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<?php
/**
 * Enqueue scripts and styles.
 *
 * @since 1.0.0
 */
function ja_global_enqueues() {

	wp_enqueue_style(
		'jquery-auto-complete',
		'https://cdnjs.cloudflare.com/ajax/libs/jquery-autocomplete/1.0.7/jquery.auto-complete.css',
		array(),
		'1.0.7'
	);

	wp_enqueue_script(
		'jquery-auto-complete',
		'https://cdnjs.cloudflare.com/ajax/libs/jquery-autocomplete/1.0.7/jquery.auto-complete.min.js',
		array( 'jquery' ),
		'1.0.7',
		true
	);

	wp_enqueue_script(
		'global',
		get_template_directory_uri() . '/js/global.min.js',
		array( 'jquery' ),
		'1.0.0',
		true
	);

	wp_localize_script(
		'global',
		'global',
		array(
			'search_api' => home_url( 'wp-json/ja/v1/search' )
		)
	);
}
add_action( 'wp_enqueue_scripts', 'ja_global_enqueues' );

/**
 * WP REST API register custom endpoints
 *
 * @since 1.0.0
 */
function ja_rest_api_register_routes() {

	register_rest_route( 'ja/v1', '/search', array(
		'methods'  => 'GET',
		'callback' => 'ja_rest_api_search',
	) );
}
add_action( 'rest_api_init', 'ja_rest_api_register_routes' );

/**
 * WP REST API search results.
 *
 * @since 1.0.0
 * @param object $request
 */
function ja_rest_api_search( $request ) {

	if ( empty( $request['term'] ) ) {
		return;
	}

	$results = new WP_Query( array(
		'post_type'     => array( 'post', 'page' ),
		'post_status'   => 'publish',
		'posts_per_page'=> 30,
		's'             => $request['term'],
	) );

	if ( !empty( $results->posts ) ) {
		return $results->posts;
	}
}

/* globals global */
jQuery(function($){
	var searchRequest;
	$('.search-autocomplete').autoComplete({
		minChars: 2,
		source: function(term, suggest){
			try { searchRequest.abort(); } catch(e){}
			searchRequest = $.get( global.search_api, { term: term }, function( res ) {
				if ( res !== null ) {
					var results = [];
					for(var key in res) {
						results.push(res[key].post_title)
					}
					suggest(results);
				}
			});
		}
	});
});

<form class="navbar-form" role="search" method="get" action="<?php echo esc_url( home_url( '/' ) ); ?>">
	<div class="form-group">
		<input type="text" name="s" class="form-control search-autocomplete" placeholder="Search">
	</div>
	<button type="submit" class="fa fa-search"></button>
</form>