Price elasticity of demand measures the responsiveness of quantity demanded when there is a change in price of the particular good you are examining. Cross elasticity of demand measures the responsiveness of quantity demanded when there is a change in price of OTHER goods. PED is always a negative value because the quantity demanded and price have an inverse relationship, i.e when price increases, quantity demanded will decrease and vice versa. Whereas CED can be either positive or negative. It all depends on the nature of the goods you're examining.
Two types of goods that play an influencial role in determining CED of a good is Complementary goods and Substitute goods. Take for example, CED of substitute goods are always positve. This is because the quantity demanded for the substitute goods has a positive relationship with the price of the initial good, i.e when price of initial good drops, the quantity demanded for substitute goods will drop as well. This is because consumers will always opt for the cheaper alternative, which in this case is the initial good, thus quantity demanded for its substitutes will decrease.
