04/09/2023 MSc Applied Statistics 1

Kyalo Richard

Supervisors:

Dr. Anthony Waititu, PhD

Dr. Anthony Wanjoya, PhD

Department of Statistics and Actuarial Science Jomo Kenyatta University of Agriculture and Technology

Modeling Revenue collected from mobile payments in Kenya using

Artificial Neural Network

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Introduction

Background

Justification

Literature review

Methodology

Empirical Results

Conclusion

References

Overview of the presentation

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Mobile payment is a services operated under financial regulation and performed from a mobile device using Sms technology instead of using cash or credit cards.

The combined market for all types of mobile payments is expected to reach more than $600 Billion globally by 2014 this indicates that government earns billions of shillings every year through mobile payment services.

It is therefore important to model mobile payments service revenue since tax-prediction is the most important content of the tax-planning for the government every year.

ANN possess some unique characteristics like adaptability, nonlinearity and arbitrary function mapping ability, which make them quite suitable and useful for prediction.

Background and motivation

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Despite the fact that mobile payments generates huge revenue to the Kenyan government there is no structure for predicting the tax collected from this services yet it is one of the key source of government tax in Kenya.

Our study proposes to develop a model to efficiently forecast revenue collected from all mobile payments services in the country in future.

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Statement of the problem

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Currently mobile payment service facilitates an average of $320 million per month in person-to-person transfers this is equivalent to roughly 10 % of Kenya’s GDP on an annualized basis.

Extremely rapid uptake of mobile payment is a strong vote of confidence by local users in a new technology as well as an indication of significant suppressed demand for remittance services and thus increased revenue to the government.

Justification

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Objectives

Main Objective

• The main objective was to model revenue collected from mobile payments services using artificial neural network.

Specific objectives

• To identify factors that determines the revenue collected from mobile payments.

• To develop a model for predicting mobile payment revenue collection in future.

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Monthly mobile payment services data between March 2007 and June 2013 obtained from the Central Bank of Kenya website was used in this study.

The logarithmic rates were divided into 70% training set and 30% testing set. The training set was used to optimize the weights and the bias of the network, while testing set was used to determine the generalization ability of the network.

AIC and BIC criterion were used for choosing the best model that fit the data.

The transformed data was scaled using a linear function to an interval of 0 and 1. The quasi-newton method known as BFGS (Broyden, Fletcher, Goldfarb and Shanno) was used to train the model

Methodology

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To measure how well a neural network performs, the following performance measure where used.Mean Squared Error(MSE)

(1)

Mean Absolute Error(MAE)

(2)

Mean Absolute Percentage Error(MAPE)

(3)

Root Mean Squared Error(RMSE)

(4)

Methodology

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With mobile payment services being a new entity in the capital market neural networks have widely been used in share market prediction, forex exchange and forecasting of the various share price predictions, as well as for time series modeling.

Akinwale et.al (2009) used error back propagation algorithm and regression analysis to analyze and predict untranslated and translated Nigeria Stock Market Price.Translated NSMP prediction approach was more accurate than untranslated NSMP using either regression analysis or error back propagation algorithm.

Fernando and Jayawardena (1994) used various ARIMA models in forecasting monthly rainfall records. Venama et al. (1996) investigated climate change in the Senegal River basin via this approach.

Literature review

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Refenes et al. compared regression models with a back propagation network both using the same stock data. The results showed that the Mean Squared Error (MSE) for the neural network was lower than the Multiple Linear Regression (MLR) model.

McLeod et al. (1977) applied the ARIMA approach to average annual stream flows, annual sunspot number series and monthly airline passenger data and suggested a di erent ARIMA model for ffeach data set.

Zhang et al., (1998) studied models of per share earnings forecasting of neural networks with four kinds of models in 283 firms: This research shows that the use of neural network methods provides more accuracy in forecasting than linear forecasting models.

Literature review

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Objective 1:

Fitting Generalized Least Square on the data shown an attenuating sine wave pattern that reflected the random periodicity of the data and possible indication for the need for Non-seasonal and/or seasonal AR terms in the Model and hence opted for ARIMA model using Auto ARIMA function.

Based on goodness of fit the Auto ARIMA function fitted ARIMA(0,1,0)(0,1,1) to the data with Akaike criterion of 266.6817.

Test for normality of residual was normally distributed with the test statistics chi square(2)=19.3535 and p-value of 6.27264e-005.

Results

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Table 1: ARIMA model summary

Results

 Coefficient Std. error Z p-value

Const 0.053309 0.166081 0.3210 0.7482

Theta -0.42630 0.130484 -3.267 0.0011

Rate -0.0.0264 0.077430 -0.342 0.7323

Agents -0.00018 0.000126 -1.463 0.1435

Customers -0.34002 0.504228 -0.674 0.5001

Transaction 2.80757 0.174278 16.11 2.18e-05*

The selected best models were consistent with the independence assumption for all tests. Table 1 below show a summary ARIMA model fit to the data

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ResultsObservation from overall diagnostic test signifies the following• The standardized residuals don’t

show cluster of volatility• The autocorrelation function show

no significant autocorrelation between residuals

• The p-values for the Ljung-Box statistics are all large, indicating that the residuals are pattern less meaning that the residual are white noise.

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ResultsThe ACF and PACF values are all within the 95% zero bound indicating that there is no correlation amongst the residuals.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 5 10 15 20

lag

Residual ACF

+- 1.96/T^0.5

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 5 10 15 20

lag

Residual PACF

+- 1.96/T^0.5

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-6 -4 -2 0 2 4 6 8

Density

uhat1

uhat1N(-0.013338,1.859)

Test statistic for normality:

Chi-square(2) = 19.353 [0.0001] Plot of Normality test histogram shows a bell-shaped distribution. These are good indicators of Normality within the residuals

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Results Using P-values from Table 1 Exchange rate, number of customers

and number of Agents with (p-values 0.7323, 0.5001 and 0.1435 respectively) >0.05 where not significant at 95% confidence interval in the model.

The number of transaction with p-value 2.18e-05* was the only significant variable in the model at 95% CI.

The number of transactions significantly determines the revenue returns on mobile payment services unlike other predictor variables.

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ResultsObjective 2The ANN model (developed based on the training data) with 1 hidden node was found to show the least error, when compared with the testing data, thereby resulting in maximum capture of the actual trend observed with respect to monthly revenue. Lags AIC BIC1,2,3,4,5 -135.7117 -120.733

1,2,3,4 -136.3776 -124.3947

1,2,3 -138.4102 -129.4230

1,3,4 -137.3849 -128.3977

1,2,3,5 -136.8190 -124.8361

1,2,4 -138.2407 -129.2535

1,2* -140.8966 -134.2051

4,5 -125.6273 -119.6359

2,5 -134.0179 -128.0264

2,3,5 -132.3777 -123.3905

1,5 -140.2525 -134.2611

From table the model consisting of lag 1 and lag 2 respectively was identified as the optimal model using AIC selection criterion.

Therefore the final model included two input nodes, one hidden node and one output node.

*indicates the ‘best’ ANN model prediction

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Empirical Results

Lags MAE MSE RMSE MAPE

1,2,3,4,5 7.0202 77.602 8.8092 5.1459

1,2,3,4 6.7848 76.8481 8.7626 4.9354

1,2,3 3.7673 21.8320 4.6725 2.7171

1,3,4 6.4166 70.3445 8.3872 4.7011

1,2,3,5 6.7199 73.3335 8.5635 4.9209

1,2,4 6.7835 76.4936 8.7460 4.9496

1,2* 3.9977 23.7633 4.8748 2.8881

4,5 6.2191 65.1414 8.0710 4.4573

2,5 7.85672 95.1691 9.7555 5.6828

2,3,5 5.2717 49.5858 7.0417 3.8516

1,5 9.2252 118.7600 10.8977 6.7356

*indicates the best ANN model for out-of-sample prediction

To validate the ANN architecture the in sample forecasting was used where Mean Squared MSE,MAE,RMSE and MAPE test where used for forecasting accuracy measures.

The table below shows the output of the performance measure where the model with lag1 and 2 performed better than any other.

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Results

The plot shows Actual monthly revenue between November 2011 to June 2013 and predicted values using the trained neural network model (2-1-1).

we still lack sufficient data to facilitate satisfactory training but with time the model may improve with the growth of the mobile payment dataset.

ANN being a nonparametric method, choosing the number of input variables is very vital to avoid over fitting or under-fitting.

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The policy implication of this study is that ANN can be used to model revenue from mobile payments services, which is certainly useful for various financial players such as government and policy makers of the country.

Further research is recommended using advanced machine learning algorithms such as Random forest which integrates boosting and bagging of decision trees to increase predictive capability. In addition the tree base algorithm lacks sensitivity to noise and not subject to over fitting something ANN possess.

Conclusion

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Zhang, G., Patuwo, B. E. and Hu, M. Y. (1997) El-Shazly, M. R. and El-Shazly, H. E. (1997), ‘Comparing the Forecasting Performance of Neural Networks and Forward Exchange Rates’, Journal of Multinational Financial Management, 7, 345-356.

Mwita, P., Franke, J., Odhiambo, R. and Waititu, A. (2005). On conditional quantiles: Direct Kernel Estimator and its Consistency. African Journal of Science and Technology, Vol. 6(2), 67-76.

J. Yao, Y. Li and C. L. Tan, “Option price forecasting using neural networks,” OMEGA: Int. Journal of Management Science, vol. 28, pp 455-466, 2000.

T. Abe, Y. Tokuda, S. Ohde, S. Ishimatsu, and R. B. Birrer, “The influence of meteorological factors on the occurrence of trauma and motor vehicle collisions in Tokyo,” Emergency Medicine Journal, vol. 25, no. 11, pp. 769–772, 2008.

Dickey D.A. and Fuller, W.A., “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root”, Econometrica, 49, 1057-1072, 1981.

References

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Kunwar Singh Vaisla, Ashutosh Kumar Bhatt, “An Analysis of the Performance of Artificial Neural Network Technique for Stock Market Forecasting” on (IJCSE) International Journal on Computer Science and Engineering Vol. 02, No. 06, 2010, 2104-2109.

Medeiros M, Terasvirta, T, Rech, G. (2006) “Building Neural Network Models for Time Series: A Statistical Approach.” Journal of Forecasting. 25(1) pp. 49-75.

McLeod, A.I., “Diagnostic Checking Periodic Autoregression Models with Application”, The Journal of Time Series Analysis, 15, 221-233, 1995.

References

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THANK YOU

Statistics are like a bikini. What they reveal is suggestive, but what they conceal is vital.