Advisors and indicators based on the SSA models and non-linear generalizations. А.М. Аvdeenko

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1 Advisors ad idicators based o the SSA models ad o-liear geeralizatios А.М. Аvdeeko The Natioal Research Techological Uiversit, Moscow, Russia , Moscow, Leisk prospekt, 4 aleksei-avdeek@mail.ru Abstract This paper cosiders method of creatio of a advisor ad idicator based o the spectral stochastic aalsis model, both with liear ad o-liear approximatio. The problem of etrace to oe or aother trade positio is solved o the basis of combied aalsis of damics of quotatios of all currec pairs, what allows to activel hedge ope positios. Kewords: Forex market, advisor, idicator, sigular stochastic aalsis 1. Itroductio Great umber of models is kow, which are used for automatio of exchage trade (advisors) ad visualizatio of the recommedatios (idicators). These are models of slidig average MA(q), autoregressio AR(p), mixed models, such as ARMA(p,q) [1,2], ITRIX, Boliger bads, Elliott waves, momet ad stochastic models, etc. Models of ARCH(q) tpe represet coditioal dispersio as liear fuctio of squares of past disturbaces. I models GARCH(p,q) coditioal dispersio at give time is liear fuctio of coditioal dispersio ad squares of disturbaces at past times [3,4]. Further rectificatio of the GARCH(p,q) model model EGARCH(p,q) is able to allow for asmmetr effects egative correlatio betwee profitabilit ad volatilit. Actual applicatio of these models for creatio of automated tradig sstems or visualizatio of the tedecies is ot too efficiet. It frequetl happes that the results are trivial the model s coefficiets are either statisticall o-sigificat, or are determied with accurac, which does ot suffice for makig of efficiet decisios. I this work, for icrease of reliabilit of forecasts of damics of give currec pair, we propose to use iformatio o damics of other currec pairs. It will allow to partiall avoid effects of o-stabilit (slow drift of the descriptio parameters i stadard models of tpes MA(q), ARCH(q), etc), ad thereb to improve forecastig power ad practical efficiec of the model.

2 2. SSA model Let us assume that iput iformatio is discrete fiacial sequece x x t ) of quotatios of a currec pair at time t. I order to exclude uessetial oscillatios (lesser tha the spread), let us uderstad x as weighted average of prices of opeig ad closig, ad of maximum ad miimum for give time frame, which will be assumed equal to miimum possible 1 mi. Let us itroduce value x 1 x - chage of x i the course of evolutio of the sstems. Value will be cosidered as radom process. Dozes of currec pairs are simultaeousl traded o the market, so let i ( - be relevat chage for pair i 0 M 1. Elemetar estimatios show that currec pairs are correlated, so, for istace, for pairs EURUSD ad GBPUSD the correlatio factor i averagig iterval equal to time frames is positive ad is withi the iterval , etc. Therefore, whe makig decisio o etrace to / exit from short or log positio for give pair, it is expediet to allow for damics of chages for the rest currec pairs. To this ed, we offer the followig algorithm. Let us itroduce iformatio matrix, which reflects damics of chage of all currec pairs at give time t U 0 1 M 1 K K 1 K M 1 I this case M - is umber of aalzed currec pairs. Now let us determie the two-poit correlatio fuctio square matrix with dimesios ( M K ) ( M K ), where value K is T U U averagig iterval i the space of currec pairs at give time: R, while ( 1 K M ). 2 K The matrix is smmetric, therefore eige values that is solutios of equatio det( R 2 I ) 0, are real. To fid them, it is coveiet to use Jacobi algorithm, which is based o sequece of rotatios of the iitial matrix, which sequece is implemeted i such a wa that at each rotatio step the value of o-diagoal elemet, which is maximum b absolute value, is made equal to zero.

3 Compoets of the rotatio matrix i A at each step i are si( m ),cos( m ), where i1 1 Rm i1 m arctg, R - is maximum o-diagoal elemet at the precedig step, if i 1. m 2 R R i1 mm i1 2 Maximum umber of iteratios is 0.5(( M K) M ), but actuall the procedure ma be stopped whe modulus of the maximal o-diagoal elemet becomes less tha pre-established value. Usuall it is assumed that Colums of the rotatio matrix c 1 2 A A A A are the iitial matrix s eige vectors, while correspodig eige values are diagoal elemets of matrix R. A T RA c c Let us regularize eige values b absolute value, ad let us assig them to eige vectors. The idea of liear filtratio of the forecast i the SSA algorithm cosists i retaiig of several eige vectors correspodig to maximum eige values. Liear filtratio (forecast) i this model is carried out b meas of restoratio of the process b l eige values correspodig to maximal, b absolute value, eige values; i other words, future is forecasted as l c i 1 1 Aiq q while l M K q0 1. I the o-liear filtratio model the aforesaid algorithm is implemeted for time t 1, ad the, b meas of the least-squares method, or b meas of the reverse-spread eural etworks, we build approximatio ). i ( 1i Now, the future ma be represeted as 1i ( i ) ad used as a criterio for etrace to short or log positio. Further improvemet of the SSA method is possibilit to allow for time lag. I this case, istead of the iformatio matrix U we use cellular matrix F U U I U U N I 1 1 N 1 Its elemets are the U matrix s elemets shifted for uit time, where N is total umber of shifts, 1 I N is depth of averagig.

4 Further aalsis ad filtratio are similar to described above. This ot ol allows us to take ito cosideratio joit ifluece of various currec pairs o formatio of the exchage rate, but also to allow for laggig with various characteristic time scale. Practicall, for the Forex market the algorithm is implemeted i the MetaTrader 5 medium, both as idicators SSA1 liear filtratio ad SSA2 liear filtratio with time lag, ad oe of the advisor s uit as well [8]. Peculiarit of implemetatio of the algorithm for the advisor is possibilit of liear filtratio o the basis of the reverse-spread eural etwork with T hidde laers (1<T<10). Method of adaptive behavior described i work [7] is also implemeted. 3. Testig of the algorithm Experimetal testig of the algorithms SSA1 ad SSA2 has bee carried out for pair EURUSD for period from to Currec pairs used for aalsis were EURUSD, GBPUSD, USDCHF, USDJPY, USDCAD, AUDUSD, NZDUSD, EURAUD. Time frame was 1 mi, iitial deposit $10000, shoulder 100, lot 0.1 of the stadard oe. Prelimiar averagig p 5 was take ito cosideratio for l 1 4 mai compoets. The algorithm with time lag used eural etwork with two hidde laers. The algorithm is implemeted i the MQL5 medium, ad is part of geeral algorithm [8]. Table 1 presets results of the testig. Table 1 Results of testig algorithm for the period ; l - umber of eigevectors, P - profit, Sh-Sharpe ratio ad drawdow D% l P,$ Sh D% SSA

5 SSA For oe-ear itervals all implemetatios appeared to be profitable, while for aalsis of two-moth itervals the profitabilit share was O the average, trades were made auall. The results appeared to be weakl depedig o umber of the retaied mai compoets, though we observed some decrease of profitabilit vs growth of l. The model with time lag showed o sigificat advatage as compared with liear filtratio, though scatterig of the results was somewhat smaller. The saggig was miimal, while Sharp s factor was maximal i the liear model with miimal retaiig of the mai compoets. The SSA algorithm carries out the risk hedgig. I the most simple variat the hedgig is carried out eve for trade of oe currec pair, while decisio o etrace to / exit from a positio is made for this currec pair o the basis of aalsis of all currec pairs. Whe mutual correlatios are preset, this decreases risk of etrace errors as compared with the situatio whe decisio is made o the grouds of aalsis of ol oe currec pair. More complicated hedgig ma be implemeted b redistributio of the lot value of each currec pair basig o statistics of previous trades ad some extreme priciples. Oe of the variats is cosidered i works [5-8], ad is accessible withi the package available o the website [9]. 4. Refereces 1. Bollerslev T. Geeralized Autoregressive Coditioal Heteroskedasticit / T. Bollerslev // Joural of Ecoometrics Pp Nelso D.B. Coditioal Heteroscedasticit i Asset Returs / D.B. Nelso // Ecoometrica V. 59. Pp Egle R. Estimatig Time Varig Risk Premia i the Term Structure: The ARCH-M Model / R. Egle, D. Lilie, R. Robis // Ecoometrica Egle R.F. & Patto A.J. What good is volatilit model? Quatitative Fiace 1,

6 5. A. M. Avdeeko. Chaos structures. Multicurrec adviser o the basis of NSW model ad social-fiacial ets arxiv: A. M. Avdeeko Multicurrec advisor based o the NSW model. Detailed descriptio ad perspectives 2011, arxiv: Alexe M. Avdeeko Absolute Adviser or Stochastic Model of Trade o the Heav Tails of Distributio, Joural of Mathematical Fiace, Vol, N. 2, 2013 PP Alex M. Avdeeko Use of the ARСH(1) Model Peculiarities for Creatio of Automated Tradig Sstems, SOP Trasactios o Statistics ad Aalsis, Volume 1, Number 1, pp.1-4,

Absolute Adviser or Stochastic Model of Trade on the Heavy Tails of Distributions

Joural of Mathematical Fiace, 03, 3, 68-74 http://dxdoiorg/0436/jmf03306 Published Olie May 03 (http://wwwscirporg/joural/jmf) Absolute Adviser or Stochastic Model of Trade o the Heavy Tails of Distributios