Try :
<template>
<th :class="'initial '+ active" v-on="click: myFilter">
<span class="wkday">M</span>
</th>
</template>
<script lang="ts">
active:string=''
myFilter(){
this.active='active'
}
</script>
<style>
.active{
/***your action***/
}
</style>