A C T A U N I V E R S I T A T I S L O D Z I E N S I S FOLIA OECONOMICA 192, 2005
B e r n d B r a n d i *
E X C H A N G E RATES: PREDICTABLE BUT N O T EXPLAINABLE? DATA M ININ G W ITH LEADING IN D IC A TO R S
A N D TECHNICAL TRADING RULES
Abstract. This paper presents a data mining approach to forecasting exchange rates. It is assumed that exchange rates are determined by both fundamental and technical factors. The balance o f fundamental and technical factors varies for each exchange rate and frequency. It is difficult for forecasters to establish the relative relevance of different kinds of factors given this mixture; therefore the utilization o f data mining algorithms is advantageous. The approach applied uses a genetic algorithm and neural networks. Out-of-sample forecasting results are illustrated for five exchange rates on different frequencies and it is shown that data mining is able to produce forecasts that perform well.
Keywords: exchange rates, data mining, artificial neural networks, genetic algorithms. JEL Classification: C45, C53, F31.
1. INTRODUCTION
T his p a p e r exam ines the extent to which leading ind icato rs, technical trad in g rules and financial m ark et indicators im prove exchange ra te forecasts, and ca n th u s be com bined in forecast m odels on different frequencies. A ttem p ts a t forecasting exchange rates are usually categorized into fu n d am en ta l a ttem p ts and technical attem pts. T he un derlying assu m p tio n o f fu n d a m e n tal a ttem p ts is th a t fundam entals d o m a tte r an d th e stru ctu re of forecast m odels can be described by econom ic theory. T echnical attem pts, on the other hand, assume th a t psychological dynam ics in the foreign exchange m a rk e t are o f im po rtan ce and such dynam ics can be cap tu red by technical indicators. In this p aper both categories are seen as com p lem entary and useful in p ro v id in g in fo rm atio n on fu tu re exchange ra te m o vem en ts, and
thus also fo r the generation o f forecast m odels. T h e p roblem , however, is th a t relatively less is know n ab o u t the in terrelatio nships between the two categories and how these tw o categories can be com bined. Especially as relatively less is know n a b o u t it and the interrelation sh ip s are com plex, d a ta m ining ap p ears to be effective in com bining the tw o ap pro aches. T he d a ta m ining ap p ro ach presented consists o f two stages. T h e first step is the m odel selection for which a genetic algorithm (G A ) is applied. T he G A investigates various com binations o f fundam ental variables and technical variables and m easures their ability to forecast exchange rates. As an unlimited n u m b e r o f such com binations are conceivable an au to m ated o ptim isation proccss (like th a t provided by G A ) is effective. T h e second step in the d a ta m ining a p p ro a c h consists o f an artificial neural netw ork (A N N ). T h e reason for this ap p ro ach is th a t non-linearity m ay be exploited. T h e hypothesis th a t the behavior o f exchange rates is, to som e extent, n on -lin ear has been exam ined by several a u th o rs and an A N N th erefore m ay im prov e forecast accuracy. H ow ever, the presented d a ta m ining ap p ro ach is unique in the relevant lite ratu re (n o t only in forecasting exchange rates) and presents itself as a m eth o d for com bining different philosophies (categories) o f forecasting exchange rates.
S ections 1-4 are dedicated to the relationship betw een fu n d am en tals and technical indicato rs on the foreign exchange m ark et. T h e fu n dam entals and technical in d icato rs th a t are observed, i.e. considered in the d a ta m ining search space, will be discussed. As d a ta m ining allow s the con sid eratio n o f a large n u m b e r o f fu n d a m e n tals, as well as tra d itio n a l fu n d a m e n tals, fu n d am en tals such as in particu lar leading ind icato rs are also used. This p art will therefore focus on the question o f which fundam entals and technical in d icato rs are w o rth consideration. In Sections 5 and 6 we consider the m eth o d s applied and we present the d a ta m ining process. As will be shown, d a ta m ining is a powerful tool for finding good co m bin ation s o f explanatory variables on futu re exchange ra te m ovem ents. H ow ever, the issue o f causality in p a rtic u la r will be sketched, as selection in d a ta m inin g is based on statistical n o t logical criteria. Em pirical results on a daily, weekly and m onthly frequency show th a t d a ta m ining is effective in finding com binations o f fu n d a m e n tals an d technical ind icators, bu t raises the problem o f how these results can be interpreted or explained (Section 7). It will be show n th a t even th o u g h effective and successful co m b in atio n o f variables can be detected, these com binations are h ard to describe so the q u estio n can be raised as to w hether exchange rates are p redictable bu t n o t explainable (Section 8).
T h e sem inal w orks o f M eese and R o g o ff (1983a, 1983b) showed th at fu n d am en tal forecasting is relatively unsuccessful in co m p ariso n to the naive forecast. T h e ir nam es and w ork ran k am ongst the m o st cited w hen it comes
to discussions on exchange ra te fo recastin g because th ey do cu m en ted the failure o f p o p u lar fundam ental exchange rate m odels. H ow ever, ex change rates are highly volatile, i.e., m ovem ents in n om inal exchange rates arc larg er th a n m o vem ents in m acro eco n o m ic fu n d a m e n tals. As it is d o cu m ented in the literatu re, m any foreign exchange dealers view fu n d am en tal and technical analysis as com plem entary form s o f analysis, and thus as effective fo r deals. It has been found th a t the relative im p o rtan c e o f fu ndam ental versus technical analysis d epen ds on the extent o f the horizo n focused on. F o r shorter horizons, m o re w eight is given to technical analysis, and m ore weight is given to fu n d a m e n tal analysis fo r longer h o rizo n s (e.g. T a y lo r and A llen 1992) C h eu n g and C hinn 2001. C h e u n g and W o n g 2000). In resp o n se to th e fa ct th a t on the foreign exchange m a rk e t there exist p articip an ts w ho base th eir decisions o n technical as well as on fu ndam ental in fo rm atio n , F ra n k e l and F ro o t (1988) developed a m odel th a t uses tw o appro ach es to fo recastin g exchange rates. T h ese co n sist o f th e fu n d a m e n ta list a p p ro a c h , w hich bases the forecast o n econom ic fundam entals, an d the technical a p p ro a c h , which bases th e forecast on the p a st behavior o f th e exchange rate. T his was, in fact, a new m ethodology in econom ics, as only the fu n d am en talist a p p ro a c h had been applied before. N evertheless th eir th eo retical w ork provides only little assistance for practical forecasts therefo re in som e sense this w ork m ay n arro w the gap between th eo ry an d applied forecasting literature.
2. TRADING INFORMATION ON THE FOREIGN EXCHANGE MARKET
Som e econom ists say th a t exchange rates are driven by psychological facto rs and o th e r m ark e t dynam ics, ra th e r th a n by econom ic fu ndam entals. As surveys o f p artic ip a n ts in the foreign exchange m a rk e t show , there is a large g ro u p o f currency trad e rs who base th eir decisions regarding long and sh o rt positions no t on fundam entals or theoretical econom ic relationships bu t on technical tra d in g rules (for recent surveys e.g. C h eun g an d C hinn 2001, C heu n g and W ong 2000). These m ark e t p artic ip a n ts are try in g to chase trends and feel th at by observing past price changes, enough inform ation can be collected to predict fu tu re price m ovem ents. T his m ean s n o th in g m o re th a n th a t they believe th a t p attern s can be fo u n d in p ast exchange ra te b eh av io r th a t are likely to recur. It is no surprise th a t currency trad ers tu rn aw ay from fu n d am en tal analysis an d em brace technical analysis. One reason is th a t trad itio n al (fundam ental) approaches were often out-perform ed in forecasting fu tu re exchange ra te fluctuations. T h ere is m u ch evidence in
the lite ratu re th a t sim ple technical trad in g rules are p ro fitab le (cf. Swe eney 1986, T ay lo r 1992, Neely et al. 1996, L eB aron 1999, Schulm eister 2001). H ow ever, there is m ore in favor o f the technical ap p ro ach . Ex change ra te theories which assum e th a t m ark e t p artic ip a n ts form ratio nal expectations based on com plete in fo rm atio n , struggled in explaining which re lev an t eco n o m ic fu n d a m e n tals could have p ro m p te d a c tu a l exchange ra te m ov em ents. T herefore, econom ic theory was o n the defensive and was in som e sense forced to consider alternativ e ap pro aches. A lso, as the sh are o f cu rren cy tra d e rs basing th eir ex p e ctatio n s an d decisions on “ n o n -fu n d a m e n ta l” in fo rm atio n rapidly grew, tra d itio n a l exchange rate lite ratu re was increasingly occupied with this topic. F ran k e l and F ro o t (1990) have carried o u t pioneering w ork in the field o f investigating the in te ra c tio n s o f c h a rtists and fu n d a m e n talists on th e fo reig n exchange m a rk e t and the consequential im pact on exchange rate behavior. M ore recent w ork has been carried o u t by M en k h o ff (1998) w ho investigated the im p act o f th e existence o f noise trad e rs o n th e foreign exchange m a rk e t and the consequences fo r fundam en tal ap p ro ach es o f exchange ra te d eterm in atio n .
3. TECHNICAL SOURCES OF INFORMATION ON FUTURE EXCHANGE RATE MOVEMENTS
M eth o d s and techniques for gaining ex tra p ro fits have been k now n o f for a long tim e. Especially for the prediction o f stock prices, num erous “ technical” techniques and trad in g rules have been developed (e.g. K ing 1932 and R oos 1955). M o st studies on the profitab ility o f technical trad in g focus on m oving average rules. O ne reason for this focus is the fact th at m oving average rules are easy to express algebraically, w hereas, foreign exchange m a rk e t particip an ts use various o th e r techniques like b a r charts, gaps, islands, key reversals (which define price objectives an d form gaps an d p a tte rn s on b a r charts), candle charts and cand le p a tte rn s, p o in t and figure c h a rts (construction, scale, box reversal, objective co u n tin g ) graphical m eth o d s (head and shoulders, flags, triangles, diam onds, b ro ad ening patterns, p en n a n ts an d wedges etc.), and m om en tum in d icato rs an d oscillators (rate o f change, stochastics, m oving average convergence divergence, parabolics, etc.). E ven th o u g h a variety o f technical rules are evident in this pap er, in m ost o f the literature on the interrelation between fundam entals and technical rules m oving average rules are em ployed. T h e m o ving average is mt(n) defined as
W / ч l nV c m Án) = - L s t - i
n 1 = 1
where S, is th e nom inal exchange ra te and n is the length o f th e m oving average. Sim ple (b u t com m only applied) technical trad in g rules consider the signal Ф( n lt n 2) to be defined by Ф(п1, п 2) = »ir( n i) — m t( n 2), w hereas < n2 an d nj and n 2 are the sh o rt and long m oving averages. H ow ever, if Ф (п1, n2) exceeds zero, the short-term m oving average exceeds th e long-term m oving average to a certain extent. A s a consequence, a signal fo r buying is o b ta in e d . In case th a t 0 ( n t , n2) is negative, a signal fo r selling is generated. In this p ap e r several such m oving average rules are observable and are th u s in tegrated in the d a ta m ining search space. D ep en d in g on the frequency considered (daily, weekly an d m on th ly ) different m ov in g average rules are constructed ranging from [1, 20], [1, 25], [1, 30] to [1, 100] and [2, 20], [2, 25] and so on, to [10, 100] and beyond. T h e First n u m b er o f such p airs d eno tes the s h o rt period and the second n u m b er d en o tes the long periods.
4. FUNDAMENTAL SOURCES OF INFLUENCE ON FUTURE EXCHANGE RATE MOVEMENTS
Even th o u g h technical trad in g rules are p o p u lar, the effectiveness o f such rules is th e subject o f d ebate in the literature. A s m en tio n ed before, there exists lite ratu re which stresses the pro fitab ility o f technical treading rules. N evertheless, som e econom ists are skeptical ab o u t the pro fitab ility o f technical trad in g rules (e.g. M alkiel 1990). O ne reason fo r this skeptical p o in t o f view is th e view th a t the price o f m oney m ust som ehow be related to fun d am en tals. T h ere are num erous fun d am en tals th a t are w o rth being considered, b u t these m ay actually rath er problem atically conceal w hatever inform ation they m ay contain on exchange rate behavior. O ther th an technical sources o f influence, all o th er variables are labeled as fu ndam entals. T his definition is com prised o f a m onthly frequency tra d itio n a l series such as industrial production (final products, m aterials and m ore), capacity utilization ra te (different sectors), p urchasing m anagers indices, perso nal incom e (with spreads etc.), em ploym ent (unem ploym ent, civilian la b o r force, etc.), average weekly h o u rs o f p ro d u c tio n (different sectors), real retail, m an u fa ctu rin g and tra d e (n o n -d u rab le goods, d u rab le goods, m erc h an t w holesalers, etc.), c o n su m p tio n , h ousing starts and sales (non -farm , p rivate h o u sin g un its etc.), real inventories and inventory-sales ratios, orders and unfilled orders (various sectors), m oney and credit quantity aggregates (M l, М 2, М 3, M 4, com m ercial
and in d u strial loans outstanding, etc.), price indexes (com m odity price index, p ro d u c er price index, consum er price index, etc.), average hourly earnings (different sectors), interest rates (with spreads) and especially on higher frequencies, for exam ple financial m ark e t d a ta (exchange rates, bon ds, stock prices, sector indexes, etc.).
5. ON THE USE OF FINANCIAL MARKET DATA
A s well as “ tra d itio n a l” fundam entals and technical in dicators, finan cial m a rk e t d a ta has been added to the search space. T h e categorization o f financial m a rk e t series sum m arizes a b u lk o f d a ta such as stock m a rk e t indices (sector indices, country indices), bon ds (governm ent bonds and c o rp o ra te bonds) as well as swaps, forw ard and fu tu re rates (on them ). T h u s, th ere is a pool o f series on financial assets, and asset prices and derivatives respectively. H ow ever, the reason fo r the con sid eratio n o f such d a ta in the d a ta m ining search space is tw ofold. F irstly, there is a sim ple reason for the availability o f o th er fu nd am en tal series, such as series fo r econom ic grow th and inflation. F in an cial m a rk e t d a ta can be used to proxy fu ndam ental influences. T he second, and p ro b ab ly m ore im p o rta n t, reason for the presence o f financial m a rk e t series in the fore cast m odels is th a t financial m a rk e t d a ta reflects in tern a tio n al flows o f capital, which in tu rn can influence exchange rates. F ro m a theoretical p o in t o f view the causality between, fo r exam ple, stock prices and ex change rates is in tw o directions. T his m eans th a t a change in exchange rates m ay change stock prices as variations in exchange rates alter com pan ies’ p ro fits and this in tu rn affects stock prices. M o re interesting for the p u rp o se o f this p ap e r is the o th er direction, which m ean s th a t an increase in dom estic stock prices creates an increase in dom estic wealth and will therefo re lead to an increase in the d em and fo r m oney, so th at interest rates will also increase. T hus, higher interest rates are likely to cause capital inflows th a t result in an ap p reciatio n o f the dom estic c u r rency! It has to be stressed th a t the use o f financial m a rk e t d a ta is obvio us, as currency trad e rs also base th eir ex pectations o f th e future beh av io r o f exchange rates an d th u s their decisions o n such financial m a rk e t d ata. In this sense, such series could also be labeled as fu n d am en tals. In ad d itio n to this argum ent there is a m o re sim ple reason why currency trad e rs base their actions on such fu nd am entals, nam ely because besides c h a rt analysis th ere is n o th in g else left to consider on higher frequencies. T h e argum ents regarding the ad vantages o f using financial m a rk e t d a ta to co n stru ct forecast m odels on high frequencies are th erefo
re qu ite stro ng. T h u s, the fun dam en tal influences o n exchange ra te fluc tu atio n s in the short-term can certainly be sought in the sphere o f the financial w orld.
6. THE DATA MINING APPROACH
D a ta m ining is applied for the purpose o f finding an optim al m ix tu re of fu n d am en tals an d technical indicators, and th u s fo r finding optim al forecast m odels. T h e tw o m eth o d s used in the d a ta m in in g a p p ro a c h are A N N and G A . D e p en d in g on the frequency, the search space o f fun d am en tals and technical indicators consists o f some thousand variables to be examined, taking also into co n sid eratio n various form s o f d a ta tra n sfo rm a tio n s and lags. T he use o f A N N and G A in the field o f finance now h as a tra d itio n o f m any years behind it an d these m eth o d s recently spilled over in to the field o f econom ics. T h e specific com bination and co o rd in a tio n o f A N N and G A in this w ork is unique. In this paper a G A is applied as a to o l for m odel selection. T his m eans th a t the A N N is provided by in fo rm atio n w hich has been sorted o u t by a G A (in a previous step). G A are pow erful instrum ents for finding solutions for optim ization problem s in p o o rly u n d ersto o d large spaces and can be quite effective in solving large-scale com binatorial optim iza tion problem s (like the problem o f finding a w ell-perform ing m ixtu re o f fu n d a m e n tal and technical sources o f influences on exchange rates). It is therefore no surprise th a t G A have become m ore and m ore p o p u la r n o t only in applied fo recasting literature, b u t (e.g. A rifovic 2001) also regarding the theoretical issues on exchange rates. F o r exchange ra te forecasting the utiliza tion o f G A is m anifold (e.g. Allen and K aijalainen 1999) on the application o f G A to find technical forecasting rules). However, the G A m aintains a so-called population o f solution candidates for the given problem . Elem ents are selected o u t o f this p o p u la tio n random ly and are allow ed to reprod uce. In the G A literature, the term reproduction is frequently heard, although it m eans nothing m o re th a n a co m b in atio n o f som e aspects o f tw o p a re n t solutions.
F o r this p ap e r this m eans th a t fundam entals and technical in fo rm ation (aspects) o f forecast m odels (solutions) are com bined. T h e criteria fo r the allow ance o f re p ro d u ctio n are called fitness, bu t this is n o th in g m o re th an a fu n ctio n o f th e cost o f the solution it represents. In this w ork th e fitness is m easured by the R 2 and by the hi trate (direction o f change) in out-of-sample evaluations. F itn ess is crucial because elem ents w hich do n o t m eet a specific fitness level die. T his m eans they are tak en from the p o p u latio n an d replaced by offspring th a t are m o re successful. T his m ean s n o th in g m o re th an th a t forecast m odels th a t are m o re successful th a n o thers are replacing less
successful forecast m odels. As can be seen, th is basic idea is very simple and appealing for the large search space (universe o f possibly influencing variables on future exchange rate fluctuations) focused on in this work. N evertheless, for specific tasks, such as finding op tim al co m b in atio n s o f inp ut-tim e series (fundam entals, technical trad in g rules and financial m ark et series) in this p ap er, the application o f a G A has som e ad vantages in com parison to o th er optim ization tools such as for exam ple the hill clim bing m ethods (e.g. M ichalewicz 1996 for a m ore detailed discussion on hill climbing m eth o d s and G A ). Experience has show n th a t th e use o f v ario u s form s of G A beat o th er optim ization techniques by far for finding w ell-perform ing forecast m odels, when considering aspects o f calcu lation tim e. T h e use o f new technologies such as G A and A N N in a sophisticated d a ta m ining ap p ro ach possibly allows the detection o f tem p o rary inefficiencies, which firstly econom ists can no t observe o r describe and secondly, are seen earlier th an o th e r m a rk e t p articipants. T his is a fu nd am en tal ad v an tag e o f the a p p ro a c h presented in this paper, and in general for d a ta m ining. One d isad v an tag e o f such d a ta m ining is th a t it is h ard to distin gu ish between “ re al” relationsh ips and spurious causality in (lim ited) results, so th a t the risk is quite high to be blinded by the goodness o f th e achieved results. H ow ever, in general fo r the p u rp o se o f forecasting it is n o t necessarily im p o rta n t to distinguish betw een “ re al” causalities an d spu rio u s causalities if (and only if) forecast perform ance over tim e does n o t suffer, which m eans th a t seemingly spurious causalities are stable and provide well- p erfo rm ing forecast results. As will be show n in the discussion on the results, the ap p earan ce o f variables in th e forecast m odels are som etim es h ard to describe (from a theoretical perspective) b u t are p ro du cin g well- perform ing forecasts. This m eans th a t those “m achine driven fo u n d ” variables are p redicting exchange rates w ith a considerably good p erfo rm an ce rate, b u t are no t explaining exchange rates in the sense th a t they are delivering causal re latio n sh ip s such as relationships from econom ic theory . M oreover, the ex p lan a to ry variables in the forecast m odels a p p e a r to be case specific and tim e d epend ent.
7. RESULTS
T h e success o f the applied ap p ro ach is evaluated in ou t-of-sam p le tests. O n a m o n th ly frequency, a period o f (the last) 30 m o n th s w as chosen to m easure the perform ance, o n a weekly frequency (the last) 60 weeks and on a daily frequency (the last) 100 days. As m en tio n ed , the results are o u t-of-sam ple forecasts and for every tim e step f, th e weights o f the A N N
are train ed to new inform ation available a t tim e t — 1! T o describe the d a ta used in this w ork it can be sum m arized th a t th e en tire d a ta set covers 128 periods (02.28.1991 - 09.28.2001) o n a m o n th ly frequency, 274 periods (08.02.1996 - 10.26.2001) on a weekly frequency an d 860 periods (07.15.1998 - 10.30.2001) on a daily frequency. T h e success o f the applied d a ta m ining ap p ro ach in constructing forecast m odels is m ixed (see the A ppendix 1 for details on the em pirical results an d A ppendix 2 fo r the variables included by the d a ta m ining ap p ro ach ). O ne m a in ch aracteristic o f the applied ap p ro ach is th a t technical ind icato rs were n o t selected (included in forecast m odels), i.e. are seen as n o t info rm ativ e fo r future exchange ra te beh av io r (even a t higher frequencies). A t a m o n th ly freq u ency success is m o st prom ising, as for m o st exchange rates relatively stable perfo rm ances can be stated and as the inpu ts (exp lan ato ry v ariab les) selected by d a ta m ining are reasonable (in p a rtic u la r cf. T ab le 1 and 4). A t the weekly and daily frequency (in p artic u la r cf. T a b le 2, 3 and 4) the applied d a ta m ining ap p ro ach som etim es resulted in a loose co m b in atio n o f in p u t tim e series to explain fu tu re exchange rates (cf. A p pen dix 2). T h e conccrn for the latter frequencies is th a t m o st o f th e forecast m odels fo u n d by d a ta m ining m ay be ill-fitted a n d /o r th e result o f d a ta snooping. M oreover, the com position o f the d a ta m inin g forecast m odels at a daily and weekly frequency allows alm ost n o p ro fo u n d statem ents a b o u t fou nd econom ic structu res, dependencies and relation ships to be m ade! T h e selection o f in p u t variables app ears to be ch ao tic as series frequently are included which are from outside th e underlying bilateral exchange ra te (currency) relation. In c o n tra st to the forecast m odels at a daily and weekly frequency, a t the m o n th ly frequency a co m m on stru c tu re is observable w hich is to say th a t nearly all m odels selected by d a ta m ining include variables to explain relative econom ic grow th. Leading in dicato rs in p artic u la r, such as new ca r sales and registratio n s, housing starts and m o re have been chosen by d a ta m inin g in m od eling the grow th differential to explain fu tu re exchange ra te fluctuatio n.
8. CONCLUSIONS
In this p aper an attem p t was m ad e to find exchange rate forecast m odels o n different frequencies o n the basis o f a bro ad an d large d a ta base (search space) which included fundam entals, technical indicators an d financial m arket series. T h erefo re a d a ta m ining ap p ro ach which is based on a G A for m odel selection a n d an A N N for the gen eration o f forecasts was applied, w hereas d a ta m ining included no technical ind icato rs in fo recast m odels.
This is surprising, as on higher frequencies (daily and weekly) foreign exchange m a rk e t p artic ip a n ts base their trad in g decision on such technical indicators. O n the o th e r hand, on higher frequencies financial m ark e t d a ta has been included and proved to be effective in ou t-of-sam ple evaluations. On a low forecasting frequency (m onthly), m ore m acroeconom ic d a ta was available for the co n stru c tio n o f forecast m odels and d a ta m ining resulted in the inclusion o f various m acroeconom ic variables, especially reg ard in g leading indicato rs which are associated with relative econom ic grow th. All this suggests, th a t fu ndam entals can be inform ative for fu tu re exchange rate m ovem ents also o n higher frequencies. N evertheless, from a strict theoretical perspective d a ta m ining results m ay be judged as a loose co m b in atio n o f ex p lan ato ry variables. T his result is not surprising as the criteria for d a ta m ining are exclusively statistical and no t theoretical plausibility. T his leads to the conclusion th a t exchange rates m ay be predictable using d a ta m ining techniques but their m ovem ents are hard to describe and explain by econom ic theory.
APPENDIX 1: Forecasting Results (Perform ance)
Table 1. Forecasting results on a monthly frequency
Monthly Frequency Euro/US dollar
Pound/US dollar
Yen/US
dollar Euro/Pound Euro/Yen Correlation (Target, Forecast)
Stdev (Target) Stdev ( f orecast) Stdev (Residual) R2 Hi trate 0.3880 0.0305 0.0106 0.0281 0.1505 60% 0.2714 0.0200 0.0098 0.0197 0.0737 60% 0.3588 0.0339 0.0157 0.0319 0.1287 67% 0.3552 0.0232 0.0098 0.0217 0.1262 67% 0.3946 0.0406 0.0128 0.0374 0.1557 63%
Table 2. Forecasting results on a weekly frequency
Weekly Frequency Euro/US dollar
Pound/US dollar
Yen/US
dollar Euro/Pound Euro/Yen Correlation (Target, Forecast)
Stdev (Target) Stdev (Forecast) Stdev (Residual) R2 Hitrate 0.4863 0.0170 0.0077 0.0148 0.2365 73% 0.3086 0.0138 0.0043 0.0131 0.0952 72% 0.4406 0.0132 0.0096 0.0124 0.1941 70% 0.3250 0.0120 0.0041 0.0114 0.1057 75% 0.3581 0.0191 0.0085 0.0179 0.1282 72%
Table 3. Forecasting results on a daily frequency
Daily Frequency Euro/US dollar
Pound/US dollar
Yen/US
dollar Euro/Pound Euro/Yen Correlation (Target, Forecast)
Stdcv (Target) Stdev (Forecast) Stdev (Residual) R 2 Hitrate 0.0259 0.0067 0.0017 0.0069 0.0007 54% 0.0943 0.0050 0.0012 0.0050 0.0089 58% 0.0500 0.0062 0.0019 0.0064 0.0025 55% -0.0611 0.0055 0.0006 0.0056 0.0037 60% 0.1221 0.0063 0.0024 0.0065 0.0149 52%
Table 4. Forecast errors of the data mining models
Evaluation Period Exchange rate ME MAE MSE MPE MAPE
30 months Euro/US dollar -0.0036 0.0199 0.0007 -0.4070 2.1408 30 months Pound/US dollar -0.0045 0.0248 0.0009 -0.2932 1.6376 30 months Y en/US dollar 0.1067 2.8760 13.0058 0.0516 2.5127
30 months Euro/Pound -0.0030 0.0103 0.0002 -0.4913 1.6649
30 months Euro/Yen -0.3497 2.9167 14.8819 -0.3991 2.7826
60 weeks Euro/US dollar 0.0014 0.0098 0.0002 0.1527 1.0977
60 weeks Pound/US dollar -0.1X108 0.0139 0.0003 -0.0613 0.9654
60 weeks Yen/US dollar 0.1832 1.1985 2.1612 0.1581 1.0118
60 weeks Euro/Pound 0.0007 0.0052 0.0000 0.1113 0.8396
60 weeks Euro/Yen 0.2417 1.4840 3.4281 0.2212 1.4182
100 days Euro/US dollar 0.0016 0.0047 0.0000 0.1729 0.5273
100 days Pound/US dollar 0.0007 0.0054 0.0001 0.0463 0.3722
100 days Yen/US dollar -0.0037 0.5843 0.5952 -0.0051 0.4808
100 days Euro/Pound 0.0000 0.0028 0.0000 -0.0023 0.4483
100 days Euro/Yen 0.1035 0.5697 0.4910 0.0944 0.5274
Note: mean error (ME) = ' — , mean absolute error (MAE) = —■1-1
n n
a, - f;
I- 1 4
, mean
100
squared error (MSE) = --- , mean percentage error (MPE) = --- , mean
n n
100
absolute percentage error (MAPE) = --- -— --- , with F denoting forecasts and A de-n
APPENDIX 2: Description o f the F orecast M odels
F o recast m odels on a m o nthly frequency:
EURl+ t - ( ( Д £ 1 / / Р ,_ а - Д 1 Ш Р ,_ а), AEU1P,_2, A U SN C A R ,_3, ADEGDP,_2)
OBPl + l = ((ALIGBP3MD, - ALIGBPl YD,), (A U S3M T ,— M JS30YT,), AS PC,, AFTSE,, (,A U SC PI,_t -A G B C P I
= ((AUSNCARt_ , — AJPNCARi_ ,), A U 5 M 1 ,.,, AFGBLc 1„ Д7Тс1„ Д5Рс1„ А /Р /Р , 2, ДU SN C A R ,_2, A JPY
EURGBP - ( (ADEGDP<-‘ iüBGDP, J - № G D P ,_ t -AUSGDP,_t ), (AD EHST ART, ^ - AG BUST AR T „
1+1 \(A E U IP ,_ 3 -A U S IP ,_ 3), AUSNCAR,_3, ADENCAR,_2 E U R JP Y ,+ l = (A JP IP ,_5, A U SN C A R ,_s, ADECP1,_2, A F D X e l,_ t )
F o recast m odels on a weekly frequency:
£ { /л = ALIGBP3MD,, ALIGBPl YDt_ v A J P Y ,.2, \ 1+1 \A E U R J P Y ,_ 2, AUSD12XI»F„ A JPY IM Z,, A U S JO B C ,_J
GBP, + J = (AFTSE,_4, AUSD7X10F,, AGBP9X12F,, A JP1YT,_9, ДСВ30У7',_„ A JPY 10Y Z ,_3)
JPY, + i = (AN225,, ASPC„ AGDAXI,, ALIGBPIMD,, A G B30YT,_3, AG B3M T,^3)
EURGBP, + i = (AU SJOBC,_2, AUSD 1X\0F„ AUSD3X9F,, AJPY, 6, AS PC,, GREXIO. ,, EU RG BP,_%)
E U R J P Y l + l = (A JP 2 0 Y T p AJPY9YZ,, AUS30YT,_s, HFLGc\t_ y A J P Y IM Z ,.,, GBP6X\2F,_9, DJI,)
F o rec ast m odels on a daily frequency:
1 = (AFTSE,_3, AGREX 5„ AGREX10,, ADJI,, ALIU SD \M D „ AS PC,, L IJ P Y \M D ,_ 3, FDBcl,, ASPc 1„ A JN Icl,)
GBP, + i ~ (AFDBcl,, AUSc\„ ASPcl,, A T Y cl,, AJN Icl,, LIU SD IYD ,_3, GREX 1(1 „ GB2M T,_3)
( A FG B M cl„ A JN Icl,, ASPC,, A FD X ci„ AGDAXI,, AG R EX5,, N225,,) E U R JPY,, AAORD,, A EU 1 YT„ AEU30YT,, A T Y clS,, FGBLcl, )
v , , n, , n„ (AEURJPY,, AJPY,, AGREX 1„ ASTOXXSOE,, AGB10YT,, AGBIMT,, US10YT,, JP 1 YT,'
Ł U R ü t i r . = I
\FDXc 1„ AJNIcl,, AFDBcl,, AUSIQYT,, AGBIMT,, AJP1MT,, US30YT,
Abbreviation Variable name Abbreviation Variable name
A O R D Australia all orders index J P 3 M T Japan 3 month government bond
D E C P I Germany consumer price index J P IP Japan industrial production
D E G D P Germany gross domestic product
J P N C A R Japan car sales
D E H S T A R T Germany housing starts J P Y X 0 Y Z Japan 10 year zerobond
D E N C A R Germany car sales J P Y I M Z Japan 1 month zerobond
DJ1 D ow Jones industrial index J P Y 9 Y Z Japan 9 year zerobond
E U ] Y T European Union 1 year go vernment bond
L 1 G B P IM D Great Britain LIBOR 1 month
E U 3 0 Y T European Union 30 year go vernment bond
L IG B P l YD Great Britain LIBOR 1 year
E U 1 P European Union industrial production
U G B P 3 M D Great Britain LIBOR 3 month
FDBcX L1FFE gilt future U U S D X M D United States LIBOR 1 month
F D X c1 German D A X future L IU S D IY D United States LIBOR 1 Year
F G B L c1 Bund future N225 Nikkei 225 index
F G B M c l Great Britain bond future R T X Russian traded index
F L G c \ LIFFE long gilt future SPC Standard and Poor’s 500 index
FRcX French Franc/US dollar future SPc1 Standard and Poor’s future
F T S E FTSE index SSM1 Swiss market index
G B 1 0 Y T Great Britain 10 year govern ment bond
S T O X X 5Q E Eurostoxx 50 index
G B X M T Great Britain 1 month govern ment Bond
T Y c1 United States T-note future
G B 3 0 Y T Great Britain 30 year govern ment bond
U S W Y T United States 10 year govern ment bond
G B 3 M T Great Britain 3 month govern ment bond
U S 3 0 Y T United States 30 year govern ment bond
G BCP1 Great Britain consumer price index
U S 3 M T United States 3 month govern ment bond
G BG D P Great Britain gross domestic product
USc1 United States bond future
G B H S T A R T Great Britain housing starts U S C P I United States consumer price index
G B P 6 X 1 2 F Great Britain 6M-12M swap U S D \2 X \S F United States 12M-18M swap
G B P 9 X1 I F Great Britain 9M-12M swap U S D IX 1 0 F United States 1M-10M swap
G D A X I German D AX U S D 3 X 9 F United States 3M-9M swap
G R E X l German rent index 1 year U S D IX IO F United States 7M-10M swap
G R E X10 German rent index 10 year U SG D P United States gross domestic product
G R E X5 German rent index 5 year U S IP United States industrial pro duction
I X I С Nasdaq composite index U S JO B C United States jobless claims
J N I c1 Japan Nikkei 225 index future US M l United States money supply (M l)
J P \ Y T J P 2 0 Y T
Japan 1 year government bond Japan 20 year government bond
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B e r n d B r a n d i
MOŻLIWOŚCI MODELOWANIA I PROGNOZOWANIA KURSÓW WALUTOWYCH: WSKAŹNIKI WYPRZEDZAJĄCE I ANALIZA TECHNICZNA
(Streszczenie)
W artykule przedstawiono proces eksploracji danych statystycznych w prognozowaniu kursów walutowych. Zakładamy, że kursy walutowe pozostają pod wpływem zarówno czyn ników o charakterze fundamentalnym, jak i czynników pozaekonomicznych. Równowaga pomiędzy tymi czynnikami różni się w zależności od rodzaju kursu walutowego i częstotliwości jego pomiaru.
Prognostykom trudno jest ustalić względną siłę wpływu różnych czynników, stąd analiza polegająca na eksploracji danych ma określone zalety. W proponowanym podejściu wykorzystano algorytmy genetyczne i sztuczne sieci neuronowe. Przedstawiliśmy wyniki eksperymentów prognostycznych poza próbą statystyczną w odniesieniu do pięciu kursów walutowych, obserwowanych z różną częstotliwością. Pokazaliśmy, że metoda eksploracji danych może stanowić skuteczne narzędzie prognostyczne.
