JavaScript (ES6), 84 bytes
s=>(new Set(s).size>2)*(![...s].some((c,i)=>c>s[i+1])-![...s].some((c,i)=>c<s[i+1])) Assumes the input is all in the same case. Returns 1 for raising wavy, -1 for decreasing wavy, 0 or -0 (both are falsy) for not wavy.