Following recent changes to Latvian immigration laws, the Latvian Resident Permit is pretty much the easiest and most cost effective resident permit to get within the EU or Schengen Area.
It is usually possible to get a 5- year permit within 10 business days for an investment of €40,000, but from Yemen, it may take up to 90 days as additional security checks are required.
http://www.investco.lv/additional-security-checks/
It is also work noting that work permission is also included with your resident permit, so, you have the ability to work locally.
Regarding residency requirements, Latvia does not have any residency requirements for maintaining the resident permit, however, if you wish to apply for permanent residency status or even citizenship after 5 years, you must demonstrate that you have been resident in Latvia with the exception of 10 months within the 5 year period.
If you are not interested in permanent residency and citizenship, the 5-year permit is renewable without ANY requirement to be resident in Latvia or even within the Schengen Area.