Moving average in postgresql

SQL Fiddle

select
    "date",
    shop_id,
    amount,
    extract(dow from date),
    case when
        row_number() over (order by date) > 3
        then
            avg(amount) OVER (
                ORDER BY date DESC
                ROWS BETWEEN 1 following AND 3 FOLLOWING
            )
        else null end
from (
    select *
    from ro
    where extract(dow from date) = 4
) s

What is wrong with the OP’s query is the frame specification:

ROWS BETWEEN 0 PRECEDING AND 2 FOLLOWING

Other than that my query avoids unneeded computing by filtering Thursdays before applying the expensive window functions.

If it is necessary to partition by shop_id then obviously add the partition by shop_id to both functions, avg and row_number.