Calculate rolling sum of an array in PySpark using Window()?

For Spark 2.4+ you can use array functions and higher-order functions. This solution will work for different array sizes (event if different between each row). Here are the steps explained:

First, group by 2 seconds and collect the vars in an array column :

df = df.groupBy((ceil(col("timestamp") / 2) * 2).alias("timestamp")) \
       .agg(collect_list(col("vars")).alias("vars"))

df.show()

#+---------+----------------------+
#|timestamp|vars                  |
#+---------+----------------------+
#|6        |[[1, 1, 1], [1, 2, 3]]|
#|2        |[[1, 1, 1], [1, 2, 1]]|
#|4        |[[1, 1, 1], [1, 3, 4]]|
#+---------+----------------------+

Here we grouped each consecutive 2 seconds and collected the vars arrays into a new list. Now, using a Window spec you can collect cumulative values and use flatten to flatten the sub arrays:

w = Window.orderBy("timestamp").rowsBetween(Window.unboundedPreceding, Window.currentRow)
df = df.withColumn("vars", flatten(collect_list(col("vars")).over(w)))
df.show()

#+---------+------------------------------------------------------------------+
#|timestamp|vars                                                              |
#+---------+------------------------------------------------------------------+
#|2        |[[1, 1, 1], [1, 2, 1]]                                            |
#|4        |[[1, 1, 1], [1, 2, 1], [1, 1, 1], [1, 3, 4]]                      |
#|6        |[[1, 1, 1], [1, 2, 1], [1, 1, 1], [1, 3, 4], [1, 1, 1], [1, 2, 3]]|
#+---------+------------------------------------------------------------------+

Finally, use aggregate function with zip_with to sum the arrays :

t = "aggregate(vars, cast(array() as array<double>), (acc, a) -> zip_with(acc, a, (x, y) -> coalesce(x, 0) + coalesce(y, 0)))"

df.withColumn("vars", expr(t)).show(truncate=False)

#+---------+-----------------+
#|timestamp|vars             |
#+---------+-----------------+
#|2        |[2.0, 3.0, 2.0]  |
#|4        |[4.0, 7.0, 7.0]  |
#|6        |[6.0, 10.0, 11.0]|
#+---------+-----------------+

Putting all together:

from pyspark.sql.functions import ceil, col, collect_list, flatten, expr
from pyspark.sql import Window

w = Window.orderBy("timestamp").rowsBetween(Window.unboundedPreceding, Window.currentRow)
t = "aggregate(vars, cast(array() as array<double>), (acc, a) -> zip_with(acc, a, (x, y) -> coalesce(x, 0) + coalesce(y, 0)))"

nb_seconds = 2

df.groupBy((ceil(col("timestamp") / nb_seconds) * nb_seconds).alias("timestamp")) \
  .agg(collect_list(col("vars")).alias("vars")) \
  .withColumn("vars", flatten(collect_list(col("vars")).over(w))) \
  .withColumn("vars", expr(t)).show(truncate=False)

Using sum window function to compute the running sum and row_number to pick every second timestamp row.

from pyspark.sql import Window
w = Window.orderBy(col('timestamp'))
result = df.withColumn('summed_vars',array([sum(col('vars')[i]).over(w) for i in range(3)])) #change the value 3 as desired
result.filter(col('rnum')%2 == 0).select('timestamp','summed_vars').show()

Change the %2 as needed per your time interval.

Edit: Grouping by time intervals with window. Assuming timestamp column is of data type timestamp.

from pyspark.sql import Window
from pyspark.sql.functions import window,sum,row_number,array,col 
w = Window.orderBy(col('timestamp'))
result = df.withColumn('timestamp_interval',window(col('timestamp'),'2 second')) \
           .withColumn('summed_vars',array(*[sum(col('vars')[i]).over(w) for i in range(4)])) 
w1 = Window.partitionBy(col('timestamp_interval')).orderBy(col('timestamp').desc())
final_result = result.withColumn('rnum',row_number().over(w1))
final_result.filter(col('rnum')==1).drop(*['rnum','vars']).show()