Transcript global currency movement and generalized rule induction

GLOBAL CURRENCY MOVEMENT
AND
GENERALIZED RULE INDUCTION
A. G. Malliaris
M. E. Malliaris
Loyola University Chicago
Northeast Decision Sciences Institute, Montreal, Canada, April 13-15, 2011
MOTIVATION
• If it is possible to isolate some assets that have
consistent patterns of movement, then this
knowledge can be used in two ways:
to make money if one has moved and the
other has not moved yet, or,
to build a more diverse portfolio by not
including both in the basket.
INTRODUCTION
• Are there certain currency markets that move up
or down together sufficiently often for us to form
a conclusion about their inter-relationships?
• This paper investigates the relationships among
directional movement of eight major currencies
around the globe.
• Data over ten years was studied to see if there
are movement rules among these currencies that
might be stable over time.
ASSOCIATION ANALYSIS
• Association analysis is a popular data mining
method that originated with the study of
market baskets to see which items people
purchased at the same time.
• Association analysis generates a set of rules of
the form IF A THEN B
ASSOCIATION ANALYSIS
• The set of rules that is generated also depends
on the values of support and confidence.
• Support: percent of times that some
combination of inputs (also called
antecedents) occurs in the data set.
• Confidence: when the antecedent
combination does occur, reflects the percent
of time that the output, or consequent, is also
true.
METHODOLOGY
• Generalized Rule Induction is an association
analysis methodology that was introduced in
1992 by Smyth and Goodman
• GRI is an effective, parsimonious method for
detecting relationships in a large set of
variables
OTHER APPLICATIONS OF
ASSOCIATION ANALYSIS
• These methods continue to be popular for
approaching problems in finance, for example:
• time series databases
• stock selection
• forecasting time series
• co-movement in international stocks
DATA
• January 2000 through July 2009
• Downloaded from Bloomberg.
• These prices were split into two disjoint sets for
training and validation.
• Data from January 1 2000 to June 30 2008 was
used as the training set (2215 rows)
• July 1 2008 to July 21 2009, used as the validation
set (276 rows).
• To study the simultaneous market movements, all
data was transformed into “Up” or “Down”
THE EIGHT CURRENCIES
Original data was daily cash closing prices for
the price of 1 US Dollar in the foreign currency
that day
Australian Dollar, Japanese Yen
British Pound, Euro, Swiss Franc
Canadian Dollar, Mexican Peso, Brazilian Real
RELATIVE MOVEMENT
In order to view them all in a similar scale, the Mexican Peso has been
multiplied by 10 and the Japanese Yen by 100 for the graph.
PROBLEM SETUP
• The Generalized Rule Induction methodology was
run using the SPSS product Clementine
• There were two runs of the model
• In the first run of GRI, the Australian dollar and
Japanese Yen were used as inputs with the Euro,
the Swiss Franc and the British Pound as possible
outputs.
• Following this run, the Australian dollar, Japanese
Yen, the Euro, the Swiss Franc and the British
Pound were used as inputs, with the Mexican
Peso, the Brazilian Real and the Canadian dollar
as outputs.
RESULTS
• The GRI models generated a total of 151 rules.
• Here we show a selection of 18 of those rules
where the validation set results supported the
training set results, sorted by the market of
the consequent.
• Each rule displays the antecedent and
consequent followed by the support and
confidence in both the training and validation
data sets.
BRAZILIAN REAL
BRITISH POUND
CANADIAN DOLLAR
EURO
MEXICAN PESO
SWISS FRANC
PAIR-WISE
UP AND DOWN MOVEMENTS
• In addition to rule generation, Clementine allows
us to generate a picture of pair-wise relationships
among non-numeric data variables using a web
graph.
• Stronger relationships, that is, ones that occur
more often, have darker lines connecting them.
• This graph does not combine up and down
movement in the various markets as we can do
with GRI, but it does give us some indications of
places we might expect rules to be generated.
DOWN and UP, PAIRWISE
CONCLUSIONS
• Today, the daily volume of currency transactions
in currency futures, forwards, swaps and options
dominates all other types of trading volumes.
• Whether currencies move together or
independently is a matter of importance for
investors wishing to spread the impact of their
portfolio decisions.
• The results of this study suggest that there is
reason to believe that co-movement among
some specific markets exists over relatively long
periods of time.