The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

ALTER TABLE `tbl2` ADD INDEX `tbl2_idx_time` (`time`);

The optimized query:

WITH cte AS (SELECT
        t1.time,
        t1.b_value,
        t2.u_value * t1.b_value AS bu_value,
        last_value(t2.u_value) OVER (PARTITION 
    BY
        DATE_TRUNC('DAY',
        t1.time) 
    ORDER BY
        DATE_TRUNC('DAY',
        t2.time)) AS daily_u_value 
    FROM
        stackoverflow.tbl1 t1 
    LEFT JOIN
        stackoverflow.tbl2 t2 
            ON t1.time = t2.time) SELECT
            DATE_TRUNC('DAY',
            c.time) AS time,
            AVG(c.daily_u_value) AS daily_u_value,
            SUM(SUM(c.b_value)) OVER (ORDER 
    BY
        DATE_TRUNC('DAY',
        c.time)) AS b_value_cum_sum,
        AVG(c.daily_u_value) * SUM(SUM(c.b_value)) OVER (ORDER 
    BY
        DATE_TRUNC('DAY',
        c.time)) AS daily_u_value_mul_b_value 
    FROM
        cte c 
    GROUP BY
        1 
    ORDER BY
        1 DESC