Repetitiveness of Daily Trading
Behavior and Price Directions for
Canola Futures: A Discriminant
Analysis Approach
SANGHOON LEE
SENIOR ECONOMIST, GYEONGGI RESEARCH
INSTITUTE, KOREA
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Three Basic Techniques to
Forecast Price Movement in
Futures Market
1. Fundamental analysis: study of supply and
demand factors affecting the price of
a
commodity
- current stock of a commodity
- the condition of the new crop in the field
- the growing environment for the new crop
- the present consumption rate
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2. Technical analysis: prices can be projected
based on historical price movement and
current market activity.
- generally assume that all fundamental
factors are reflected in the day-to-day
prices and their parameters.
- charts, trends, oscillators, volume, open
interest, etc.
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3. Sentiment Analysis: the actions of market
participants power the market and determine
prices
- sentiment is a measure of the traders’
degree of bullishness or bearishness toward
a given futures market.
- Bullish Consensus(a weekly market letter
published by Market Vane Corporation)
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Introduction
 HYPOTHESIS: MARKET EFFICIENCY
- The changes of futures prices are independent overtime
and price series and market activities are random walk.
 Forecasting futures price through past price
series are not efficient.
- Market is not perfect
 some range to forecast futures price by past data series.
- Common Technique to detect market efficiency
Estimate the degree of serial correlation
Test the homogeneity of pricing behavior
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Review of Literature
Failed to Reject Market Rejected Market
Efficiency Hypothesis
Efficiency Hypothesis
-Goldenberg(89)
-Fung and Lo(93)
- Helms and others(84)
- Martell and Trevino(90)
Composite Results
-Kamara(82)
-Kawaller and others(94)
-Corazza and others(97)
- DeCoster and others(92)
- Chowdhury(91)
- Schroeder and Goodwin(91)
- Bessler and Covey(91)
- Olszewski(98)
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Objective of This Paper
 To estimate the repetitiveness of daily market
behavior and directions of closing prices
- price moves in futures market
 results of market participant’s activities
- find some repetitive rules of market
participant
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Testable Hypothesis
1. Daily trading behaviors are repetitive
 the direction of closing prices can be forecasted
2. This repetitiveness is homogeneous
across the contracts and years
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Discriminant Analysis
 Predict class membership of an individual
observation based on a set of predictor variable
From known information
 develop DCR(discriminant classification rule)
 DCR assign new observation into
one of several population groups
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Developed DCR and Assignment
New entry
Decline
Group
Declining
Canola
Trading
Data
Constant
Rising
Develop
DCR
Constant
Group
Rising
Group
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Discriminant Rules
 Likelihood Rule
 Mahalanobis Distance Rule
 Posterior probability Rule
 Bays Rule
 Nonparametric Nearest Neighbor Rule
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Likelihood Rule
- Suppose populations are multivariate normal
distributions i ~ (i, i)
Choose i if L(x; i, i) > L(x; j, j )
for i  j = 1, 2, 3.
where, i : mean vector of i th population
i : variance-covariance matrix of
i th population
L(x; i, i): the likelihood function for the ith
population evaluated at x, i=1, 2, 3
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Mahalanobis Distance Rule
- Suppose three populations (declining, rising, and constant)
have equal variance-covariance matrices(1 = 2 = 3), then
the likelihood rule is also equivalent to:
Choose i when d i 2 < d j 2
where di 2 = (x- i)´ ˉ1 (x –i)
for i  j =1, 2, 3.
The Mahalannobis squared distance rule classifies an
observation into the population to whose mean it is
closest.
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Posterior Probability Rule
-When the variance-covariance matrices are
equal, the quantity P(i | x) defined by
k
P(i | x) = exp[(-½)di2] / exp[(-½)di2]
j=1
is called the posterior probability of population I
given x, for i = 1, 2, 3.
Then a discriminant rule of posterior probability is:
Choose i if P(i | x) > P(j | x)
for i  j = 1, 2, 3.
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Bayes Rule for Discriminant
- Pi: the prior probability for group i, the
probability that a randomly selected observation comes
from i, for i=1, 2, 3.
- C(i/j): cost of misclassifying an observation
from j into i
- P(i/j): probability of misclassifying an
observation from j into i.
Than the average cost of the misclassification of a randomly
selected observation is
Pi·C(j/i)·P(j/i) + Pj·C(i/j)·P(i/j) for i  j = 1, 2, 3.
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Bayes Rule
Minimizes the average cost of misclassification
with respect to prior probabilities P1, P2, and P3.
Choose i which minimizes di2
di2 = (x - i)´-1(x - i) + log  i 
-2 logPi C(j/i)],
for i j = 1, 2, 3.
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Data and Empirical Procedure
- Data: canola futures data(1982 –2000) from WCE
- Contracts: Nov., Jan., Mar., Sept.
- Daily Trading Behavior: open, high, low, closing,
open interest, volume of trade
- Three directions: declining, rising, constant in
closing price
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Variable Selection Procedure
Stepwise method was applied to select subsets
of variables that might have chances at being
good discriminators.
- 11variables(before stepwise): previous day’s open(t-1),
high(t-1), low(t-1), closing(t-1), open interest(t-1), volume(t-1)
and current day’s open(t), high(t), low(t), open interest(t),
and volume(t).
- 8 variables(after stepwise): previous day’s open(t-1)
closing(t-1), open interest(t-1), volume of trade(t-1), current
day’s open(t), high(t), low(t), volume(t) (t-1)
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Discriminant Classification Rule (DCRi (t))
 DCRi(t) will determine the group i, which minimizes di2
di2 = (x - i)´-1(x - i) - log  i 
-
-2 logPi  C(j/i)],
for i j = 1, 2, 3.
where, x: observation vector,open(t-1), closing(t-1),
volume(t-1), open interest(t-1), open(t),
high(t), low(t), volume(t)
i: mean vector of x in population i
Pi: prior probability of population i
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Results of Bayes DCR(1982-2000)
Contract
Nov.
Jan.
Sept.
Mar.
Total
Declining
Forecasted/
Real,day,(%)
Rising
Forecasted/
Real,day, (%)
1,695/1,870
(90.6)
1,199/1,377
(87.1)
1,076/1,213
(88.7)
960/1,083
(88.6)
4,930/5,543
(88.9)
1,655/1,853
(89.3)
1,111/1,294
(85.9)
924/1,137
(81.3)
902/1,007
(89.5)
4,592/5,291
(86.8)
Constant
Forecasted/
Real,day, (%)
0/57
(0.0)
1/40
(2.5)
6/48
(12.5)
1/38
(2.6)
8/183
(4.4)
Total
day
3,780
2,711
2,398
2,128
11,017
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Results of Nonparametric DCR(1982-2000)
Contract
Nov.
Jan.
Sept.
Mar.
Total
Declining
Forecasted/
Real,day,(%)
Rising
Forecasted/
Real,day, (%)
1,634/1,870
(87.4)
1,195/1,377
(86.8)
1,050/1,213
(86.6)
957/1,083
(88.4)
4,836/5,543
(87.2)
1,638/1,853
(88.3)
1,106/1,294
(85.5)
966/1,137
(84.0)
889/1,007
(88.3)
4,599/5,291
(86.9)
Constant
Forecasted/
Real,day, (%)
0/57
(0.0)
0/40
(0.0)
0/48
(0.0)
0/38
(0.0)
0/183
(0.0)
Total
day
3,780
2,711
2,398
2,128
11,017
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Rate of Correct Forecasting across the Year
(1982-2000)
Rate of Correct Forecasting by Bayes DCR (1982-2000)
120
80
Nov. Declining
Nov. Rising
60
Sept. Declining
Sept. Rising
40
Jan. Declining
Jan. Rising
20
Mar. Declining
Mar. Rising
0
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
Rate of Correct Forecasting(%)
100
y ear
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Rate of Correct Forecasting by Nonparametric
DCR (1982-2000)
120
80
Nov. Declining
Nov. Rising
60
Sept. Declining
Sept. Rising
40
Jan. Declining
Jan. Rising
20
Mar. Declining
Mar. Rising
0
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
Rate of Correct Forecasting(%)
100
y ear
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Repetitiveness across the Year,
Contracts, and Directions
 A GLM model was used to test homogeneity of
the results Bayes DCR Results
- DCR results across the year is not different at 95%
significant level
- DCR results across the contracts is not different at 95%
significant level
- repetitiveness across directions is different at 95%
significant level
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 Nonparametric DCR Results
- DCR results across the year is not different at 95%
significant level
- DCR results across the contracts is different at 95%
significant level
- repetitiveness across directions is different at 95%
significant level
 Bayes and Nonparametric
- DCR results are different at 95% significant level
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Summary
The results showed existence of
repetitiveness of daily trading behavior of
canola futures
Repetitiveness were homogeneous across
the year and contract except directions in
Bayes DCR
Repetitiveness were homogeneous across
the year but different in contracts and
directions for nonparametric DCR.
Repetitiveness of Bayes and Nonparametric
DCR were different.
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General Conclusions
Futures prices can be predictable with the past
data series.
Emphasize the existence of repetitiveness as
efficient forecasting tools, and technical systems
could work in canola futures market.
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Thank You
THE END
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