6. Runs in the Stock Market 75
Pattern Average z-Value Standard Deviation Units Percent Positive
UU -0.010 -0.21 50.1
DD -0.074 1.56 51.7
UD 0.005 0.10 51.0
DU 0.002 0.04 51.0
UUU -0.035 -0.74 44.9
UUUU -0.020 -0.41 46.2
DDD 0.064 1.34 50.8
DDDD -0.060 -1.26 43.7
Table 5. Simulated z-values for various patterns in weekly
price changes
The results in these tables should be compared with simulated
data from the model in which weekly changes for a given stock are
mutually independent events. For each stock in our set, we used the
observed probabilities of a positive and a negative weekly change in
the stock price to create a simulated set of stock prices. Then, using
the same algorithms as were used above, we calculated the average
z-values for various patterns over our set of stocks. The results are
shown in Table 5.
The simulated data from this model is much different than the actual
data. This supports the observation that both daily and weekly stock
prices are anti-streaky.
In their book [29], Andrew Lo and Craig MacKinlay discuss a
parameter they call the variance ratio. Here is a description of this
concept. Suppose that {Xi}i=0
n
is a sequence of n logarithms of a
stock’s price. The time increment between successive values might be
days, or weeks, or even something as small as minutes. The log price
increments are the values {Xi+1
Xi}i=01. n−
A central question that
concerns this sequence of log price increments is whether it can be
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