05AB1E, 6 bytes
Çü-0‹Ù Wavy Cases:
0 - Decreasing Wavy
1 - Increasing Wavy
Not Wavy Cases:
[0,1] - Not wavy, initially decreasing, but then has an increase/equality that broke the pattern.
[1,0] - Not wavy, initially increasing, but then has a decrease/equality that broke the pattern