Abstract— Investors take huge risk in making investments because
they lack the information about the future sale of the company or we can also
say that they lack forecasting. Due to which they may have to face loss in
future. Similar is the case with transportation, especially when it comes to
airline mode because of huge increase in investment and risk factor. Keeping in
mind the above discussed issue this paper deals with forecasting. The paper
proposes the use of Long Short-Term Memory Network. Unlike the existing
schemes, the proposed scheme is capable enough to minimize the Root Mean Square
Error to maximum extent which ultimately would lead to better forecasting
results. The proposed scheme consist of four steps LSTM model construction,
data processing and making data suitable for LSTM model, fitting a stateful
LSTM network model to the training data and at last we evaluate the static LSTM
model on the test data and report the performance of forecast .Furthermore, the
obtained results indicates that the proposed scheme reduces the chances of
false positive to great extent and is practical enough to be implemented in
real-time scenario.

 

Keywords- LSTM , Time series prediction ,
Forecasting

                                                                                                                                                   
I.      Introduction

Time series modeling is a dynamic research area which has
attracted attentions of researcher’s community over last few decades. The main
aim of time series modeling is to carefully collect and rigorously study the
past observations of a time series to develop an appropriate model which
describes the inherent structure of the series. This model is then used to
generate future values for the series, that is to make forecasts. Time series
forecasting thus can be termed as the act of predicting the future by
understanding the past 1.

Now a days travelling is playing most important role in
life of people because of which huge amount of investment is made by various
people. Faster you travel from one place to another better it is for user and
because of which airlines are major targets to investors. This paper deals with
the airline dataset which gives the current and previous records of number of
passengers travelled using airline. With help of the theses records this paper
will analyse the number of passengers in the upcoming months and years. This
information will be the key factor for investors to decide whether they want to
investment in the airline business or not depending the change in rate of the
number of customers whether its positive or negative.

For solving the above problem we have used Stacked
Stateful LSTM with memory between the batches. In the proposed schema we will
construct a LSTM model. LSTM is the type of Recurrent Neural Network (RNN). The
benefit of this type of network is that it can learn and remember over long
sequences and does not rely on a pre-specified window lagged observation. The
dataset loaded contains information of the number of passengers who had travelled
through the airline in particular month and year. The dataset needs to be
transformed to make it more suitable for LSTM model which include.

 

A. MOTIVATION

 

Risk factor for any investment increases as the amount of
investment increases because of which investors do keep tract of the company’s
profile and measure the stability of the company. But predictions from the
above method turn out of to give huge amount of error. This paper proposed a
scheme to reduce this error and for more accurate forecasting. The major
motivation of this paper is to reduce the risk factor and also to analyse the
company.

 

B. CONTRIBUTION

 

The primary contribution of this paper is to Long
Short-Term Model is to that it reduces the Root Mean Square Error of LSTM model
with use of Keras deep learning library. The another major contribution of this
paper is the combination of Keras deep learning library with LSTM.

 

 

C. ORGANIZATION

 

The rest of the paper is organized as follows. Section II
gives the relative work which are done in this field.  Section III gives the brief description about
the working of the proposed scheme. Section IV elaborates the LSTM model. The
results and discussion are presented in Section V. The paper is finally
concluded in Section V.

                                                                                                                                               
II.    RELATED  WORK

The model we present in
the next section is the result of inspiration we have taken from prior work on
prediction on airline based on various factors. 18 This paper used the
back-propagation neural network and genetic algorithm to forecast the air
passenger demand in Egypt(International and Domestic). The factors that
influence air passenger are identified, evaluated and analyzed by applying the
back-propagation neural network on the monthly data from 1970 to 2013. 19
This paper is based on comparative study of new method and traditional
forecasting technique such as moving average, exponential smoothing,
regression, etc. All methods were compared on the basis of a standard error
measure- mean absolute percentage error. 20 This paper proposes an ensemble empirical mode decomposition
(EEMD) based support vector machines (SVMs) modeling framework incorporating a
slope-based method to restrain the end effect issue occurring during the
shifting process of EEMD. Along with above research papers One
of the most popular and frequently used stochastic time series models is the
Autoregressive Integrated Moving Average (ARIMA) 3, 5 model. The basic
assumption made to implement this model is that the considered time series is
linear and follows a particular known statistical distribution, such as the
normal distribution. ARIMA model has subclasses of other models, such as the
Autoregressive (AR) 6, 8, Moving Average (MA) 5 and Autoregressive Moving
Average (ARMA) 4, 5 models.

 

For
seasonal time series forecasting, Box and Jenkins 8 had proposed a quite
successful variation of ARIMA model, viz. the Seasonal ARIMA (SARIMA) 5, 8.
The popularity of the ARIMA model is mainly due to its flexibility to represent
several varieties of time series with simplicity as well as the associated
Box-Jenkins methodology 3, 5 for optimal model building process. But the severe
limitation of these models is the pre-assumed linear form of the associated
time series which becomes inadequate in many practical situations.

 

 

III PROPOSED SCHEME

 

This section illustrate the
proposed scheme. To solve the problem of airlines passenger time series prediction  we have developed a model which consists of a
Sequential , 2 LSTM and one Dense Layer. Fig 1 shows the flow of data across
the various layers of the  model.

 

 

LSTM  LAYER

 

                                                           

 

 

 

 

 

SEQUENTIAL LAYER:

It is used to create a sequential model. It acts as a
linear stack of layers. All the other layers like LSTM and Dense are added to
it to create a model.

LSTM LAYER:

Long Short Term Memory networks –
usually just called “LSTMs” – are a special kind of RNN, capable of learning
long-term dependencies. They were introduced by Hochreiter & Schmidhuber
(1997)21.LSTMs are explicitly
designed to avoid the long-term dependency problem.All recurrent neural
networks have the form of a chain of repeating modules of neural network. In
standard RNNs, this repeating module will have a very simple structure, such as
a single tanh layer.

                                              Fig:2

LSTMs also have this chain like
structure, but the repeating module has a different structure. Instead of
having a single neural network layer, there are four, interacting in a very
special way.

                                    Fig:3

DENSE LAYER:

A
dense layer is simply a layer where each unit or neuron is connected to each
neuron in the next layer.

                      

                
IV PROPOSED METHODOLOGY

The
steps that we had taken to solve the problem at had were:

1.       In
the first step we imported the required modules which were namely numpy ,
matplotlb , keras, math , pandas and sklearn .

2.       In
the second step the dataset “international-airlines-passenger.csv” was loaded
using pandas read_csv() function.

3.       In
the third step the data was normalised using MinMaxscaler() function of sklearn
module .

4.       In
the fourth step the dataset was broken into two parts for one for training(67%)
and the other for testing(33%) and the broken data chunks were reshaped so that
they could be feed into the model.

5.       In
the fifth step we trained  and fitted our
model.

6.       In
the sixth step we made prediction for the training and testing dataset.

7.       And
finally in the last step graphs were plotted for the predicted values.

 

                                   V RESULTS

 

The
result obtained after working through the above algorithm or methodology can be
summarised using a graph . The graph so plotted shows how accurately the above
model predicts the actual data points.

 

        

                                    Fig:4                           

 

The
key to read the graph shown in Fig 4 is present in the table 1.

 

 

 

COLOUR

DATA
POINTS

BLUE

ACTUAL DATA POINTS

ORANGE

PREDICTED PONTS OF TRAINING DATA

GREEN

PREDICTED POINTS OF TESTING  DATA

                              Table:1

 

                           VI CONCLUSION

From
the graph shown in Fig 4 we can conclude that the model so used works quite
well for recreating the values that had been used in training but lacks
efficiency in predicting the unseen data. But overall the model works fairly
well. Also there is a sudden jump that can be seen while shifting from training
to testing data.

 

                        VII FUTURE WORK

In
future one might look at extending the model by incorporating convolution
layers and try making the model even more deeper so that the efficiency of the
network improves and the sudden observed change also fades away while moving
from training to testing data points.

 

                        VIII REFERENCES

1 T. Raicharoen, C. Lursinsap, P. Sanguanbhoki, “Application
of critical support vector

machine to time series prediction”, Circuits and Systems,
2003. ISCAS ’03.Proceedings of

the 2003
International Symposium on Volume 5, 25-28 May, 2003, pages: V-741-V-744

2 G.P. Zhang, “A neural network ensemble method with
jittered training data for time

series
forecasting”, Information Sciences 177 (2007), pages: 5329–5346.

3 G.P. Zhang, “Time series forecasting using a hybrid ARIMA
and neural network

model”,
Neurocomputing 50 (2003), pages: 159–175.

 

4 John H. Cochrane, “Time Series for Macroeconomics and
Finance”, Graduate School

of Business,
University of Chicago, spring 1997.

5 K.W. Hipel, A.I. McLeod, “Time Series Modelling of Water
Resources and

Environmental
Systems”, Amsterdam, Elsevier 1994.

6 J. Lee, “Univariate time series modeling and forecasting
(Box-Jenkins Method)”, Econ

413, lecture
4.

7 C. Hamzacebi, “Improving artificial neural networks’
performance in seasonal time

series
forecasting”, Information Sciences 178 (2008), pages: 4550-4559.

8 G.E.P. Box, G. Jenkins, “Time Series Analysis,
Forecasting and Control”, Holden-Day,

San Francisco,
CA, 1970.

9 H. Tong, “Threshold Models in Non-Linear Time Series
Analysis”, Springer-Verlag,

New York,
1983.

10 Chu KL, Sahari KSM. Behavior recognition for humanoid
robots using long short-term memory. 2016;13(6):172988141666336.

11 Palangi H, Deng L, Shen YL, Gao JF, He XD, Chen JS, et al. Deep
Sentence Embedding Using Long Short-Term Memory Networks: Analysis and
Application to Information Retrieval. IEEE-ACM Trans Audio Speech Lang.
2016;24(4):694–707

12 Palangi H, Ward R, Deng L. Distributed Compressive Sensing: A Deep
Learning Approach. IEEE Transactions on Signal Processing. 2016;64(17):4504–18.

13 Yue J, Zhao W, Mao S, Liu H. Spectral—spatial classification of
hyperspectral images using deep convolutional neural networks. Remote Sensing
Letters. 2015;6(6):468–77

14 Hinton G, Deng L, Yu D, Dahl GE, Mohamed A, Jaitly N, et al. Deep
Neural Networks for Acoustic Modeling in Speech Recognition. IEEE Signal
Processing Magazine. 2012;29(6):82–97.

15 Dahl GE, Yu D, Deng L,
Acero A. Context-Dependent Pre-Trained Deep Neural Networks for
Large-Vocabulary Speech Recognition. IEEE Transactions on Audio Speech &
Language Processing. 2012;20(1):30–42.

16 Mesnil
G, He X, Deng L, Bengio Y. Investigation of recurrent-neural-network
architectures and learning methods for spoken language understanding.
Interspeech. 2013

17 Hochreiter S, Schmidhuber J. Long Short-Term Memory. Neural
Computation. 1997;9(8):1735–80. pmid:9377276

18 
International Journal of Computer Application (0975-8887) on “Airline
Passenger Forecasting in EGYPT (Domestic and International) by M.M.Mohie
El-Din, M. S. Farag and A. A. Abouzeid. Department of Mathematics, Faculty of
science, Al-Azhar University Nasr City, Cairo 31884, Egypt

19 Journal of Revenue
and Pricing Management, Volume 1, Number 4 on “Neural network forecasting for
airlines : A comparative analysis ” by Lawrence R. Weatherford, *Travis W.
Gentry and Bogdan Wilamowski.

20  “Forecasting Air Passenger Traffic by Support
Vector Machines with Ensemble Empirical Mode Decomposition and Slope-Based
Method” by Yukun Bao, Tao Xiong, and Zhongyi
Hu Department of Management Science and Information System,
School of Management, Huazhong University of Science and Technology, Wuhan
430074, China

 

21 In addition to the original authors, a lot of people
contributed to the modern LSTM. A non-comprehensive list is: Felix Gers, Fred
Cummins, Santiago Fernandez, Justin Bayer, Daan Wierstra, Julian Togelius,
Faustino Gomez, Matteo Gagliolo, and Alex Graves.

 

 

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