Master Thesis Presentation

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

• Abstract
• Introduction
• Literature review
• Forecasting models
• Empirical methodology
• Results
• Conclusions
• Bibliography

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
• Random walk
• Using the following statistical techniques
• artificial neural networks
• OLS

• 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

• Abstract
• Introduction
• Literature review
• Forecasting models
• Empirical methodology
• Results
• Conclusions
• Bibliography

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

• Abstract
• Introduction
• Literature review
• Forecasting models
• Empirical methodology
• Results
• Conclusions
• Bibliography

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

• Abstract
• Introduction
• Literature review
• Forecasting models
• Forecasting exchange rates
• Macro model
• Micro-based model
• Empirical methodology
• Results
• Conclusions
• Bibliography

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,
• Thus,
• 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

• Abstract
• Introduction
• Literature review
• Forecasting models
• Empirical methodology
• Data
• Neural Networks
• Forecast comparisons
• Results
• Conclusions
• Bibliography

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.

ANN
Technique

• 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.

Granger-causality

• 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) Pesaran,and Timmermann (1992)
17
We Calculated The Interest Rate Differential on a
Daily Basis, and Adjusted Coefficients of OLS
models
Empirical Methodology
Model Estimation

• Macro Model

• Micro Model
• Combined Model

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

• Abstract
• Introduction
• Literature review
• Forecasting models
• Empirical methodology
• Results
• Conclusions
• Bibliography

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 (-0,25) 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
OLS,While Macro Slightly Outperforms Micro Model
Results
Legend
29
Success Ratio Shows Support for ANN Against
OLS,While 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

• Abstract
• Introduction
• Literature review
• Forecasting models
• Empirical methodology
• Results
• Conclusions
• Bibliography

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

• Abstract
• Introduction
• Literature review
• Forecasting models
• Empirical methodology
• Results
• Conclusions
• Bibliography

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.