It seems you need define an user agent.
Try this;
$url = "https://api.gdax.com/products/BTC-USD/candles?start=2015-05-07&end=2015-05-08&granularity=900";
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch,CURLOPT_USERAGENT,"Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.8.1.13) Gecko/20080311 Firefox/2.0.0.13");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$result = curl_exec($ch);
curl_close($ch);
var_dump($result);
If you still insist on using file_get_contents
then it is still possible to use user agent;
$url = "https://api.gdax.com/products/BTC-USD/candles?start=2015-05-07&end=2015-05-08&granularity=900";
$options = array(
"http"=>array(
"header"=>"User-Agent: Mozilla/5.0 (iPad; U; CPU OS 3_2 like Mac OS X; en-us) AppleWebKit/531.21.10 (KHTML, like Gecko) Version/4.0.4 Mobile/7B334b Safari/531.21.102011-10-16 20:23:10\r\n" // i.e. An iPad
)
);
$context = stream_context_create($options);
$result = file_get_contents($url, false, $context);
var_dump($result);
For more information you can check file_get_contents and stream_context_create (for using headers) documentation