You can use this filter to add current-archive class to element (as current-cat in wp_list_categories() function):

function example_get_archives_link($link_html) {
    if (is_day() || is_month() || is_year()) {
        if (is_day()) {
            $data = get_the_time('Y/m/d');
        } elseif (is_month()) {
            $data = get_the_time('Y/m');
        } elseif (is_year()) {
            $data = get_the_time('Y');
        }

        // Link to archive page
        $link = home_url($data);

        // Check if the link is in string
        $strpos = strpos($link_html, $link);

        // Add class if link has been found
        if ($strpos !== false) {
            $link_html = str_replace('<li>', '<li class="current-archive">', $link_html);
        }
    }

    return $link_html;
}
add_filter("get_archives_link", "example_get_archives_link");