Unsupervised extreme learning machine and support vector regression hybrid model for predicting energy commodity futures index

Abstract

Support vector regression (SVR) has been successfully applied in various domains, including predicting the prices of different financial instruments like stocks, futures, options, and indices. Because of the wide variation in financial time-series data, instead of using only a single standard prediction technique like SVR, we propose a hybrid model called USELM-SVR. It is a combination of unsupervised extreme learning machine (US-ELM)-based clustering and SVR forecasting. We assessed the feasibility and effectiveness of this hybrid model using a case study, predicting the one-, two-, and three-day ahead closing values of the energy commodity futures index traded on the Multi Commodity Exchange in India. Our experimental results show that the USELM-SVR is viable and effective, and produces better forecasts than our benchmark models (standard SVR, a hybrid of SVR with self-organizing map (SOM) clustering, and a hybrid of SVR with k-means clustering). Moreover, the proposed USELM-SVR architecture is useful as an alternative model for prediction tasks when we require more accurate predictions.

Appendix A: Technical indicators (features) used in this study

Formulas for technical indicators (features)
Notation: i: i-th day [i days ($i=1,2,\ldots ,N$) counted from reference date, February 1, 2010]
HP $_{i}$: highest index value of i-th day
LP $_{i}$: lowest index value of i-th day
OP $_{i}$: open index value of i-th day
CP $_{i}$: closing index value of i-th day

l Sl No.	Technical Indicator Name	Technical Indicator Description & Formula
1	10-day moving average	The most current 10-day average closing value of the financial instrument.
		$MA _{10,i} = \frac{\sum _{j=i-9}^i {CP_j } }{10}$
2	20-day bias	Closing value and the moving average value deviation for the past 20 days.
		$BIAS _{20,i} = \frac{CP_{i } - MA _{20,i} }{MA _{20,i} } ,where MA _{20,i} = \frac{\sum _{j=i-19}^i {CP_j } }{20}$
3	Moving average convergence/divergence (MACD)	MACD is the change between a 26-day and 12-day exponential moving average (EMA). **
		$\begin{array}{l} MACD _i = EMA _{12,i} -EMA _{26,i} ,where \\ EMA _{N,i } = (CP_i - EMA _{N,i-1} ) \times ( 2/ (N+1)) + EMA _{N,i-1} \\ \end{array}$
		**EMA gives more weight to recent values and decreasing weight to older data.
4	Stochastic indicator %K	Stochastic %K a security’s closing value relative to its value range over a given period (9 days in this experiment).
		$\% K_i = \frac{(CPi-LLP)}{(HHP-LLP)} \times 100,$
		where LLP is the lowest low index value and HHP is the highest high index value over the last N periods.
5	Stochastic indicator %D	Moving average of %K (three-period simple moving average)
		$\% D_i = \frac{\sum _{j=0}^2 { \% K_{i-j} } }{3}$ /
6	Stochastic slow %D	Moving average of %D (three-period simple moving average)
		$\% SD_i = \frac{\sum _{j=0}^2 { \% D_{i-j} } }{3}$
7	Larry William’s %R	Larry William’s %R is a momentum indicator that measures overbought/oversold levels (9 days in this experiment).
		$\% R_i = \frac{(HP-CP_i )}{(HP-LP)} \times 100$
		where LP is the lowest index value and HP is the highest index value over the last N periods.
8	Rate of change (ROC)	Ratio of current closing value to the value a certain number of periods (n periods) ago (10 days in this experiment).
		$ROC_i = \frac{CP_i }{CP_{i-n} } \times 100$
		where ${CP }_{i-n}$ is the closing index value of the ($i-n$)-th day.
9	Relative strength index (RSI)	RSI is a momentum oscillator that compares the magnitude of recent gains to the magnitude of recent losses (we used a period of 5 days in this experiment).
		$\begin{array}{l} RSI_i = \frac{AG_i }{AG_i +AL_i } \times 100, \\ where \\ G_i = \left\{ {\begin{array}{l} CP_{i-1} -CP_i , if CP_{i } >CP_{i-1} \\ 0 \\ \end{array}} \right. { and}\ L_i = \left\{ {\begin{array}{l} CP_{i-1} -CP_i , if CP_{i } <CP_{i-1} \\ 0 \\ \end{array}} \right. \\ AG_{i } = \frac{4}{5} \times AG_{i-1} + \frac{1}{5} \times G_i \ { and}\ AL_{i } = \frac{4}{5} \times AL_{i-1} + \frac{1}{5} \times L_i \\ \end{array}$
10	Commodity channel index (CCI)	CCI measures the variation of a security’s value from its statistical mean (we used a period of 24 days in this experiment).
		$\begin{array}{l} CCI_i = \frac{TP_i -MATP_i }{0.015 \times MD_i }, \\ where \\ TP_i = \frac{HP_i +LP_i +CP_i }{3} , MATP_i = \frac{\sum _{j=i-23}^i {TP_j } }{24}, MD_i = \frac{\sum _{j=i-23}^i {|TPj - MATPi|} }{24} \\ \end{array}$
		where $TP_{i}$ is the typical value for the i-th day, $MATP_{i}$ is the 24-day simple moving average of the typical value for the i-th day, and MD$_{i}$ is the 24-day mean deviation for the i-th day.
11	Psychological line	Psychological line is the volatility indicator based on the number of time intervals that the market was rising during the preceding period (13 days in this experiment).
		$PSY_{i } = \frac{TDU_i }{13} \times 100~\% ,$
		where $TDU_{i}$ is the total number of days with regard to the rise in index value in the previous 13 days.
12	Buying/selling momentum indicator	Buying/selling momentum indicator (26 days)
		$BSMI_i = \frac{\sum _{j=i-25}^i {(HP_j - OP_j )} }{\sum _{j=i-25}^i {(OP_j - LP_j )} }$
13	Buying/selling willingness indicator	Buying/selling willingness indicator (26 days)
		$BSWI_i = \frac{\sum _{j=i-25}^i {(HP_j - CP_{j-1} )} }{\sum _{j=i-25}^i {(CP_{j-1} - LP_j )} }$
14	Momentum	Momentum measures the amount that a security’s value has changed over a given period (4 days)
		$MO_i = CP_i -CP_{i-4} .$
15	Disparity 5	Measures the distance between the current value and the moving average over 5 days
		$DIS_{5,i} = \frac{CP_i }{MA_{5,i} },$
		where $MA_{5,i }$ is the 5-day moving average for the i-th day.
16	Disparity 10	Measures the distance between the current value and the moving average over 10 days
		$DIS_{10,i} = \frac{CP_i }{MA_{10,i} },$
		where $MA_{10,i}$ is the 10-day moving average for the i-th day.
17	Moving average oscillators (MAO)	Value oscillator that displays the difference between two moving averages of different lengths (5 and 10 days)
		$MAO_i = \frac{MA_{5,i} - MA_{10,i} }{MA_{5,i} },$
		where ${MA}_{5,i}$ and ${MA}_{10,i}$ are the 5- and 10-day moving averages for the i-th day.