public function format_term_ids( $term_ids, $taxonomy ) {
    $term_ids = wp_parse_id_list( $term_ids );

    if ( ! count( $term_ids ) ) {
      return '';
    }

    $formatted_terms = array();

    if ( is_taxonomy_hierarchical( $taxonomy ) ) {
      foreach ( $term_ids as $term_id ) {
        $formatted_term = array();
        $ancestor_ids   = array_reverse( get_ancestors( $term_id, $taxonomy ) );

        foreach ( $ancestor_ids as $ancestor_id ) {
          $term = get_term( $ancestor_id, $taxonomy );
          if ( $term && ! is_wp_error( $term ) ) {
            $formatted_term[] = $term->name;
          }
        }

        $term = get_term( $term_id, $taxonomy );

        if ( $term && ! is_wp_error( $term ) ) {
          $formatted_term[] = $term->name;
        }

        $formatted_terms[] = implode( ' > ', $formatted_term );
      }
    } else {
      foreach ( $term_ids as $term_id ) {
        $term = get_term( $term_id, $taxonomy );

        if ( $term && ! is_wp_error( $term ) ) {
          $formatted_terms[] = $term->name;
        }
      }
    }

    return $this->implode_values( $formatted_terms );
  }