See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/299044518 ALTERNATIVE FORECASTING METHOD FOR JAKARTA INTERBANK OFFERED RATE Conference Paper · November 2015 CITATIONS READS 137 authors: Arum Handini Primandari Ayundyah Kesumawati Universitas Islam Indonesia Universitas Islam Indonesia PUBLICATIONS   0 CITATIONS    12 PUBLICATIONS   2 CITATIONS    SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Ayundyah Kesumawati View project A Segmentation Group by Kohonen Self Organizing Maps (SOM) and K -Means Algorithms (Case Study : Malnutrition Cases in Central Java of Indonesia) View project All content following this page was uploaded by Ayundyah Kesumawati on 20 March 2016 The user has requested enhancement of the downloaded file 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 primandari.arum@uii.ac.id 2) Department of Statistics, FMIPA, UII ayundyah.k@uii.ac.id 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 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 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 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 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 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 L1  Y i 1 i (5) 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    (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) 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 (a) (b) (c) (d) Figure 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 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 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 Source Columns Error Total df 260 263 Table 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 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 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 Reference [1] Acar, Y (2014) Forecasting Method Selection Based on Operational Performance Boaziỗi 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] http://www.bi.go.id/en/moneter/jibor/tentang/Contents/Default.aspx, 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 View publication stats ... 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... (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. .. Thus, the accuracy of SES was significantly different from the others method Keywords: JIBOR, interest rate forecasting, deterministic methods, exponential smoothing Introduction The Jakarta Inter