There is a package that can be used to do this for you.

sudo apt-get install unattended-upgrades

or if unattended-upgrades already installed. Or you can checkout the Ubuntu docs

sudo dpkg-reconfigure -plow unattended-upgrades

That is the package you need to install. Once its installed edit the files

/etc/apt/apt.conf.d/10periodic

/etc/apt/apt.conf.d/20auto-upgrades

In that file you can set how often you want the server to update.

APT::Periodic::Update-Package-Lists "1";

APT::Periodic::Download-Upgradeable-Packages "1";

APT::Periodic::AutocleanInterval "7";

APT::Periodic::Unattended-Upgrade "1";

The file should look like that. The 1 means it will update every day. 7 is weekly.

/etc/apt/apt.conf.d/50unattended-upgrades

This files will let you chose what updates you want to make by choosing where apt can search for new updates and upgrades. ( My personal opinion on this is I would set it to security if this is a server )

Unattended-Upgrade::Allowed-Origins {

        "${distro_id}:${distro_codename}-security";

//      "${distro_id}:${distro_codename}-updates";



};

The variables ${distro_id} and ${distro_codename} are expanded automatically. I would comment out the updates entry and just leave security.