Can the cointegration coefficient be negative? I am trying to understand the cointegration coefficient, $\gamma$. In the following case,
$$P_{A,t }- \gamma P_{B,t}= \varepsilon_t$$
where $P_{A,t}$ and $P_{B,t}$ are the prices of the assets A and B at time $t$, respectively. If $P_{A,t}$ and $P_{B,t}$ are I(1) and $\varepsilon_t$ is I(0), I can say that the assets A and B are cointegrated and I should buy 1 unit of stock A and $\gamma$ units of stock B. But what if $\gamma$ is negative? Do I need to buy $\gamma$ units of asset B? Or is it not possible that $\gamma$ is negative?
Thank you for your attention!

In general, there are no sign restrictions on the cointegrating vector.
Within the application domain that you've outlined, in a typical example $\gamma$ would be positive, but it doesn't necessarily have to be.
However, your interpretation of a positive $\gamma$ is incorrect: the transactions for A and B have opposite signs, you buy one and short the other. The idea being that the combined portfolio whose value is $P_{A,t} - \gamma P_{B,t}$ is stationary, so if its value is observed to be far from its historical mean, you should either buy it (buy 1 A, short $\gamma$ B) if it's well below, or short it (short 1 A, buy $\gamma$ B) if it's well above, counting on it to return to its mean.
Whether this actually works in practice is a different question.
