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represents the posterior probability of transitioning to a regime given the current regime.
To compute the Markov transition matrix, for each of the past games we compute the
mean normalized price every day, we then estimate the regime probabilities dependent
on that price, and we select the regime which has the maximum probability as the
regime for the given day.
The prediction of regime probabilities is based on two distinct operations: a correc-
tion (recursive Bayesian update) of the posterior probabilities for the regimes based on
the history of measurements of np obtained since the time of the last regime change,
t
0
, until the previous day,
t
), and a subsequent predic-
tion of regime posterior probabilities for the current day,
t
,
P
(
r
t
|{
−
1,
P
(
r
t−
1
|{
np
t
0
,...,
np
t−
1
}
.
Equation 7 describes a recursive computation for predicting the posterior distribution
of regimes at time
t
+
n
days into the future, where
k
=
n
+1.
np
t
0
,...,
np
t−
1
}
P
(
r
t
+
k
|{
np
t
0
,...,
np
t−
1
}
)=
r
t
+
k−
···
k
P
(
r
t−
1
|{
np
t
0
,...,
np
t−
1
}
)
·
T
predict
(
r
t
+
j
|
r
t
+
j−
1
)
(7)
r
t−
1
j
=1
We measure the accuracy of regime prediction using two separate values:
1. a count of how many times the regime predicted is the correct one,
2. a count of how many times the predicted day of the regime switch is correct. We
assume the prediction is correct when the regime switch prediction is -2/+2 days
from the correct day of change.
As ground truth we measure regime switches and their time off-line using data from
the game. We tested our approach on all 16 final games in the 2005 TAC SCM tourna-
ment. Starting with day 1 until day 199, we forecast every day the regimes for the next
20 days and we forecast when a regime transition would occur. Experimental results are
in Table 1.
The reason for limiting the prediction to 20 days is that every 20 days the agent
receives a report which includes the mean price of each of the computer types sold since
the last market report, and so it can correct, if needed, its current regime identification.
Ta b l e 1 .
Percent of correct predictions of future regime (using Markov model) and predictions
of time of regime change (using Semi-Markov model). We assume the prediction of the time
of change is correct if it is within -2/+2 days. For the number of regime changes we show the
average and standard deviation. Results shown are computed every day for the next 20 days from
day 1 to day 199 (for a total of 3184 trials).
low market medium market high market
avg/stdev
avg/stdev
avg/stdev
# regime changes
9.75/9.85
7.88/4.97
3.69/1.72
correct regime
73.87%
85.30%
97.83%
correct time
74.43%
74.18%
93.12%
We hypothesized that the time a regime switch occurs is not exponential (Markov),
i.e. the future depends not only on the present state, but also on the length of time the
