Abstract

The volatile nature of stock market creates problems

in developing robust prediction system for financial time series data

prediction , it become unreliable when stock market fluctuates suddenly due to

unexpected event like demonetization, earthquake or any other financial

decisions taken by government. Due to recent demonetization in India, stock

market fell down suddenly and was criticized as well as appreciated by many

financial experts and hence needed to be analyzed in terms of stability of the

stock market. This research work emphasizes on developing a robust model using two

popular neural network techniques with help of validation along with training data

instead of only training data. Models were developed with two financial time

series data: BSE 30 and INR/USD foreign Exchange (FX) using two neural network techniques:

Radial Basis Function Network (RBFN) and Error Back Propagation Network (EBPN)

Models were measured with Mean Absolute Percentage Error (MAPE). The empirical results show that RBFN is performing

better than EBPN for next day prediction with k-fold cross validation. It was

also observed that models developed through validation data is performing

better than others with lowest MAPE of 0.316 and 0.303 respectively for BSE30

and INR/USD.

Keywords: Radial Basis Function Network (RBFN), Error

back PropagationnNetwork (EBPN), Validation Data.

1.

Introduction

and Literature

Fluctuating

behavior of time series data is the primary focus for researchers of financial

time series data; this time series data fluctuates mostly due to occurrence of

any unexpected event. Stock prices and foreign exchange data are affected by

various factors and events, some of which influence stock prices directly and

others that do so indirectly and hence economy of a country may be affected.

Company stock prices and the stock market, in general, can be affected by

various events such as war, natural disasters, demonetization, political

events, and terrorism or any other monitory policy or decision taken by

government. This paper gives attention to development of a robust forecasting

system using validation data which may incorporate any event which takes place

suddenly. The recent demonetization in India was considered to check the

robustness of developed models and to check its impact on the stock market and

Foreign Exchange (FX) rate. Demonetization is the action of stripping a

currency unit of its status as legal tender. In India history Demonetization

took place three times: First in 1946 during this period currency note of

1,000, 5,000 and 10,000 were removed from the circulation, this Demonetization

did not have much impact as these types of the higher denomination was not

accessible to the ordinary people. The second demonetization took place in 1978

to drive away black money out of circulation in the economy, and third time

recently in 2016 when the currency of 500 and 1000 was banned. The objective of

this demonetization was to pull out black money and to fight against funding

for terrorism. Soon after this

demonetization, various sectors like real estate, Industry as well as

agriculture along with export and import were affected. BSE Sensex and NIFTY50

stock indices fell over 6% on the day of demonetization.

There

are many research articles found in the field of forecasting of time series

data 10, but there are very few papers which focus on the impact of events in

time series data using artificial intelligent techniques. Author 18 has

examined the relationship between market return after each Election Day and

economic performance during the presidential term. Author 19 represents the

result of the pattern of common stock return over four years election cycle and

different administrations like democratic and administrative. Author 20 analyze the impact of the

presidential election in the USA on stock returns flow. The analysis is focused

on securities of financial institutions listed on the New York Stock Exchange

and show the negative impact of the event in stock return. Author 21 analyzes

the performance of share prices around national elections in India during 2014

general elections. Event study methodology has been used for result analysis

and observed the positive reaction of changes in government after elections. Author

22 focuses on the effect of political uncertainty and the political process

on the stock market during US presidential election. The findings indicated

that the presidential election affects stock market volatility with positive

changes.

In

literature, many research papers have been published in the field of time

series data to develop a predictive model using different intelligent

techniques. Some authors 5 6 7 have developed models based on Back

Propagation Network (BPN) and Radial Basis Function Network (RBFN). For data

smoothing authors 8 have used hybridization of different techniques called

Stationary Wavelet Transform (SWT) for data preprocessing 2. Feature

extraction and the selection were also applied in data, and this data was

applied to ANN for Stock data prediction for next day close using Error Back

Propagation Network (EBPN) and Radial Basis Function Network (RBFN). Author 3

also used Exponent Back Propagation Neural Network (EBPN) to develop prediction

model and compared the EBPNN model with EBPN model. Author 11 suggested a

novel hybrid algorithm for automatic selection of input variables, number of

hidden nodes of RBF network and optimizing network parameters.

As

per above, it can be concluded that event is a natural process which occurs

time to time and needs to be studied to see the impact on the economy of a

country. On the other hand, we need to develop such type of model which can be

able to incorporate event which takes place suddenly. In this paper two neural

network techniques: Radial Basis Function Network (RBFN) and Error Back

Propagation Network (EBPN) were used for financial time series data prediction 13

to incorporate event. Experiments were carried out using self-written MATLAB

codes for both RBFN and EBPN. Data were partitioned with static partition as

well as k-fold cross-validation; the empirical results show that RBFN is

producing better results than EBPN.

2. Financial Time Series Data and Process Flow Diagram

To develop model, six years’ time series data

from January 2011 to March 2017 of BSE30 and INR/USD FX rate data were

collected from financial site www.yahoofinance.com and http://fx.sauder.ubc.ca

respectively. Out of which data up to Nov-8, 2017 are before demonetization and

data after this is of after demonetization. The detail of financial time series

data is shown in Table 1.

Table 1: Financial Time series data.

Particular

Detail

Financial Time Series Data

• Stock Index Data: BSE30

• Foreign Exchange Data: INR/USD.

Period of samples

1st January-2011 to 14th

March-2017 of BSE 30 and

1st January-2011 to 14th

March-2017 of INR/USD FX.

Total # of Samples

1545 (BSE 30),1545 (FX)

Downloaded From

• BSE30 Data: www.yahoofinance.com

• INR/USD Data: www.fx.sauder.ubc.ca

Data Partition

• Case I- Static Partition (Training-80%,

Testing-20%).

• 10 Fold cross validation (90% Training ,

remaining 10% Validation)

Testing

Data

• 9th November 2016 to 14 March

2017 of BSE30 and FX.

Figure 1 shows the nonlinear flow of BSE 30

data, which shows sudden fall in stock price 9 from the date of

demonetization. However, FX data trends shown in Figure 2 is almost stable even

after demonetization.

(a)

(b)

Fig. 1.

Trends of (a) BSE30 ndex data and (b) INR/USD FX data from Jan-2011 to

March-2017.

BSE30 stock data was prepared with four inputs

Open, High, Low and close value and one output value next-day-close while FX

data has only one input FX rate with next-day FX rate as output. Data normalization

1 was carried out to prepare the data in the range 0 1. The process flow diagram of proposed work for financial

time series data is shown in Figure 2 where data considered for the experiment

were partitioned into three parts: training, validation and testing.

2.1

Training Set :

Training dataset is used to create the model. This dataset

presented during training a model and the network is adjusted according to

error. This sample of data used to fit the parameters i.e., weights.

2.2

Validation Set:

A validation dataset is nothing just a subset of training data which is used for unbiased evaluation of a model to be fit

on the training dataset. It is used for minimizing the overfitting as well as

underfitting. This data set is also used for tuning the parameters of a model

i.e., model architecture.

2.3

Test Set:

This sample of data used to provide an unbiased evaluation

of a final model fit on the training data set. This data set is used for

performance evaluation of model.

The development of models based on partition of dataset into

training, validation and testing sets are divided into two cases; Case I: The

static partition of data as training and testing sets, Case II : Dynamic

partition of data as training, validation and testing sets. After partitioning

of data based on these two cases; intelligent techniques RBFN and EBPN were

applied to these datasets to validate the models, then testing dataset were

given to this predictive e model to test the accuracy of model.

Fig 2. Process Flow Diagram of proposed work.

3. Methodology

3.1

Radial Basis Function Network (RBFN)

Radial basis function network (RBFN) is a type of ANN many authors

use this technique to use it as non- classifiers 13

14 17 . In this technique radial basis functions has been used as activation

functions. Linear combination of inputs and parameters of neurons are work as

output of the network. RBFN is also used for classification, Time series forecasting

13 as well as for function approximation. In the hidden layer of RBFN,

transfer function is used for network’s characterization with respect to center.

In architecture of RNFN there are three layers are used: First layer is input

layer, second layer is called hidden layer and output is then send to output

layer from hidden layer where output is computed by each neurons.

3.2

Error Back Propagation Network (EBPN)

EBPN is popularly used prediction technique 6 which

can be trained using popular Error backpropagation algorithm and it is a

generalization of delta rule. The delta value for a given input vector compares

the output vector to the correct answer. Backward propagation of the

propagation’s output activated through the neural network using the training

pattern target in order to generate the deltas of all output and hidden

neurons. This technique is also known as the backward propagation of errors

because after calculation of errors at the output it goes back through the

network layers and repeats until the error comes to

the desired output.

3.3 K-Fold cross validation

K-fold validation is a technique where dynamically partitioned of

data is done in training and testing data sets 15. This method is

better than the static method of data portioning as all the data sets are used

as training as well as the testing dataset. Static data partition with a fixed

percentage of training and testing data may bias 12 and may have the problem

of network paralysis. Dynamic partitioning of data as training and testing

changes the fold dynamically. In k-fold cross- validation the data set is

divided into k subsets. At each fold, one subset is used as the test set, and

remaining subsets are merged together and used as a training set. Then the

average error of all k trials is calculated so that each fold takes part in training

and testing both.

4.

Result Analysis

Experimental work is done using MATLAB software to develop models;

various parameters of RBFN and EBPN were adjusted using trial and error

methods. Financial time series data considered for event analysis were normalized

using equation 1.Comparative results obtained through MATLAB code for both the

cases are shown in Table 2 and 3 respectively for BSE30 and INR/USD data in

term of MAPE calculated using equation

4. The convergence curve shown in Figure 6 and 7 respectively for RBFN and EBPN

shown that training models were converged in appropriate direction to meet out

the objective with minimum errors.

(1)

Where X is a time series data of a particular day and Xmax is

the highest value, Xnew is obtained normalized value. Financial data

were supplied one by one and developed models were evaluated using MAPE as

shown in equation 2:

*100 (2)

Where

is the actual observation of ith

term and

is the predicted observation of ith

term and n is the number of observations.

Table 2: Comparative MAPE for BSE 30 stock data.

Case

RBFN

EBPN

Training

Validation

Testing

Training

Validation

Testing

Case I

0.769

Not applicable

0.983

0.7861

Not applicable

1.0203

Case II

0.760

0.813

0.316

0.7754

0.8009

0.8051

Table 3: Comparative MAPE for INR/USD FX rate data.

Case

RBFN

EBPN

Training

Validation

Testing

Training

Validation

Testing

Case I

0.398

Not applicable

1.559

0.410

Not applicable

1.6854

Case II (ii)

0.366

0.6143

0.303

0.381

0.6658

0.3569

Results shown in Table 2 are quite

satisfactory as RBFN is performing better than EBPN, also RBFN model in case of

case II is performing better at testing stage with MAPE = 0.316 similarly Table

3 reflects the results for INR/USD FX rate with lowest MAPE 0.303 at testing

stage using RBFN. These tables also reflects the fact that model developed with

validation data set (Case II) is better than model developed with only training

set (Case I).

These developed models are clearly

reflecting the impact of demonetization in terms of testing, however model

developed for case II is much better than the model developed for case I, these

models (Case II) are producing better results with data after demonetization

which shows the strength and robustness of the model and able to incorporate

the down fall due to unexpected events occurred. Analytical results of Table 2

and 3 are also shown in form of graphical representation in Figure 3 (a) and 3

(b) respectively for BSE30 data and INR/USD FX rate data respectively of RBFN

and EBPN for both cases (Case I & Case II). Figure 4 and 5 depict the Performance convergence curve of BSE30 and

INR/USD using RBFN respectively.

(a)

(b)

Fig. 3. Comparative results of Case I

and Case II using RBFN and EBPN for (a) BSE30 and

(b) INR/USD FX.

Fig. 4. Performance convergence curve of

BSE30 using RBFN

Fig. 5. Performance convergence curve of

INR/USD FX using RBFN.

5. Conclusion

This research work is focused on development of a

robust financial time series forecasting system based on ANN techniques to incorporate

any unexpected event occurred from time to time. The demonetization data was

considered as an event. Experimental results drawn with the help of self

written MATLAB codes stabilizes the following facts:

·

Out of two cases considered in this research work the performance of

model developed with case II is performing better than that of case I.

·

Out of two ANN techniques considered in this research work RBFN is

outperforming EBPN in all cases.

·

RBFN model with 10-fold cross validation is best among all other models

and can be considered as robust financial time series prediction system as MAPE

obtained at testing stages are better which concludes that models developed

with dynamic partition of data has the capability to incorporate the sudden

fall of stock market and foreign exchange rate due to unexpected event like

demonetization.

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