p represents non-seasonal AR order, d represents
non seasonal differencing, q represents non seasonal MA
order, P represents seasonal AR order, D represents
seasonal differencing, Q represents seasonal MA order, S
represents seasonal order (for monthly data S = 12 ) ty
represents time series data at period t, B is the backward
shift operator (
k
t t kB y y  ) and t is the random shock
(white noise error).
Stationarity Analysis
One of the important types of data used in empirical
analysis is time series data. The empirical work based on
time series data assumes that the underlying time series
is stationary. The time series analysis based on the
stationary time series data. In this section we briefly
discuss on stationary and non-stationary time series. A
stochastic process is said to be stationary if its mean and
variance are constant over time. Otherwise it will be non-
stationary. Why are stationary time series so important?
Because if a time series is non-stationary, we can study its
behavior only for the time period under consideration.
Each set of time series data will therefore be for a
particular episode. As a consequence, it is not possible to
generalize it to other time periods. Therefore, for the
purpose of forecasting, such (non-stationary) time series
may be of little practical value. How do we know that a
particular time series is stationary? There are several tests
of stationary. Here we used graphical and analytical
recognized test. Graphical test: if we depend on common
sense, it would seem that the time series depicted in figure

Int. J. Stat. Math. 110
is non-stationary, at least in the mean value. Here we
applied most widely used popular formal test over the past
several years are Autocorrelation function (ACF), Partial
Auto-correlation function (PACF), augmented dickey-fuller
(ADF) test and Kwiatkowski, Phillips, Schmidt and Shin
(KPSS) test.
Autocorrelation and Partial Autocorrelation (ACF and
PACF) Functions
When using the SARIMA models, Model specification and
selection is a crucial step of the analysis process. A proper
model for the series is identified by analyzing the ACF and
PACF. They reflect how the observations in a time series
are related to each other. It is useful that the ACF and
PACF are plotted against consecutive time lags for the
purposes of modeling and forecasting (Brockwell, 2002).
The order of the AR and MA are determined by these plots.
For a time series, the auto-covariance function ACVF at
lag k is defined as:



 
kn
t
kttk yy
n
c
1
))((1 
If tx is a stationary process with mean μ, the
autocorrelation of order k is simply the relation between ty
and kty  . The ACF estimate for the sample at lag k is thus
defined as
)}{(
)})({(





 
t
ktt
k
yE
yyE
The PACF of a stationary process ty denoted hh is
)1(),( 111    tt yycorr
,3,2,
1
ˆ
1
1
11
1,1 








 p
r
rr
p
j
jpj
p
j
jppjp
pp



Where, 1,1,1,1
ˆˆˆˆ
  jpppppjjp 
The ACF and PACF plots are used to identify the terms of
the SARIMA model.
ADF & KPSS Tests
Stationarity can also be checked using Augmented Dickey
Fuller (ADF) & Kwiatkowski–Phillips–Schmidt–Shin
(KPSS) tests. The literatures of these tests are described
in many textbooks (Corliss, 2009; Chris, 2004; Spyros,
1998).
Augmented Dickey-fuller (ADF) test
Testing for a unit root is equivalent to testing 1 in the
following model
ADF test equation:
tjt
p
j
jtt YYY   


  0
1
1
1)1(
tjt
p
j
jtt YYY   


  0
1
1
1
Hypothesis
1:0 H
1||:1 H
Reject 0H if ValueCriticalt 1
Or
0:0 H
0:1 H
Reject 0H if ValueCriticalt 0
The ADF the test statistic has same asymptotic distribution
as the DF statistic, so the same critical values can be used.
Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test
To be able to test whether we have a deterministic trend
vs stochastic trend, we are using KPSS (Kwiatkowski,
Phillips, Schmidt and Shin) Test (1992).
)0(~:0 IYH t Level (or trend) stationary
)1(~:1 IYH t Difference stationary
STEP 1: Regress tY on a constant and trend and
construct the OLS residuals ),,,( 21 T 
STEP 2: Obtain the partial sum of the residuals.


T
t
ttS
1

STEP 3: Obtain the test statistic



T
t
tS
TKPSS
1
2
2
2
ˆ
where
2
ˆ is the estimate of the long-run variance of the
residuals.
STEP 4: Reject 0H when KPSS is large, because that is
the evidence that the series wander from its mean. It is the
most powerful unit root test but if there is a volatility shift it
cannot catch this type non-stationarity.
Model selection criterion
Even though the Autocorrelation and Partial
Autocorrelation Functions help in determining the model’s
order, it only hints on where model building can begin from
(Aidoo, 2010). Several models can therefore be
considered from this case. However the final model is
chosen using a penalty function statistics such as Akaike
Information Criterion (AIC). Burnham & Anderson (1998)

Doulah 111
states that the motivation behind the selection criteria of
the model is to identify the best model that neither under-
fits nor over-fits the data.
Model Diagnostic
Here, each selected model is assessed to determine how
well it fits the temperature data. For a model that fits the
data well, Ljung-Box test based on ACF and PACF of the
residuals are used in determining the goodness of fit of the
selected model which is discussed in (Chris, 2004). The
Ljung-Box test is defined below-
0H : the model does not exhibit lack of fit
1H : the model exhibit lack of fit
The test statistic is defined as:



m
k
k
kn
r
nnQ
1
2
ˆ
)2(
Where, krˆ is the estimated autocorrelation of the series at
lag k, m is the number of lags being tested, n is the sample
size. The statistic Q follows a
2
( )m . For a level of
significance α, the critical region for rejection of the
hypothesis is
2
(1 , )mQ   where m is the degrees of
freedom.
Forecasting
Forecasting is important in decision making process
(Brockwell et al. 2002; Box et al. 1976). The chosen model
should therefore produce accurate forecasts. The selected
model does not always necessarily provide the best
forecasting therefore it is important to apply other tests
such as MAE, MSE and MAPE to confirm the forecasting
accuracy of the model.
Forecasting an ARMA process with mean y , m-step-
ahead forecasts can be defined as
jmn
mj
jymny 


  
The precision of the forecast is assessed with a prediction
interval of the form
n
mn
n
mn PCy  
2

Where
2
C is identified such that the desired degree of
confidence is achieved. Suppose it is Gaussian process,
then having 2
2
C will yields approximately 95%
prediction interval for mny  .
Data Analysis
The statistical software R package has been used in this
analysis. The results and discussions of the temperatures
data set are shown in the following below:
Figure 2: Time plot of Maximum and Minimum
temperatures
From Figure 2, it is to be noted that there is no evidence of
systematic variation about the mean on the time series plot
for maximum and minimum temperatures. For both
temperatures, it is clear that the series is non stationary.
However, both series exhibit seasonality which is evident
from the strong yearly cycles.
Table 1: Summary statistics of maximum and minimum
temperatures
Temperature
(°C)
Range
Minimum
Value
Maximum
Value
Mean
Standard
Deviation
Variance
Maximum 11.9 23.02 34.92 30.7 2.7 7.3
Minimum 15.8 11.09 26.86 21.4 4.8 23.2
From Table 1, it is observed that the minimum temperature
is more varying (standard deviation=4.8) compared to the
maximum temperature (standard deviation=2.7).
Figure 3: Decomposition of Maximum temperature

Figure 4. Decomposition of Minimum temperature
Ordinarily, time series data exhibit trend, seasonal, cyclical
and random components. From Figure 3 & Figure 4, it is
evident that both maximum and minimum temperature
series have seasonal, random and trend components. The
upward trend is clearly evident for the minimum
temperature series.
Stationarity checking
Why are stationary time series so important? Because if a
time series is non-stationary, we can study its behavior
only for the time period under consideration. Each set of
time series data will therefore be for a particular episode.
As a consequence, it is not possible to generalize it to
other time periods. Therefore, for the purpose of
forecasting, such (non-stationary) time series may be of
little practical value. How do we know that a particular time
series is stationary? There are several tests of stationary.
Here we used graphical and analytical recognized test.
Maximum temperature
Minimum temperature
Figure 5: Autocorrelation and Partial Autocorrelation
function
From Figures 5, it is to be exhibited the plots of the ACFs
and the PACFs for the monthly maximum and minimum
temperature series. The plots show strong seasonal wave
patterns that decline moderately. The non-seasonal lags
decay rapidly. This confirms the presence of seasonality
behavior and thus the time series is non-stationary.
Therefore, from the time series and autocorrelation plots,
it is obvious that both maximum and minimum temperature
series have seasonal variation. To make the series
stationary, seasonal differencing is required.
Formal tests of Stationarity are performed next to confirm
the conclusions from visual inspection of seasonal and
non-seasonal Stationary.
Table 2: Augmented Dickey – Fuller (ADF) Test
Temperatures
Dickey-
Fuller
Lag
order
Critical
Value
p-
value
Maximum -2.8429 12 0.05 .2229
Minimum -2.4787 12 0.05 .3755
According to the ADF tests results for both maximum and
minimum temperature series shown in Table 2, we do not
reject the null hypothesis and conclude that the two series
are not stationary. This is because the more negative the
Dickey –Fuller is, the stronger the rejection of the null
hypothesis which is not the case here.
Table 3: KPSS Test
Temperatures
KPSS
level
Lag
parameter
Critical
Value
p-
value
Maximum .0087 3 0.05 0.1
Minimum .0071 3 0.05 0.1
According to the Table 3 shows the test results of the
KPSS tests. It tests the null hypothesis that a series is
trend-stationary verses an alternative of non-stationarity. It
is important to note that any absence of a unit root in a
KPSS test is not enough proof of general stationarity but
of trend Stationarity. From the results, for maximum

Doulah 113
temperature series we do not reject the null hypothesis
because the p-value of 0.1 ≥ 0.05 at 5% level of
significance. Thus the maximum temperature is trend
stationary. From the results, for minimum temperature
series we do not reject the null hypothesis because the p-
value of 0.1 ≥ 0.05 at 5% level of significance. Thus the
minimum temperature is trend stationary.
Model building for monthly temperature series
According to Shumway and Stoffer (2006), the process of
model fitting involves data plotting, data transformation if
necessary, Identification of dependence order, estimation
of parameter, diagnostic analysis and choosing
appropriate model. In this section, a univariate SARIMA
methodology is used to model maximum and minimum
monthly temperatures of Bangladesh.
Model Identification
ACF and PACF plots are used in the identification of the
values p, q, P and Q. For the non-seasonal part, spikes of
the ACF at low lags are used to identify the value of q while
the value of p is identified by observing the spikes at low
lags of the PACF. For the seasonal part the value of Q is
observed from the ACF at lags that are multiples of S while
for P, the PACF is observed at lags that are multiples of S.
Looking at the ACF plots and PACF plots for maximum and
minimum differenced time series, the models are
suggested in the following Table 4.
Table 4: Suggested Models
Maximum temperature Minimum temperature
SARIMA (0, 0, 0) (0, 1, 0)12 SARIMA (2, 0, 2) (1, 1, 0)12
SARIMA (0, 0, 1) (0, 1, 0)12 SARIMA (0, 0, 0) (0, 1, 0)12
SARIMA (1, 0, 0) (0, 1, 0)12 SARIMA (1, 0, 0) (1, 1, 0)12
SARIMA (0, 0, 1) (1, 1, 0)12 SARIMA (2, 0, 1) (1, 1, 0)12
SARIMA (1, 0, 0) (1, 1, 0)12 SARIMA (2, 0, 1) (2, 1, 0)12
Analyzing the aforementioned models for both Maximum
& Minimum temperatures, the results of the estimated
models are shown in the following Table 5.
Table 5: Suggested Models Estimation Results
Maximum temperature
Model P-value
Chi-
square
DF AIC
SARIMA (0, 0, 0) (0, 1, 0)12 3.49e-0740.582 6 592.35
SARIMA (0, 0, 1) (0, 1, 0)12 .03504 13.544 6 574.97
SARIMA (1, 0, 0) (0, 1, 0)12 .174 8.993 6 569.15
SARIMA (0, 0, 1) (1, 1, 0)12 .0963 10.754 6 532.07
SARIMA (1, 0, 0) (1, 1, 0)12 .3157 7.0564 6 527.79
Minimum temperature
Model P-value Chi-
square
DF AIC
SARIMA (2, 0, 2) (1, 1, 0)12 .3899 6.3049 6 526.6
SARIMA (0, 0, 0) (0, 1, 0)12 .00153 21.412 6 557.52
SARIMA (1, 0, 0) (1, 1, 0)12 .3157 7.0564 6 527.79
SARIMA (2, 0, 1) (1, 1, 0)12 .3521 6.673 6 531.37
SARIMA (2, 0, 1) (2, 1, 0)12 .7639 3.349 6 505.45
The best model is the one with the lowest value of AIC.
From Table 5, it is to be noted that the best model for
maximum temperature is SARIMA (1, 0, 0) (1, 1, 0)12 while
for minimum temperature is SARIMA (2, 0, 1) (2, 1, 0)12.
The lowest value of AIC is 527.79 and the Ljung -Box test
yielded a chi square of 7.0564 with a p value equal to
0.3157. From the Ljung -Box test, the p value of 0.3157 >
0.05 and this confirms that SARIMA (1, 0, 0) (1, 1, 0)12 is
adequate for forecasting of maximum temperature. The
lowest value of AIC is 505.45. and the Ljung -Box test yield
a chi square of 3.349 with a p value of 0.7639. From the
Ljung -Box test, the p value of 0.7639 > 0.05 and this
confirms that SARIMA (2, 0, 1) (2, 1, 0)12 is adequate for
forecasting of minimum temperature.
Parameter Estimation
Non-linear least-squares estimation or Maximum
likelihood estimation methods are employed to estimate
the coefficients of the models. A more complicated
iteration procedure is required when estimating the
parameters of SARMA models (Box et al. 1976; Chris
2004).
Table 6: Select models Parameter Estimates Results
Model SARIMA (1, 0, 0) (1,
1, 0)12 for Maximum
temperature
Model SARIMA (2, 0, 1) (2,
1, 0)12 for Minimum
temperature
Parameter Estimate Std.
error
Parameter Estimate Std.
error
AR(1) .3476 .0675 AR(1) -.6536 .0706
SAR(1) -.4498 .0633 AR(2) .2717 .0702
MA(1) 1.00 .0166
SAR(1) -.6165 .0689
SAR(2) -.3595 .0694
From Table 6 we observed that the models are estimated
well because of very low standard error of the estimated
parameters.
Diagnostic Analysis
For a well fitted models, for maximum temperature is
SARIMA (1, 0, 0) (1, 1, 0)12 while for minimum temperature
is SARIMA (2, 0, 1) (2, 1, 0)12, the standardized residuals
estimated from the models should behave as an
independently and identically distributed sequence with
zero mean and constant variance. Now the identification of
normality is shown in the following figures-

Figure 6: Selected Model Residuals Q-Q Plot for
Maximum Temperature
A normal probability plot or a Q-Q plot can help in
identifying departures from normality. From figure 6, the
residuals are approximately normal distributed with zero
mean.
Figure 7: Selected Model Residuals Plots for Maximum
Temperature
From Figure 7, it is to be observed three different plots
such as standardized residuals; ACF of residuals and p-
values for Ljung –Box statistic. Based on standardized
residuals plot, it looks like an independently and identically
distributed sequence of mean zero with a constant
variance. The plots of the ACF of the residuals lack enough
evidence of significant spikes which clearly shows that the
residuals are white noise. The results also showed that the
residuals are non-significant with Ljung –Box test p-value.
From the above tests, it is clear that the fitted model is
adequate since the residuals are white noise. That is,
SARIMA (1, 0, 0) (1, 1, 0)12 is adequate for modeling the
monthly maximum temperature series in Bangladesh.
Figure 8: Selected Model Residuals Q-Q Plot for Minimum
Temperature
From Figure 8, we observed that the residuals are
approximately normal distributed with zero mean and
constant variance.
Figure 9: Selected Model Residuals Plots for Minimum
Temperature
According to the Figure 9, it is to be observed three
different plots such as standardized residuals; ACF of
residuals and p-values for Ljung –Box statistic. Based on
standardized residuals plot, it looks like an independently
and identically distributed series of mean zero with a
constant variance. The plots of the ACF of the residuals
lack enough evidence of significant spikes which clearly

Doulah 115
shows that the residuals are white noise. The results also
showed that the residuals are non-significant with Ljung –
Box test p-value. From the above tests, it is clear that the
fitted model is adequate since the residuals are white
noise. That is, SARIMA (2, 0, 1) (2, 1, 0)12.is adequate for
modeling the monthly minimum temperature series in
Bangladesh.
Model validation & Forecasting
In order to test the adequacy and predictive ability of the
chosen models, the actual data sets, predicted values,
lower and upper limits are plotted and displayed in Figure
10 & 11. The graphs show that the predicted values are
well-fitted through the original data with the lower and
upper limits containing majorities of the original data. This
indicates that the models chosen for maximum and
minimum temperature series are the best fitted ones for
the data sets.
Figure 10. Validation and Forecasted values of maximum temperature up to 2019
Figure 11. Validation and Forecasted values of minimum temperature up to 2019

From Table 7, it is to be remarkable that the observed values verses the predicted values as well as the noise residuals
that affirms the adequacy of the chosen maximum and minimum time series models.
Table 7: Observed and fitted values for the Period 2004-2005
Year observed predicted LCL UCL Noise
Residual
observed predicted LCL UCL Noise
Residual
JAN 2004 25.17 25.21 23.32 27.09 -.04 11.99 12.18 10.31 14.04 -.19
FEB 2004 26.88 28.01 26.15 29.88 -1.13 14.32 15.14 13.28 17.01 -.82
MAR 2004 31.70 31.97 30.11 33.83 -.27 20.32 20.31 18.44 22.17 .01
APR 2004 30.93 34.09 32.23 35.95 -3.16 20.88 23.43 21.57 25.29 -2.56
MAY 2004 33.49 32.82 30.96 34.69 .67 24.18 25.38 23.52 27.24 -1.20
JUN 2004 32.65 31.89 30.03 33.75 .76 25.17 25.16 23.30 27.02 .01
JUL 2004 31.36 31.64 29.78 33.51 -.28 25.69 25.82 23.96 27.68 -.13
AUG 2004 32.08 31.30 29.44 33.17 .78 26.03 25.69 23.83 27.55 .34
SEP 2004 31.37 32.41 30.55 34.28 -1.04 25.11 25.74 23.87 27.60 -.63
OCT 2004 31.69 31.57 29.71 33.43 .12 22.37 23.64 21.78 25.50 -1.27
NOV 2004 30.23 29.36 27.50 31.23 .87 19.40 18.98 17.13 20.84 .42
DEC 2004 24.98 27.17 25.30 29.03 -2.19 14.41 14.11 12.25 15.96 .30
JAN 2005 23.02 24.54 22.67 26.40 -1.51 12.39 11.98 10.30 13.65 .42
FEB 2005 27.79 26.84 24.98 28.71 .95 15.72 14.80 13.13 16.48 .92
MAR 2005 29.94 32.05 30.19 33.91 -2.10 18.09 20.01 18.33 21.68 -1.92
APR 2005 32.36 31.52 29.66 33.38 .84 22.63 22.51 20.84 24.18 .12
MAY 2005 33.27 33.70 31.84 35.56 -.43 25.07 24.96 23.29 26.63 .12
JUN 2005 33.49 32.24 30.38 34.11 1.24 26.86 25.74 24.07 27.41 1.12
JUL 2005 31.31 31.93 30.06 33.79 -.61 25.92 25.80 24.13 27.47 .12
AUG 2005 31.40 31.52 29.66 33.38 -.12 26.09 26.15 24.48 27.82 -.05
SEP 2005 32.33 31.86 30.00 33.73 .47 25.89 25.42 23.75 27.09 .46
OCT 2005 32.76 31.79 29.93 33.66 .97 25.14 23.37 21.70 25.04 1.77
NOV 2005 30.86 30.46 28.60 32.33 .40 20.91 19.80 18.13 21.47 1.10
DEC 2005 27.82 26.23 24.36 28.09 1.60 15.21 14.60 12.93 16.27 .61
Forecasting
Forecasting helps in planning and decision making process since it gives an insight of the future uncertainty using the
past and current behavior of given observations. Further accuracy tests such as MAE, MAPE and RMSE must therefore
be carried out on the model. The Table 8 shows a summary of ME, RMSE and MAE for both maximum and minimum
temperature models.
Table 8: Forecasting Accuracy Statistic
Maximum temperature model
SARIMA (1, 0, 0) (1, 1, 0)12
Minimum temperature model
SARIMA (2, 0, 1) (2, 1, 0)12
Stationary R-squared .304 .314
R-squared .877 .968
RMSE .949 .867
MAPE 2.378 3.362
MAE .716 .622
Here, it is to be forecasted the monthly temperature based on the selected models SARIMA (1, 0, 0) (1, 1, 0)12 for maximum
temperature and SARIMA (2, 0, 1) (2, 1, 0)12 for minimum temperature. The outcomes are shown in the following Table 9.

Doulah 117
Table 9: Forecasting Monthly temperatures
95% CI 95% CI
Year Forecast LCL UCL Forecast LCL UCL
JAN 2018 23.95 22.09 25.82 12.25 10.58 13.92
FEB 2018 28.80 26.83 30.78 15.30 13.62 16.97
MAR 2018 32.60 30.61 34.58 20.14 18.45 21.83
APR 2018 33.69 31.70 35.67 23.86 22.16 25.55
MAY 2018 33.43 31.45 35.42 24.70 23.01 26.40
JUN 2018 32.46 30.48 34.45 26.03 24.33 27.72
JUL 2018 32.27 30.29 34.26 26.12 24.43 27.81
AUG 2018 32.02 30.04 34.01 25.97 24.27 27.66
SEP 2018 32.20 30.21 34.19 25.80 24.11 27.50
OCT 2018 32.59 30.60 34.58 23.80 22.10 25.49
NOV 2018 30.13 28.15 32.12 18.91 17.21 20.60
DEC 2018 25.89 23.91 27.88 14.04 12.35 15.74
JAN 2019 24.01 21.77 26.24 11.87 10.03 13.71
FEB 2019 28.79 26.53 31.06 15.21 13.37 17.05
MAR 2019 32.27 30.00 34.54 20.85 19.01 22.69
APR 2019 33.45 31.18 35.71 24.45 22.61 26.29
MAY 2019 33.32 31.05 35.59 24.93 23.09 26.77
JUN 2019 32.44 30.18 34.71 25.99 24.15 27.83
JUL 2019 32.20 29.93 34.46 26.27 24.43 28.11
AUG 2019 31.73 29.46 34.00 26.14 24.29 27.98
SEP 2019 32.12 29.86 34.39 25.82 23.98 27.66
OCT 2019 32.70 30.43 34.96 24.15 22.30 25.99
NOV 2019 30.03 27.76 32.30 19.33 17.49 21.17
DEC 2019 25.74 23.47 28.00 14.10 12.26 15.94
CONCLUSIONS
To sum up the whole discussion it is to be noteworthy that
for both maximum and minimum temperatures are
unsteady from month to month though the maximum
temperature is more fluctuating (standard deviation=2.7)
compared to the minimum temperature (standard
deviation=4.8). However, through the years, there is a
distinct increasing trend for minimum temperature proving
the fact that global warming is in fact a reality. On the other
hand, maximum temperatures seem to be comparatively
steady. Both maximum and minimum temperature series
exhibited high seasonality. The minimum temperature also
displayed an upward trend. The two series were made
stationary. The best model for maximum temperature is
SARIMA (1, 0, 0) (1, 1, 0)12 and for minimum temperature
is SARIMA (2, 0, 1) (2, 1, 0)12. The model residuals for both
series are near normality as most points fall on the straight
line with a few close to it. From the model validation
results, the projected values are well-fitted through the
original data with the lower and upper limits encompassing
bulks of the original data. The selected SARIMA models
give two-year projected monthly maximum and minimum
temperatures that can help decision makers to establish
priorities for equipping themselves against upcoming
weather changes. The forecasts also show that the
minimum temperature of Bangladesh will continue with the
upward trend.
ACKNOWLEDGEMENTS
The author would like to thank the anonymous reviewers
for their helpful comments.
REFERENCES
Aidoo E (2010). Modeling and forecasting inflation rates in
Ghana: An application of SARIMA models. Högskolan
Dalarna, School of Technology and Business Studies.
Brockwell, Peter J, Davis RA (2002). Introduction to Time
Series and Forecasting, 2nd.edn. Springer-Verlang.
Box GEP, Jenkins GM, Reinsel GC (1976). Time Series
Analysis, Forecasting and Control, 3rd edn. Prentice
Hall, Englewood Clifs, NJ.
Burnham KP, Anderson DR (1998). Model Selection and
Inference. Springer Verlag, New York.
Corliss D (2009). Time series Analysis: an introduction
using Base SAS and STAT, NewYork, U.S.A.
Chris C (2004). The Analysis of Time Series: An
Introduction, John Wiley & Sons, NewYork, U.S.A.
Gurudeo AT, Mahbub I. (2010). “Time Series Analysis of
Rainfall and Temperature Interactions in Coastal
Catchments”, J of Math. and Stat. 6 (3): 372-380.
Nigar S, Mahedi H. (2015). Forecasting Temperature in
the Coastal Area of Bay of Bengal-An Application of
Box-Jenkins Seasonal ARIMA Model, Civil and Enviro.
R. 7(8): 149-159.

Oluwafemi SO, Femi JA, Oluwatosi TD. (2010). Time
Series Analysis of Rainfall and Temperature in South
West Nigeria, The Pacific J. of Sci. and Techno.
11(2):552-564.
Syeda J. (2012). Trend and Variability Analysis, and
Forecasting of Maximum Temperature in Bangladesh,
J. Environ. Sci. & Natural Resources. 5(2): 119 -128.
Spyros M, Wheelwright SC, Hyndman RJ (1998).
Forecasting: Methods and Applications, John Wiley &
Sons, Inc., U.S.A.
Shumway RH, and Stoffer DS (2006). Time Series
Analysis and Its Applications With R Examples,
Springer Science & Business Media, LLC, NY, USA.
www.data.gov.bd
Accepted 5 September 2018
Citation: Doulah S. (2018). Forecasting Temperatures in
Bangladesh: An Application of SARIMA Models.
International Journal of Statistics and Mathematics, 5(1):
108-118.
Copyright: © 2018 Doulah. This is an open-access article
distributed under the terms of the Creative Commons
Attribution License, which permits unrestricted use,
distribution, and reproduction in any medium, provided the
original author and source are cited.

Forecasting Temperatures in Bangladesh: An Application of SARIMA Models

More Related Content

Similar to Forecasting Temperatures in Bangladesh: An Application of SARIMA Models

More from Premier Publishers

Recently uploaded

Forecasting Temperatures in Bangladesh: An Application of SARIMA Models