1. Understanding the SQL statement:

The given SQL statement is trying to fetch the customer_id, first_name, and last_name of customers who have rented a movie more than 12 months ago and haven't rented any movie in the last 12 months. The rental table is joined with the customer table using an INNER JOIN, and the result is filtered based on the rental_date and return_date conditions. The result is then grouped by the customer_id.

2. Suggesting optimization for PostgreSQL:

To optimize the SQL statement for PostgreSQL we can use the following approaches:

• Use a Common Table Expression (CTE) to fetch the filtered rental data before joining it with the customer table.
• Remove the GROUP BY clause and use DISTINCT instead to eliminate duplicate customer records.

3. Writing a better SQL statement:

Here's the optimized SQL statement for PostgreSQL:

            

              Copy
            
            WITH filtered_rentals AS (
  SELECT
    customer_id
  FROM
    rental
  WHERE
    rental_date < (CURRENT_DATE - INTERVAL '12 months')
    AND (
      return_date IS NULL
      OR return_date > (CURRENT_DATE - INTERVAL '12 months')
    )
  EXCEPT
  SELECT
    customer_id
  FROM
    rental
  WHERE
    rental_date >= (CURRENT_DATE - INTERVAL '12 months')
)
SELECT DISTINCT
  c.customer_id,
  c.first_name,
  c.last_name
FROM
  customer c
  INNER JOIN filtered_rentals fr ON c.customer_id = fr.customer_id;
          

In this optimized SQL statement we use a CTE named filtered_rentals to fetch the filtered rental data before joining it with the customer table. We also use the EXCEPT clause to exclude customers who have rented a movie in the last 12 months. Finally, instead of using GROUP BY, we use DISTINCT to eliminate duplicate customer records.