generate_series for multiple record types in postgresql. Fill missing with last previous value

my question is closely related to the following question asked in this thread generate_series for multiple record types in postgresql. The only difference is, that instead of only inserting missing values, I want to fill the gaps with the last previous value. To illustrate it with the same example. I have two tables.

CREATE TABLE pests(id,name)
AS VALUES
  (1,'Thrip'),
  (2,'Fungus Gnosts');

CREATE TABLE pest_counts(id,pest_id,date,count)
AS VALUES
  (1,1,'2015-01-01'::date,14),
  (2,2,'2015-01-02'::date,5);

The desired output should be nearly identical. However, I want to fill missing values with previous values, if possible. So the second entry for Thrip should be 14, since a previous value exists and the first value of Fungus Gnats should be 0, since no previous value exists. Is it possible to do this using Postgres?

expected results

name         | date       | count
-------------+------------+-------
Thrip        | 2015-01-01 | 14
Thrip        | 2015-01-02 | **14** <- fill with existing previous value.
....
Fungus Gnats | 2015-01-01 | 0
Fungus Gnats | 2015-01-02 | 5
...

Example data with two rows added:

insert into pest_counts(pest_id, date, count) values
    (1, '2015-01-03', 10),
    (2, '2015-01-04', 7);

select * from pest_counts;

 id | pest_id |    date    | count 
----+---------+------------+-------
  1 |       1 | 2015-01-01 |    14
  2 |       2 | 2015-01-02 |     5
  3 |       1 | 2015-01-03 |    10
  4 |       2 | 2015-01-04 |     7
(4 rows)

Use count() as a window function to generate groups. Each not null value starts a new group:

select name, day, count, count(count) over (partition by name order by day) as grp
from (
    select id, name, day::date
    from pests
    cross join generate_series('2015-01-01'::timestamp, '2015-01-04', '1 day') day
) d
left join pest_counts on d.id = pest_id and day = date;

     name     |    day     | count | grp 
--------------+------------+-------+-----
 fungus gnats | 2015-01-01 |       |   0
 fungus gnats | 2015-01-02 |     5 |   1
 fungus gnats | 2015-01-03 |       |   1
 fungus gnats | 2015-01-04 |     7 |   2
 thrip        | 2015-01-01 |    14 |   1
 thrip        | 2015-01-02 |       |   1
 thrip        | 2015-01-03 |    10 |   2
 thrip        | 2015-01-04 |       |   2
(8 rows)

Now you can use sum() as a window function over partitions by names and generated groups:

select name, day, coalesce(count, sum(count) over (partition by name, grp order by day), 0) as count
from (
    select name, day, count, count(count) over (partition by name order by day) as grp
    from (
        select id, name, day::date
        from pests
        cross join generate_series('2015-01-01'::timestamp, '2015-01-04', '1 day') day
    ) d
    left join pest_counts on d.id = pest_id and day = date
) s;

     name     |    day     | count 
--------------+------------+-------
 fungus gnats | 2015-01-01 |     0
 fungus gnats | 2015-01-02 |     5
 fungus gnats | 2015-01-03 |     5
 fungus gnats | 2015-01-04 |     7
 thrip        | 2015-01-01 |    14
 thrip        | 2015-01-02 |    14
 thrip        | 2015-01-03 |    10
 thrip        | 2015-01-04 |    10
(8 rows)