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ALTERNATIVE FORECASTING METHOD FOR JAKARTA INTERBANK OFFERED
RATE
Conference Paper · November 2015

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Arum Handini Primandari

Ayundyah Kesumawati

Universitas Islam Indonesia

Universitas Islam Indonesia

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Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015
Lombok Island, Indonesia, November 4-5, 2015
Paper No. XXX

ALTERNATIVE FORECASTING METHOD FOR JAKARTA
INTERBANK OFFERED RATE
Arum Handini Primandari1), Ayundyah Kesumawati2)
1)

Department of Statistics, FMIPA, UII.
2)
Department of Statistics, FMIPA, UII.

Abstract-The Jakarta Interbank Offered Rate (JIBOR) is an indicative rate for unsecured loan transactions
on the money market offered by one contributor bank to another in order to lend the rupiah of certain tenors
in Indonesia. Knowing JIBOR in advance will help to organize financial system in order to maintenance its
stability. The most appealing method for interest forecasting is stochastic methods which can handle some
sort of problems such as heteroscedasticity, extreme data, multivariate data and so all. However, these
methods work in stationary data that we rarely find of. The simpler method for forecasting is deterministic
methods that do not require any assumptions. Using smoothing parameters, these methods follow the pattern
of data to predict the previous value. We carried out this research using single exponential smoothing,

exponential smoothing with additive trend, and exponential smoothing with damped additive trend. The
measurement of Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE) were used
to compare the effectiveness of the methods. For further discussion, we used Analysis of Variance (ANOVA)
and Tukey-Kramer as posttest. Thus, the accuracy of SES was significantly different from the others

method.
Keywords: JIBOR, interest rate forecasting, deterministic methods, exponential smoothing.

1. Introduction
The Jakarta Inter Bank Offered Rate is an indicative rate for unsecured loan transactions on the
money market offered by one contributor bank to another in order to lend the rupiah of certain tenors in
Indonesia. JIBOR is a reference rate used for financial transactions, including a reference rate for floating
and derivative transactions, as well as to evaluate rupiah denominated financial instruments. JIBOR is
determined based on indicative rates submitted by contributor banks. JIBOR is published through the Bank
Indonesia website daily at 10:00 WIB.
JIBOR is calculated by taking simple average of rates, after omitting 15% of the highest rates and 15%
of the lower rates of contributor banks. Bank Indonesia (BI) decides the contributor banks from local banks
in Indonesia. In April 2015, BI has trimmed contributor bank from 30 to 21. Thus, JIBOR can be more
credible for reflecting market condition and economic liquidity.
Nowadays BI is making effort to boost the credibility of JIBOR. Thus, in the future, local firms could
use the rate for their financial transactions, such as a bank’s lending or deposit facilities, or other derivative
transactions from interest-rate swaps to hedging.
Forecasting JIBOR will help companies to manage their financial. It makes them possibly for applying
hedging strategy, arranging portfolio, making some lending, and so all.
The use of deterministic method for forecasting, even this is a traditional way, is simpler than stochastic
method. Thus due to the stochastic model assumption, that is stationary. In most of real data especially
financial data, we rarely find stationary data. Although we can perform transformation, sometimes the data
still remains non-stationary. Moreover, it is hard to choose the best transformation parameter value so that we
have stationary data. In the contrary, deterministic models do not require any assumptions.

Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015
Lombok Island, Indonesia, November 4-5, 2015
Paper No. XXX

Indonesian historical of financial data, such as JIBOR, mostly was non-normal data. This data usually
have heavy tail or high peak, called leptokurtic. The consequent of this non-normality is non-stationary.
Earlier research, Hyndman (2001) [3] showed that exponential smoothing performed better than first order
ARIMA models when data are non-normal. Therefore we used deterministic methods, instead of stochastic
methods.
JIBOR historical data had trend characteristic on it, so we carried out four deterministic models that are
Single Exponential Smoothing (SES), Holt’s Exponential Smoothing, Damped Holt’s Exponential (DHE),
and Damped Pegel’s Multiplicative Trend (DPMT). We compared these four methods to obtain best
forecasting result.

2. Method
2.1.
Single Exponential Smoothing
The simplest exponential smoothing is Single Exponential Smoothing. This method has one
parameter to smooth the curve of data.

Ft 1  Yt  (1  ) Ft ,
2.2.

0 1

(1)

Holt Exponential Smoothing with Additive Trend

Holt’s exponential smoothing is deterministic method overcoming data with trend. The formula
of HES is given bellow.

Lt  Yt  1   Lt 1  Tt 1 ,

Tt  Lt  Lt 1   1  Tt 1 ,

01
01

Ft  m  Lt  mTt

(2)
(3)
(4)

Where Lt is the level at time t, Tt is the local growht at time t, Ft+m is the forecast value at time t+m.
The smoothing constant α and β are respectively constant for level and local growth (trend). The
initial values have to be calculated to be able to update for level and trend.
3

L1 

Y
i 1

i

(5)

3
b1  Y2  Y1
2.3.

(6)
Damped Holt Exponential Smoothing with Additive Trend

Gardner and McKenzie (1985) [7] describe how a dampening parameter, ϕ, can be used within
Holt’s method to give more control over trend extrapolation. The formula for DHE is presented as
follow.

Lt  Yt  1   Lt 1  Tt 1 

Tt  Lt  Lt 1   1  Tt 1

(7)
(8)

m

Ft  m  Lt    iTt
i 1

The damped parameter 0    1 .

(9)


Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015
Lombok Island, Indonesia, November 4-5, 2015

Paper No. XXX

2.4.

Damped Pegel’s Multiplicative Trend

Pegels’ classifications have nine different method for forecasting, including additive or
multiplicative trend with either seasonality or non-seasonality. The formula for DPMT is given as
follow [7]:





(10)

Tt 1

(11)

Lt  Yt  1    Lt 1Tt 1

Tt  Lt / Lt 1   1  
m



i

Ft  m  Lt T i 1

(12)

3. Numerical Result
We used monthly JIBOR data taken from January, 2010 until August, 2015. We defined the
smoothing constant α=0.5, β=0.7, and γ=0.3. The curve fitting data of four methods was presented
at Figure 1.

(a)

(b)

(c)

(d)

Figure 1. JIBOR original data against the four method of exponential smoothing.

The forecasting result for three periods is written as follow.
Period
Sept., 2015
Okt., 2015
Nov., 2015

Table 1. Forecast Result
SES
HES
6.946814
7.300764
6.946814

7.510377
6.946814
7.71999

DHE
7.107946
7.165989
7.200815

DPMT
7.112859
7.173558
7.210226


Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015
Lombok Island, Indonesia, November 4-5, 2015
Paper No. XXX

We used Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) to
measure the precision of each method for curve fitting data. The MSE and MAPE was presented
as follow.

Method
SES
HES
DHE
DPMT

Table 2. Measurement of Error

MSE
0.1642
0.0831
0.0811
0.0915

MAPE
4.8907
3.6351
3.3718
3.8067

According to Table 2., Damped Holt Exponential smoothing has the smallest MSE with 3.3718%
of error relative to the data. The three method, that are HES, DHE, and DMPT, have little different
of measurement of error, either MSE or MAPE. Testing this difference of accuracy prediction, we
conducted ANOVA of error forecasting. The result of ANOVA test was given in Table 3.

Source
Columns
Error
Total

df
3
260
263

Table 3. ANOVA Result
SS
MS

2.7718
0.9239
22.3602
0.0860
25.1319

F
10.7432

Prob>F
1.1146×10-6

According to Table 1., we rejected H0, means that at least a pair of exponential method has
different accuracy to predict data. We continued to do posttest ANOVA using Tukey-Kramer Test.
Thus, the accuracy of SES was significantly different from the others method. In addition, the
accuracy of HES, DHE, and DPMT have no difference on accuracy.

4. Conclusion
We can apply exponential smoothing to forecast JIBOR because it does not require any
assumption, such as normality. Among the four exponential smoothing, Damped Holt’s
Exponential Smoothing has the least MSE. Furthermore, Holt’s Exponential, Damped Holt’s
Exponential, and Damped Pegel’s Multiplicative were not significantly different to predict JIBOR.

5. Reference
[1] Acar, Y. (2014). Forecasting Method Selection Based on Operational Performance.
“Boğaziçi Journal Review of Social Economic and Administrative Studies” vol. 28(1), pp.
95-114.
[2] Acar, Y. and Gardner Jr., E. S. (2012). Forecasting Method Selection in Global Supply
Chain. “International Journal of Forecasting”, vol. 28, pp. 842-848.
[3] Gooijer, J. G., and Hyndman, R. J. (2006). 25 Years of Time Series Forecasting.

“International Journal of Forecasting,” vol. 22, pp. 443-473.
[4] consulted 25 Sep.
2015.


Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015
Lombok Island, Indonesia, November 4-5, 2015
Paper No. XXX

[5] Livera, A. M., Hyndman, R. J., and Snyder, R. D. (2010). Forecasting Time Series with
Complex Seasonal Pattern Using Exponential Smoothing. “Working paper Monash
University Department od Econometrics and Business Statistic.”
[6] Rasmussen, R. (2004). On Time Series Data and Optimal Parameters. “International
Journal of Management Science”, vol. 32, pp. 111-120.
[7] Taylor, J. W. (2003). Exponential Smoothing with a Damped Multiplicative Trend.
“International Journal of Forecasting”, vol. 19, pp. 715-725.

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