advanced-algorithmic-trading

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library:
> library("tseries")
> adf.test(comb)
Augmented Dickey-Fuller Test
data: comb
Dickey-Fuller = -10.321, Lag order = 9, p-value = 0.01
alternative hypothesis: stationary
Warning message:
In adf.test(comb) : p-value smaller than printed p-value
The p-value is small and hence we have evidence to reject the null hypothesis that the series
possesses a unit root. Now we try the Phillips-Perron test:
> pp.test(comb)
Phillips-Perron Unit Root Test
data: comb
Dickey-Fuller Z(alpha) = -1016.988, Truncation lag parameter = 7,
p-value = 0.01
alternative hypothesis: stationary
Warning message:
In pp.test(comb) : p-value smaller than printed p-value
Once again we have a small p-value and hence we have evidence to reject the null hypothesis
of a unit root. Finally, we try the Phillips-Ouliaris test (notice that it requires matrix input of
the underlying series constituents):
> po.test(cbind(2*x,-1.0*y))
Phillips-Ouliaris Cointegration Test
data: cbind(2 * x, -1 * y)
Phillips-Ouliaris demeaned = -1023.784, Truncation lag parameter = 9,
p-value = 0.01
Warning message:
In po.test(cbind(2 * x, -1 * y)) : p-value smaller than printed p-value
Yet again we see a small p-value indicating evidence to reject the null hypothesis. Hence it
is clear we are dealing with a pair of series that are cointegrated.
What happens if we instead create a separate combination with, say p = −1 and q = 2?
> badcomb <- -1.0*x + 2.0*y