1 Order Flow Analysisand Exchange Rate ForecastingComparison of Neural Networksand Linear Regression
Master Thesis Presentation
Professor Moisa Altar PhD Student Furtuna Dumitru Bucharest June 8 2007 2 TABLE OF CONTENT
3 We Forecast the Daily Exchange Rate and Find That the Micro Model Outperforms Other Models Abstract Abstract and Brief Presentation of the Structure of the Paper What How Why Results Conclusions Introduction Literature review Forecasting models Empirical analysis
This paper tries to forecast daily exchange rate changes by comparing the true ex-ante forecasting performance of several models.
We employ the following models
A micro-based model
A standard macro model
A combined model
Using the following statistical techniques
artificial neural networks
Micro-based model out-performs the random walk the macro model and the combined model.
Our results support the central idea of the micro-based literature
order flow is the mechanism by which private information becomes embedded in exchange rates
4 TABLE OF CONTENT
5 The Paper Evaluates the Practical Value of Order Flow Data in Terms of Their Relationship to Exchange Rate Introduction Introduction
Conventional models of exchange rate determination state that the exchange rate is determined by fundamental variables such as money supplies outputs and interest rates. However when analysing these models the conclusion1) is that the results do not point to any given model/specification combination as being very successful. On the other hand it may be that one model will do well for one exchange rate but not for another.
The recent literature on foreign exchange market microstructure reflects an attempt to understand the mechanisms generating exchange rate deviations from macroeconomic fundamentals.
This paper tries to find out whether order flow has true ex-ante forecasting power allowing for the direction of Granger-causality and the accuracy of derived out-of-sample exchange rate forecasts using (a) OLS2) and (b) ANN3) as statistical techniques.
Note (1) Cheung Chinn and Pascual (2002) (2) Ordinary Least Squares (3) Artificial Neural Networks 6 TABLE OF CONTENT
7 Order Flow Provides the Link Between Fundamentals and Exchange Rates by an Information Aggregation Process Literature Review Literature Review
Martin Evans and Richard Lyons1) were among the first to formulate the micro aspects of exchange rates as well as to analyse the forecasting power of order flow
Evans and Lyons (2005) compare the true ex-ante forecasting performance of a micro-based model against a standard macro model and a random walk using customer order flow (1993 1999) showing that order flow from US corporations and US long-term investors has predictive content with respect to future exchange rate movements over horizons from one day up to one month.
Another strand of the microstructure literature considers the explanatory power of informed versus uninformed order flow for exchange rate returns2).
There is also a strand of the market microstructure literature which addresses the issue of whether the strength of the relationship between order flow and exchange rates is dependent upon prevailing market conditions.
The central hypothesis of micro based literature is that order flow allows the wider market to learn about the private information and trading strategies of better informed participants Note (1) Evand and Lyons (2002) Evand and Lyons (2004) Evand and Lyons (2005) (2) Bjønnes Rime and Solheim (2005) (3) Froot and Ramadorai (2002) 8 TABLE OF CONTENT
Forecasting exchange rates
9 Why are Future Changes in Exchange Rates so Hard to Predict Forecasting Models Forecasting Exchange Rates
If we start with the present value expression for the spot rateand iterate forward we get where
With these results it can be shown that exchange rates will follow a process arbitrarily close to a random walk if (a) at least one forcing variable observable fundamental or unobservable shock has a unit autoregressive root (b) the discount factor is near unity
Engel and West1) point out that we view as unexceptionable the assumption that a forcing variable has a unit root while also showing that in some exchange rate models the discount factor is near unity.
The new micro-based literature reoriented the thinking if there is little room for forecasting based on because is close to unity and changes in fundamentals are not very predictable then the focus was shifted on where all the action is namely exchange rate dynamics that come from expectational surprises.
Note (1) Engel and West (2005) 10 Macro Model is Based on UIP Equation in Order to Avoid the Usage of the Discount Factor Forecasting Models Macro Model
If the risk-neutral efficient markets hypothesis holds then the expected foreign exchange gain from holding one currency rather than another the expected exchange rate change must be just offset by the opportunity cost of holding funds in this currency rather than the other the interest rate differential
Rejecting the risk-neutral efficient markets assumptions distorts the uncovered interest parity as agents demand a higher rate of return than the interest differential in return for the risk of holding foreign currency risk premium
We consider macro forecasts based on the assumption thatmeaning that deviations in UIP are perfectly correlated with the interest differential.
11 Microstructure Literature is Concerned With the Details and Importance of the Mechanics of Foreign Exchange Trading Forecasting models Forecasting Power of Micro-Based Models Rests on Two Features Micro based models Feature I Feature II Fundamentals based models
Delay between the time information first generates transaction flows and the time this fact is widely recognized by marketmakers
It takes time for the implications of aggregate order flow to be recognized across all marketmakers and hence reflected in spot prices.
Transactions flows contain information relevant for fundamentals
Agents initiating trades have information they believe they can take advantage of.
Agents are trading for allocative reasons and the aggregate of those trades correlates with the current state of the macroeconomy.
12 Micro-Based Models Assume that Marketmakers Obtain Information about Fundamentals from the Order Flow Forecasting Models Micro Model
Exchange rate dynamics in the micro-based model also focus on the present value relation
Under the assumptions that
aggregate order flow during period follows an AR(1) process
changes in fundamentals also follow an auto-regressive process but innovations in fundamentals growth include a common-knowledge component and a component correlated with the innovation in aggregate order flow
It can be shown1) that
This equation shows that lagged order flows can have forecasting power for spot rates even as the discount factor approaches unity
Note (1) Evans and Lyons (2005) 13 TABLE OF CONTENT
14 Data Span a Period of One Year and One Month Empirical Methodology Data
In the empirical analysis we utilize a data set that comprises daily values of end-user transaction flows F/X rates and EURIBOR and BUBID interest rates over one year and one month starting from December 5 2005 till December 29 2006.
Data were obtained from
NBR order flow1)2) RON/EUR exchange rate and BUBID interest rate.
EURIBOR FBE EURIBOR.
Two points deserve further notice
The transaction flow data used here is of a fundamentally different type than in other papers that analyse this kind of data as it is the aggregated national transaction flow.
Due to data unavailability EURIBOR rates were used as an approximation of EURIBID rates under the plausible assumption that the Euro zone financial market is a mature and competitive one and thus EURIBOR EURIBID spread is almost constant and/or changes slowly.
Note (1) Order flow is defined as transaction volume signed according to the initiator of the trade positive for a buy order negative for a sell order (2) We were unsuccessful in our attempt to obtain more data/information regarding this indicator from NBR due to confidentiality reasons 15 We Used a Single-Layer Feedforward Network With one Hidden Layer and Two Neurons Empirical Methodology Artificial Neural Networks Architecture Additional Inputs
We employ this simple architecture1) (a) to provide a simple neural network alternative (b) As a result of the short data span
We had as additional inputs two indicators3)
one for the inertia
one for the driving force.
The chosen transfer function tan-sigmoid chosen learning rule Levenberg-Marquardt
Scaling procedure DeLeo transformation2).
Note (1) For comparative purposes we note that Gradojevic and Yang (2000) employ three-layer and four-layer backpropagation ANNs. (2) McNealis (2005). (3) Zimmermann and Neuneier (2000) 16 We use Projection Statistics MSER Modified Diebold Mariano and Success Ratio Statistics to Compare Models Empirical Methodology Forecasts Comparison
We perform Granger-causality test to examine whether order flow tends systematically to precede exchange rate movements or follow them.
We can compare forecasting performance of a model against the random walk benchmark simply by testing for the significance of the coefficient in the equation
Also estimates the contribution of the model forecasts to the variance of spot rate changes over the forecasting period since
The projection statistics1)
For comparison purposes we report MSER statistics.
For assess the statistical significance of the improvement in forecast accuracy we calculate the MDM2) statistics .
MSER statistics with MDM2) test
We employ this statistics in order to test the sign of the future exchange rate returns predictions rather than the exact value.
Directional Accuracy test3) Note (1) Evans and Lyons (2005) (2) Modified Diebold Mariano test Harvey Leybourne and Newbold (1997) (3) Pesaranand Timmermann (1992) 17 We Calculated The Interest Rate Differential on a Daily Basis and Adjusted Coefficients of OLS models Empirical Methodology Model Estimation
Estimation Note (1) Svensson (1994) (2) We correct for AR(1) and AR(2) case of residuals autocorrelation following Greene (2003) procedure 18 TABLE OF CONTENT
19 Correlation Test Shows that there is a Relationship Between Order Flow and Future Exchange Rate Returns Results For a first test we compute the correlation coefficients Correlation coefficient Days The results look assuring as there is a significant negative relationship (-025) between historical order flow cumulated for ten trading days and exchange rate returns over ten future days 20 There is Strong Evidence of Simultaneous Causality Between Daily Exchange Rate Returns and Order Flow Results Granger-Causality One-day exchange rate returns Customer order flow Granger-causality shows that we could speak about a feedback system1). These results also provide support to correlation tests. Note (1) A feedback system simply shows that the variables are related. 21 Projection Statistics Shows a Strong Support for ANN Against OLS While the Micro Model is the Favourite Results Legend 22 Projection Statistics Shows a Strong Support for ANN Against OLS While the Micro Model is the Favourite Results Projection Statistics Results Comments Comments Results
Neural networks are better at explaining variance contribution of the model forecasts to the variance of spot rate changes drops from 30 when using neural networks to 16 when using linear regressions.
The results for the micro model are comparable with the results from the combined model.
The macro model outperforms the micro model in the linear regression case while neural networks are capable of exploiting better the non-linearity from the order flow data where micro model provides better results than the macro one.
23 MSER and MDM Statistics Show Support for Micro Model Against Macro Model and for OLS Against ANN Results Legend 24 MSER and MDM Statistics Show Support for Micro Model Against Macro Model and for OLS Against ANN Results MSER and MDM Statistics Results Comments Comments Results
The micro model clearly outperforms macro and combined models. However with the exception of day 17 OLS technique (MSER 68) the MDM statistics does not indicate a significant improvement between this model and the RW model.
Linear regressions provide better forecast accuracy as specified by MSE statistics when comparing with neural networks.
The combined model estimated with ANN performs very poorly when compared with micro model.
25 MSER Statistics Favours OLS Technique Because it Contains a Smaller Number of Outliers Results OLS Outperforms ANN Technique The causes for these results are the greater number of error outliers when estimating the models with ANN 26 ANN Technique has Smaller Errors But More Outliers as Compared With Linear Regressions Results Legend 27 ANN Technique has Smaller Errors But More Outliers as Compared With Linear Regressions Results Errors Analysis Results Comments Comments Results
This fact could have the following explanations
The neural network model is inappropriate for this kind of data. We support this idea as feed-forward neural networks with more layers recurrent neural networks or dynamical consistent neural networks have proven very robust in other studies1).
A small number of observations We remind that the moving window for parameters estimation had only 127 observations.
Note (1) Gradojevic and Yang (2000) employ three-layer and four-layer backpropagation ANNs while Zimmermann et. al (2006) find significant information content in the order flow employing Dynamical Consistent Recurrent Neural Networks 28 Success Ratio Shows Support for ANN Against OLSWhile Macro Slightly Outperforms Micro Model Results Legend 29 Success Ratio Shows Support for ANN Against OLSWhile Macro Slightly Outperforms Micro Model Results Success Ratio Results Comments Comments Results
The micro model performs better than or comparable with the combined model performance.
In the case when the models were estimated with linear regressions the macro model has a larger number of statistical significant success ratios although none of it passes the 60 benchmark used in other studies1).
The macro model performs slightly better than the micro model when using neural networks.
Note (1) McNelis (2005) 30 TABLE OF CONTENT
31 Order Flow Represents the Channel Through Which Marketmakers Obtain Information About Fundamentals Conclusions Conclusions
When comparing the true ex-ante forecasting performance of a micro-based model against both a standard macro model and a random walk we find that the micro-based model consistently out-performs both micro-based forecasts account for roughly 30 percent of the variance in spot rate changes1). Thus in this paper we show support for the central hypothesis of micro literature that order flow is the mechanism by which private information becomes embedded in exchange rates.
When applying ANN to this type of data we find that ANN spot nonlinearities and thus could explain a greater portion of the F/X rate variance as shown by Projections and SR statistics outperforming OLS. Also it should be noted that at least for our architecture ANN also provided a greater number of outliers.
Exchange rate OF Marketmaker j OF Marketmaker i Note (1) These results are stronger than the ones obtained by Evans and Lyons (2005). However when taking into account that we used national aggregated order flow our results look somehow disappointingly. These might be due to the fact that Romanian order flow has a significant component which runs outside national borders and which is not included in the data used here 32 TABLE OF CONTENT
33 Selected Bibliography Bibliography
Cheung Yin-Wong Menzie D. Chinn and Antonio Garcia Pascual (2002) Empirical Exchange Rate Models of the Nineties Are Any Fit to Survive mimeo Department of Economics University of California Santa Cruz.
Engel Charles and West Kenneth (2005) Exchange Rates and Fundamentals National Bureau of Economic Research (Cambridge MA) Journal of Political Economy volume 113 pages 485517.
Evans Martin D.D. and Lyons Richard K. (2007) Exchange Rate Fundamentals and Order Flow National Bureau of Economic Research Working Paper Series Working Paper 13151.
Evans Martin D.D. and Lyons Richard K. (2005) Meese-Rogoff Redux Micro-based Exchange-Rate Forecasting American Economic Review American Economic Association vol. 95(2) May pages 405-414.
Evans Martin D.D. and Lyons Richard K. (2004) A New Micro Model of Exchange Rate Dynamics National Bureau of Economic Research Working Paper Series Working Paper 10379.
Evans Martin D.D. and Lyons Richard K. (2002) Informational Integration and FX Trading Journal of International Money and Finance 21 pages 807-831.
Harvey David Leybourne Stephen Newbold Paul (1997) Testing the equality of prediction mean squared errors International Journal of Forecasting Elsevier vol. 13(2) pages 281-291.
Kilian L. and M.P. Taylor (2003) Why is it so Difficult to Beat the Random Walk Forecast of Exchange Rates Journal of International Economics 60 85-107.
34 Selected Bibliography Bibliography
Lars E.O. Svensson (1994) Estimating and Interpreting Forward Interest Rates Sweden 1992 1994 National Bureau of Economic Research NBER Working Papers 4871.
Lyons Richard K. (2001) The Microstructure Approach to Exchange Rates MIT Press Cambridge MA.
Mark N.C. (1995) Exchange Rates and Fundamentals Evidence on Long Horizon Predictability American Economic Review 85(1) 210-218.
McNelis Paul D. (2005) Neural networks in finance gaining predictive edge in the market Elsevier Academic Press.
Meese Richard and Rogoff Kenneth (1983) Empirical Exchange Rate Models of the Seventies Journal of International Economics 14 pp. 3-24.
N. Gradojevic J. Yang (2000) The application of artificial neural networks to ex- change rate forecasting the role of the market microstructure variable Bank of Canada Working Paper 23.
Pesaran M.H. and A. Timmermann (1992) A Simple Nonparametric Test of Predictive Performance Journal of Business and Economic Statistics 10 461465.
Stambaugh R. (2000) Predictive regressions. Journal of Financial Economics 54 375-421.
William H. Greene (2003) Econometric Analysis 5th Edition Prentice-Hall.
Zimmermann H.G. Bertolini L. Grothmann R. Schäfer M.A. Tietz C. (2006) A Technical Trading Indicator Based on Dynamical Consistent Neural Networks Int. Conference on Artificial Neural Networks 2006 654-663.
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