See discussions, stats, and author profiles for this publication at: https://www.researchgate.

net/publication/334089285

Rainfall Prediction: Accuracy Enhancement Using Machine Learning and

Forecasting Techniques

Conference Paper · December 2018

DOI: 10.1109/PDGC.2018.8745763

CITATIONS READS

8 2,885

5 authors, including:

Urmay Shah Sanjay Garg

Nirma University Indrashil University
1 PUBLICATION 8 CITATIONS 103 PUBLICATIONS 415 CITATIONS

SEE PROFILE SEE PROFILE

Neha Sisodiya Nitant Dube

2 PUBLICATIONS 14 CITATIONS
Space Application Center
22 PUBLICATIONS 33 CITATIONS
SEE PROFILE
SEE PROFILE

Some of the authors of this publication are also working on these related projects:

rain fall prediction using machine learning techniques View project

Image Processing View project

All content following this page was uploaded by Urmay Shah on 07 October 2019.

The user has requested enhancement of the downloaded file.

 5th IEEE International Conference on Parallel, Distributed and Grid Computing(PDGC-2018), 20-22 Dec, 2018, Solan, India

Rainfall Prediction: Accuracy Enhancement

Using Machine Learning and Forecasting
Techniques
Urmay Shah Sanjay Garg NehaSisodiya
Dept. of Computer Engg. Dept. of Computer Engg. Dept. of Computer Engg.
Nirma University, Nirma University, Nirma University,
Ahmedabad, India Ahmedabad, India Ahmedabad, India
15mcen25@nirmauni.ac.in sgarg@nirmauni.ac.in neha.sisodiya@nirmauni.ac.in

Nitant Dube Shashikant Sharma

SAC-ISRO SAC-ISRO
Ahmedabad, India Ahmedabad, India
nitant@sac.isro.gov.in sasharma@sac.isro.gov.in

Abstract—The paper is focused to provide the insights of analysis technique is also performed using no. of rainy days
climate to the clients from various businesses, e.g. and rainfall as the input variable. L. Ingsrisawang in[11] has
agriculturists, researchers etc., to comprehend the significance
done a comparative study for rainfall prediction using diff-
of changes in climate and atmosphere parameters like
precipitation, temperature, humidity etc. Precipitation erent machine learning techniques on the north-eastern part
estimate is one of the critical investigations in field of of Thailand. The paper shows that, how the feature selection
meteorological research. In order to predict precipitation, an can be used to find the correlation between other weather
endeavor is made to a couple of factual procedures and parameter and the rainfall, the paper also shows the same
machine learning techniques to forecast and estimate
meteorological parameters. For experimentation purpose daily
day, next day, and next 2-day classification using ANN,
observations were considered. The accuracy assessment of SVM, KNN. Thai meteorological department (TMD) data is
forecasting model experimentation is done using validation of used for experimental purpose. Attributes like temperature,
results with ground truth. The experimentation demonstrates humidity, pressure, wind, rain occurrence are used as input
that for forecasting meteorological parameters ARIMA and to the model. In [15] S.N Kohail has used daily historical
Neural Network works best, and best classification accuracy in
comparison to other machine learning algorithms for
data of the Gaza city and outlier analysis, prediction,
forecasting precipitation for next season was given by Random classification, and clustering is done for temperature
Forest model. prediction. The paper shows the temperature prediction and
classification for the Gaza city using many machine learning
Keywords—Precipitation, ARIMA, SVM, Decision Tree, Holt techniques, it also does outlier detection and clustering.
Winter, Machine Learning, Random Forest
Daily relative humidity, average temperature, wind speed
I. INTRODUCTION with direction, time of highest speed and rainfall is used as
In India, where the majority of agribusiness is dependent on an input parameter in the study. Onset monsoon for the
precipitation as its standard wellspring of water, the time Indian sub-continent is predicted based on features extracted
and measure of precipitation hold high importance and can from the satellite image using data mining methods. KNN
impact the entire economy of the nation. Climate plays a with euclidean distance is used for sea surface temperature
vital role in our everyday life. From the earliest starting (SST), cloud top temperature (CTT), cloud density, water
point of the human development, we are occupied with vapour attributes were used. It predicts the onset monsoon in
thinking about climatic changes. Weather forecasting is one advance 10-30 days is proposed in[13].
of the most challenging issues seen by the world, in a most Rainfall classification using supervised learning in Quest
recent couple of century in the field of science and (SLIQ), and decision tree method with different Gini index
technology. Prediction is the phenomena of knowing what is performed in[18]. Dew point, temperature, pressure,
may happen to a system in the near future. Present weather humidity, wind speed were used as an input parameter. Petre
observations are obtained by ground-based instruments and in [17](2008) proposed an approach that uses decision tree
from the satellite through remote sensing. As India's method with CART algorithm using data from
economy significantly depends on horticulture, precipitation meteorological department Hong Kong. They have used
plays an important part. year, month, average pressure, relative humidity, cloud
The monthly climatic changes using spatiotemporal mining quantity, precipitation, average temperature as an input
is being analyzed and the variability in seasonal rainfall parameter. The work is explained by S.-Y. Ji in[12] uses
using the IMD data with many rain gauge station decision tree with CART and C4.5 algorithm with
information is done by K. Chowdari in[5][1]. Cluster temperature, wind direction, wind speed, wind gust, outdoor

978-1-5386-6026-3/18/$31©2018 IEEE 776

 5th IEEE International Conference on Parallel, Distributed and Grid Computing(PDGC-2018), 20-22 Dec, 2018, Solan, India

humidity, evaporation, solar radiation, dew point, cloud elaborates the methods used. The proposed architecture is
cover, air density, vapour pressure, pressure altitude as a explained in Section III. Section IV presents the source of
parameter. The proposed method predicts rain and it is data information, parameters used with their dates are
classified into three categories in hourly rain 0.0 to 0.5 mm mentioned along with comparison of the results of the
as level 1, 0.5 to 2.0 mm as level 2, > 2.0mm as level 3. different machine learning and forecasting methods. This
A comparative study of data mining techniques is being section also includes the final classification accuracy of the
done using historical weather data set. Analysis of different rainfall. We have concluded our work in Section V with
machine learning techniques for regression as well as for the future scope.
classification, paper shows that KNN performs better for
classification and Naive Bayes performs better for II. BASIC PRELIMINARIES
regression [2]. Forecasting monthly rainfall for the Assam A. Machine learning methods for Regression
region using multiple linear regression is performed with the Multiple Linear Regression: In multiple linear regression[7],
help of 6 years data gathered from regional meteorological multiple in-dependent parameters are taken as an input and
center Guwahati[6]. Using Nigerian Meteorological Agency based on the best-fitted line dependent continuous variable
data paper individually predict the min temp, max temp, is predicted. The relation between them is derived by
evaporation, rainfall and radiation using ANN and decision equation:
tree, error in rainfall is very high compared to other Y=a*X+b*Z+c
parameters prediction error in [14]. In [19] the comparison
Where Y =Dependent Variable, a,b =Regression Parameters
of several machine learning algorithms like ANN,
X, Z=Independent Variable, c=Intercept
Multiplicative Additive Regression Spline (MARS), radial Support Vector Regression: The support vector regression
basis SVM is done to forecast average daily and monthly (SVR) [3] uses the same principles as the SVM for
rainfall of the Fukuoka city Japan. Rainfall forecasting using classification, with only a few minor differences. To
neural network through the satellite image is attempted in minimize error, individualizing the hyper plane which
[14] with parameters like relative humidity, pressure, maximizes the margin, keeping in mind that part of the error
temperature, precipitate water, wind speed. Daily rainfall is tolerated in linear support vector regression.
prediction over Dhaka station in Bangladesh using markov Prediction of the rainfall using other independent
chain model and logistic regression is performed with the parameters (temperature, humidity, pressure, wind speed
help of no of rainy days, no of dry days and rainfall as a etc.) is attempted in many studies showing the comparison
parameter in [8][16]. of different machine learning techniques and claiming the
We have observed that most of the papers higher ac-curacy with categorizing rainfall in two to three
[5][2][19][14][9][3] claiming higher accuracy have categories, but most of them have not attempted the
forecasting of rainfall for next season using machine
classified rainfall into three or less than three categories or
learning techniques. In Few papers forecasting of the
have estimated rainfall using machine learning techniques
rainfall as well as different weather parameters like
but have not done rainfall forecasting using machine temperature, relative humidity, number of rainy days etc. is
learning techniques, few of them have used few attempted. The result shows forecasting rainfall individually
meteorological parameters for the estimation of the rainfall. gives less accurate result compared to other weather
The papers which are forecasting rainfall have used the parameters.
regression techniques and forecasting techniques have less As forecasting rainfall individually using forecasting
accuracy. We have proposed a model to predict the rainfall techniques gives less accuracy and prediction of rainfall
using a fusion of forecasting and machine learning with the help of different weather parameter using machine
techniques. Prediction of rainfall depends on various other learning techniques gives higher accuracy it is necessary to
parameters along with temperature. Classifying the rainfall design the fusion model.
gives us the good classification accuracy but our ultimate
III. PROPOSED ARCHITECTURE
goal is to predict the rainfall using the other forecasted
parameters. In this study objective is not only to correctly In the first part of the proposed model retrieved weather
classify rainfall but also correctly predict the rainfall using data is cleaned and reordered, after that the rainfall data is
categorized into different categories according to IMD
various forecasted parameters. Our work is focused on
guidelines. The data is partitioned into two parts 70% for
understanding the effects of different meteorological
training and 30% for testing. Four different machine
parameters in rainfall prediction along with an exploration learning techniques like a decision tree, random forest,
of approaches which were used for forecasting rainfall, KNN, SVM were applied on the partitioned data, the
machine learning, and their limitation. The proposed model individual results were also analyzed and tuned.
predicts the rainfall for the next season using machine In the second part of the proposed model, the correlation
learning and forecasting techniques. Our contribution to this of the rainfall with minimum temperature, maximum
problem is to analyze the accuracy of different machine temperature, relative humidity and wind speed were
learning and forecasting techniques to predicts precipitation calculated. From the study, it is found that all four
for next season. parameters have significant importance with the rainfall. All
The rest of paper is organized as follows: Section II past years maximum temperature and minimum temperature

978-1-5386-6026-3/18/$31©2018 IEEE 777

 5th IEEE International Conference on Parallel, Distributed and Grid Computing(PDGC-2018), 20-22 Dec, 2018, Solan, India

were retrieved except last year. Based on the past data six detailed explanation of tuned parameters. The detailed
different forecasting methods (Holt winter method [10], analysis of the best-fitted model and comparison of all
ARIMA model [10], Simple Moving Average model [2], methods based on performance is done.
Neural Network method [10], Seasonal Naive method [10]) The data for the experimental purpose is retrieved from
were applied and the best-fitted model output was taken into global weather site and it is provided by National Centers for
consideration. Relative humidity and wind speed were Environmental Prediction (NCEP). For experimentation,
retrieved from minimum temperature and maximum daily data from 1/1/1979 to 7/31/2014 is collected from five
temperature using linear regression and support vector locations. Data also contains parameters like minimum
regression as it is found that it gives better accuracy by this
method compared to a direct forecast of the individual.

Fig. 1: Proposed Architecture

temperature, maximum temperature, relative humidity,
In the fusion part, four forecast parameters are given as wind speed, and precipitation. The rainfall is classified into
input to the trained data (1979 to 2013). Based on this input seven categories according to the forecast manual provided
parameters next year and next monsoon season rainfall is by the Indian Meteorological Department (IMD).Save As
forecasted. The individual accuracy of the model was also command, and use the naming convention prescribed by
analyzed with confusion matrix. For the experimental your conference for the name of your paper. In this newly
purpose we have taken only Jun to Dec data because in most created file, highlight all of the contents and import your
of regions of India rainfall occurs in this period. prepared text file. You are now ready to style your paper; use
Considering the forecast for whole year gives higher the scroll down window on the left of the MS Word
accuracy as there are more no. of non rainy days which gets Formatting toolbar.
correctly classified but our focus is to predict the rainfall for A. Forecasting Parameters
those months who have chances of rainfall.
Forecasting Maximum Temperature: As the temperature is
IV. RESULTS AND TABLES comparatively easy to forecast compare to other
meteorological parameters. We have forecasted maximum
This sections includes the information about the data
temperature using different forecasting techniques and
which is used for the experimentation along with the results
of the forecasting and machine learning methods with the RMSE (Root Mean Square Error) were compared with the

978-1-5386-6026-3/18/$31©2018 IEEE 778

 5th IEEE International Conference on Parallel, Distributed and Grid Computing(PDGC-2018), 20-22 Dec, 2018, Solan, India

original data set. Table 1 shows, the 365 days forecasted to December month forecast. Confusion matrix shows that
maximum temperature error. The result shows that in the very heavy rain clas-si ed to none. Results also show the
case of maximum temperature ARIMA model performs considerable accuracy for the no rain, very light rain,
better than the other model. Arima(3,0,4) is the best-fitted moderate rain. For the very heavy rain, heavy rain and rather
model. heavy rain results were not impressive.
Forecasting Minimum Temperature: Various forecasting Decision Tree: In this method, we have used Gini index
method for fore-casting the minimum temperature were algorithm for the selection of the most homogeneous node.
analyzed, neural network show significant low RMSE Higher the value of Gini higher the homogeneity and based
compared to the other model. NNR(30,1,16)[365] performs on that decision tree is generated.
the best fit model. Average of 20 networks, each of which is
a 31-16-1 network with 529 weights options were -linear
output units. Estimated sigma2 =0.01786

Table 1: Forecasted Maximum, Minimum Temperature RMSE

Method RMSE (C) Method RMSE (C)

ARIMA 3.45 ARIMA 3.05
TBATS Model 3.53 TBATS Model 3.57
Naive Method 4.33 Naive Method 3.38
Moving Average 6.93 Moving Average 7.92
Neural Network 8.66 Neural Network 2.55
Holt Winters Additive 17.47 Holt-Winters Additive 7.19
Holt Winters Multiplicative 13.57 Holt-Winters Multiplicative 7.41

Forecasting Relative Humidity: As the correlation between The process of pruning is also done in order to limit the
relative humidity and rainfall is significant 0.303. We have level of the tree. To ensure that tree is not overfitted or
also forecasted relative humidity. We have used minimum underfitted we have also tuned tree. For level 5, it shows the
temperature and maximum temperature as the input to the best result, to avoid overfitting, we have taken only up to 5
level.10-fold cross validation is done on this data set for
model and predicted relative humidity. Forecasted minimum
measuring the accuracy of the model.
and maximum temperature were given as the input instead Results were also analyzed by confusion matrix. It is
of the measured temperature to get the final model accuracy. found that unlike the KNN, this method has classified very
The result shows that support vector regression which is a heavy rain. But same as the case in KNN it only shows the
combination of linear regression and support vector machine considerable accuracy for the no rain, moderate rain and for
works best. very light rain.
Forecasting Wind Speed: Wind speed is one of the Support Vector Machine: In order to give best
important parameter for predicting the rainfall as its classification accuracy different combination of kernels,
correlation with the rainfall is 0.49. It is also impor-tant to gamma, C values were tried for the tuning purpose. Radial
forecast the wind speed(m/s). We have also applied the two base function kernel, linear kernel, sigmoid kernel were
regression techniques for predicting the wind speed giving given for kernel parameter, different gamma values and C
two input parameters minimum temperature and maximum values were also given. It is found that linear kernel with
temperature, as a result support vector regression gives less gamma value 0.1 and C value 1 gives best accuracy
RMSE compare to simple linear regression.For papers with compared to others. From the confusion matrix, it is found
that SVM is unable to classify Heavy Rain and Very Heavy
more than six authors: Add author names horizontally,
Rain. For even light rain and for very light rain results were
moving to a third row if needed for more than 8 authors. poor.
Table 2: Forecasted Relative Humidity and Wind Speed RMSE In the experimentation we have taken more number of
Forecasted Relative Forecasted Wind classes to classify the rainfall, but as SVM works best with
Humidity Speed optimal margin, there may be the case that multiple category
Method RMSE(Fraction) Method RMSE(m/s) overlap each other and because of which SVM performs
Linear Linear worst compare to others.
Regression 0.75 Regression 0.1345
Support Random Forest: Random forest [4] is a tree based model,
Vector Support Vector it is a collection of many tree models. We have applied
Regression 0.68 Regression 0.1116 different tuning parameters for tuning it. As in random forest
case, one of the parameters is how many trees should be used
to get the more accurate results. It works well with high
variance low bias models. It is noticed that after 250 number
B. Machine Learning Model trees error rate is constant. So, we will restrict number of
KNN Method: To identify the best k nearest neighbor, we trees to 250 in the forest. From the confusion matrix, it is
found that for very light rain Random forest method gives
have tried with different values of K. The study reveals that
the best accuracy. It also performs well for the no rain,
k=15 gives best classification accuracy for the 1-year moderate rain, and for light rain.
forecast, and k=9 gives best classification accuracy for June

978-1-5386-6026-3/18/$31©2018 IEEE 779

 5th IEEE International Conference on Parallel, Distributed and Grid Computing(PDGC-2018), 20-22 Dec, 2018, Solan, India

Table 3: Accuracy on 30% test data. axis against False Positive Rate (1-Speci city) on x-axis for
AUC
(Area
each categories.
Under Precisio Recal Table 5 shows the final classification accuracy of each
Method Curve) Classification Accuracy n l method with forecasted parameters as an input to the
trained model. In a country like India, where rainfall occurs
KNN 0.873 0.721 0.691 0.721 in only limited no. of the month. So for that, we have also
0.721
analyzed our accuracy for monsoon season and it is noticed
Tree 0.755 0.716 0.721
that it gives considerable classification accuracy.
SVM 0.684 0.539 0.659 0.539
Random Table 5: Confusion Matrix for the Random Forest (for Jun to Dec)
Forest 0.914 0.762 0.744 0.76
Actual(Days)
Table 4: Final Accuracy Comparison on Forecast Very Very
predicted Heavy Light Moderate No Rather Heavy Light
Final Accuracy (Days) Rain Rain Rain Rain Heavy Rain Rain
Final Accuracy(1 year-365 (for June Heavy
Method days) To Dec) Rain 0 0 0 0 0 0 0

Decision Tree 69.58 61.21 Light Rain 0 12 4 0 1 0 8

Moderate
Random Forest 70.50 70.09 Rain 0 33 0 1 1 9

KNN 66.35(k=9) No Rain 0 0 0 74 0 0 5

69.31(k=15)
Rather
SVM 67.05 69.15 Heavy 1 0 0 0 1 0 0
Very
Neural Network 68.49 68.69 Heavy
Rain 0 0 0 0 0 0 0
Very Light
Random forest uses their own sample of training data i.e. Rain 0 11 2 12 0 0 30
there are some observations which might appear several
times in the sample. The final prediction is based on V CONCLUSION AND FUTURE WORK
voting by each tree in the forest. Random Forest is
characterized by their efficiency to deal with large data set, The proposed work is an attempt to forecast rainfall using a
relatively robustness for outliers and noise and ability to deal fusion of different machine learning and forecasting
with highly correlated predictor variables. techniques. Even though the rainfall is dependent on many
parameters, we are able to get impressive classification
C. Accuracy Measurements and Analysis
accuracy using limited parameters. It is also found that even
Table 3 is the result of 70% training and 30% training data
after classifying rainfall into eight different categories, we
set. It shows that random forest out performs compared to
are getting acceptable accuracy. Validations for forecasted
another method. For the experimental purpose, we have
given actual Real time values of Maximum Temperature, parameters are done using RMSE measure. Empirical results
Min temperature, Relative Humidity, Wind Speed as an show ARIMA for maximum temperature, Neural Network
input to the trained model and analysis is done on 30% for minimum temperature and SVR for relative humidity
testing data set. But as we want to forecast the rainfall it is and wind speed works best. Validation of classification is
necessary to give forecasted maximum temperature, measured through accuracy, precision and recall. ROC
minimum temperature, relative humidity and wind speed curve for all classifiers shows random forest works best for
values as an input parameter to the trained model. This rainfall classification.
forecasted parameters also have their own error so if we As rainfall is dependent on the various parameters it is
put the forecasted value as input parameter to this also required to study how other meteorological parameters
classification technique there are chances to decrease the affect the Rainfall prediction. We can also perform the same
final accuracy of the model. As the random forest gives the exercise on hourly data using various parameters to forecast
best accuracy we have shown the final con-fusion matrix
next hour rainfall. A study can also be done using more
for the random forest only (for Jun to Dec). Table 5 shows
observations for particular region or area, and design this
the confusion matrix for the random forest. Diagonal shows
kind of model on big data framework so that computation
the correctly classified category. It is found that it shows
can be faster with higher accuracy.
good accuracy for No rain, moderate rain, very light rain,
light rain. Figure 2 shows the ROC (Receiver Operator
Characteristics) Curve analyzed through comparing results
of the different methods, category wise. Note: Individual
graphs are drawn for True Positive Rate (Sensitivity) on y-

978-1-5386-6026-3/18/$31©2018 IEEE 780

 5th IEEE International Conference on Parallel, Distributed and Grid Computing(PDGC-2018), 20-22 Dec, 2018, Solan, India

Fig. 2: ROC Curve Analysis Category wise

A. B.

C. D.

E. F.

G.

978-1-5386-6026-3/18/$31©2018 IEEE 781

 5th IEEE International Conference on Parallel, Distributed and Grid Computing(PDGC-2018), 20-22 Dec, 2018, Solan, India

ACKNOWLEDGMENT [10] Rob J Hyndman and George Athanasopoulos. Forecasting: principles

and practice. OTexts, 2014.
This work is financially supported by Space Application [11] Lily Ingsrisawang, Supawadee Ingsriswang, Saisuda Somchit, Prasert
Center-Indian Space Research Organization (SAC-ISRO) Aung-suratana, and Warawut Khantiyanan. Machine learning
under RESPOND Scheme OGP142. Authors would like to techniques for short-term rain forecasting system in the northeastern
part of thailand. Machine Learning, 887:5358, 2008.
extend their sincere thanks to SAC-ISRO authorities for the
[12] Soo-Yeon Ji, Sharad Sharma, Byunggu Yu, and Dong Hyun Jeong.
opportunity given to work with them. Designing a rule-based hourly rainfall prediction model. In
Information Reuse and Integration (IRI), 2012 IEEE 13th
International Conference on, pages 303{308. IEEE, 2012.
[13] Dinu John and BB Meshram. A data mining approach for monsoon
REFERENCES prediction using satellite image data. International Journal of
[1] Mithila Sompura Aakash Parmar, Kinjal Mistree. Machine learning Computer Science & Communication Networks, 2(3), 2012.
techniques for rainfall prediction: A review. International Conference [14] Jyothis Joseph and TK Ratheesh. Rainfall prediction using data
on Innovations in informa-tion Embedded and Communication mining techniques. International Journal of Computer Applications,
Systems, 2017. 83(8), 2013.
[2] Nishchala C Barde and Mrunalinee Patole. Classification and [15] Sarah N Kohail and Alaa M El-Halees. Implementation of data
forecasting of weather using ann, k-nn and na•ve bayes algorithms. mining techniques for meteorological data analysis. Intl. Journal of
[3] Debasish Basak, Srimanta Pal, and Dipak Chandra Patranabis. Information and Communication Technology Research (JICT), 1(3),
Support vector regression. Neural Information Processing-Letters and 2011.
Reviews, 11(10):203{224, 2007. [16] Folorunsho Olaiya and Adesesan Barnabas Adeyemo. Application of
[4] Leo Breiman. Random forests. Machine learning, 45(1):5{32, 2001. data mining techniques in weather prediction and climate change
studies. International Journal of Information Engineering and
[5] KK Chowdari, R Girisha, and KC Gouda. A study of rainfall over Electronic Business, 4(1):51, 2012.
india using data mining. In Emerging Research in Electronics,
Computer Science and Technology (ICERECT), 2015 International [17] Elia Georgiana Petre. A decision tree for weather prediction.
Conference on, pages 44{47. IEEE, 2015. BULETINUL UniversitaNii Petrol{Gaze din Ploiesti, pages 77{82,
2009.
[6] Pinky Saikia Dutta and Hitesh Tahbilder. Prediction of rainfall using
data mining technique over assam. IJCSE, 5(2):85{90, 2014. [18] Narasimha Prasad, Prudhvi Kumar, and Naidu Mm. An approach to
prediction of precipitation using gini index in sliq decision tree. In
[7] G Gregoire. Multiple linear regression. European Astronomical Intelligent Systems Modelling & Simulation (ISMS), 2013 4th
Society Publications Series, 66:45{72, 2014. International Conference on, pages 56{60. IEEE, 2013.
[8] Mina Mahbub Hossain and Sayedul Anam. Identifying the [19] Sirajum Monira Sumi, MFaisal Zaman, and Hideo Hirose. A rainfall
dependency pattern of daily rainfall of dhaka station in bangladesh forecasting method using machine learning models and its application
using markov chain and logistic regression model. 2012. to the fukuoka city case.
[9] Rob J Hyndman. Moving averages. In International Encyclopedia of
Statistical Science, pages 866{869. Springer, 2011.

978-1-5386-6026-3/18/$31©2018 IEEE 782

View publication stats