Vertica pattern match feature

As you have no column named median_ratio in your sample data, I can only guess.
But in this pattern, you already supply event names and match id, so I won't bother.
But the event series is a start, then another start, and then a series of 3 up events.

So (start up+) is one event start followed by several up events. This makes it start at 2019-09-06, and the row of 2019-09-05 falls out of the pattern.

If you want the row of 2019-09-05 to be part of the pattern, it's either (start start up+) or (start+ up+) - or also (start up*) to get two patterns, of which one consists of a single row.
Hope this helps ...

thanks, Marcothesne!
I am still not quite understand , why 2019-09-05 and 2019-09-06 both are been treated as "Start" event, why not "2019-09-05" as "Start" and "2019-09-06" as "up" event? both of them fulfilled: start as down_pct > pre_val, up as down_pct > baseline*1.05.

I thought I used "ROWS MATCH first EVENT", it should pick "09/05" as start and "09/06" as up event?

ROWS MATCH FIRST EVENT means that the first Boolean expression, in the events list, that evaluates to TRUE is picked, and the following ones won't even be evaluated. ROWS MATCH ALL EVENTS would cause an error if two Booleans evaluate to TRUE:
ERROR: pattern events must be mutually exclusive
HINT: try using ROWS MATCH FIRST EVENT

agree..but if I used: "ROWS MATCH first EVENT", it should pick "09/05" as start and "09/06" as up event?
sorry, I am still not get why "09/05" did not get pick?

The order of action is:
1. For each row, check each of the events in the DEFINE clause. With the default, ROWS MATCH FIRST EVENT, stop checking as soon as one event's Boolean expression is true. With that, both rows of 2019-09-05 and 2019-09-06 get the event_name start : Given that down_pct > pre_val is true in both cases, the up event is not even evaluated.
2. Check the pattern specified. In our case, initially: (start up+) . That means one occurrence of start, not two, followed by one or more occurrences of up .

This leaves no other option than to let the row with 2019-09-05 fall outside of the pattern you're searching for.

ROWS MATCH FIRST EVENT refers to the events in the DEFINE clause, in the order in which you specify them in there, not to the events in the pattern you're searching.

great! I got it now..
one more question: start up* and start up+ different?

why start up* can catch this pattern?

(start up*) is one of start, followed by zero, one or more up. So it can be just a start line.
You are getting two patterns, a one-lined one, and another with more lines. Check the output of the pattern_id() function here below, and note that you're getting two pattern ID-s ...

 SELECT 
   *
 , event_name()
 , pattern_id()
 , match_id()
 FROM input
 MATCH(
   PARTITION BY 1
   ORDER BY dt
   DEFINE
     start AS down_pct > pre_val
   , up    AS down_pct > baseline*1.05
   PATTERN p AS (start  up*)
 );
 -- out      dt     | down_pct | pre_val | baseline | t_value | event_name | pattern_id | match_id 
 -- out ------------+----------+---------+----------+---------+------------+------------+----------
 -- out  2019-09-05 |     2.60 |    1.26 |     2.09 |    2.19 | start      |          1 |        1
 -- out  2019-09-06 |     2.61 |    2.60 |     2.09 |    2.19 | start      |          2 |        1
 -- out  2019-09-07 |     2.60 |    2.61 |     2.09 |    2.19 | up         |          2 |        2
 -- out  2019-09-08 |     2.55 |    2.60 |     2.09 |    2.19 | up         |          2 |        3
 -- out  2019-09-09 |     2.54 |    2.55 |     2.09 |    2.19 | up         |          2 |        4
 -- out (5 rows)
 -- out 
 -- out Time: First fetch (5 rows): 65.666 ms. All rows formatted: 65.771 ms                                                                                                                                   

thanks, now I totally understand...I thought Vertica treat "start,up" as a single pattern, that is the reason I got puzzled.
if Vertica treated "start" and "up" into two different events, now it is clear.
great support!