What are the constituents of a country's inflation If we assume a country where only demand pull inflation holds, that is no imports cost inflation or currency fluctuations are a risk, then we can assume that inflation is determined by:


Consumer spending (for example for the US this should be the most important part of the economy)
Government spending


Are retail sales and house sales included in the consumer spending figure?

Aside from that, are there other economic indicators (that are neither consumer spending nor government spending) that influence a country's inflation?
The components of aggregate demand are government consumption, consumption, investment, net exports. 

While people typically assume there is a relationship between demand shocks and inflation, this does not mean that inflation will necessarily go up whenever consumption goes up, because consumption depends not only on demand shocks but also many other things that will not necessarily affect inflation in the same way. For example, if consumption goes up because labor productivity and incomes increase, inflation may even go down. On the other hand, if the central bank decreases the interest rate, demand will increase and this will cause an increase in inflation.