I have a time series like following:

Data <-
structure(list(Year = c(1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 
1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1992L, 1992L, 
1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 
1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 
1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 
1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L), Month = c(8L, 
9L, 9L, 9L, 10L, 10L, 10L, 11L, 11L, 11L, 12L, 12L, 12L, 1L, 
1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 5L, 5L, 5L, 6L, 6L, 
6L, 7L, 7L, 7L, 8L, 8L, 8L, 9L, 9L, 9L, 10L, 10L, 10L, 11L, 11L, 
11L, 12L, 12L, 12L), Day = c(30L, 10L, 20L, 30L, 10L, 20L, 30L, 
10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 28L, 10L, 
20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 
30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 
10L, 20L, 30L), Hour = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), temperature = c(72.5, 64, 62.5, 
64, 64, 53, 52, 52, 45.5, 49, 50, 50, 59, 63.5, 69.5, 61, 61, 
NaN, NaN, 39.5, 37, 45.5, 45, 39, 43.5, 52, 53, 56, 64, 66, 66.5, 
73.5, 81, 85, 89.5, 87.5, 88.5, 83, 84.5, 74, 60.5, 59, 53, 60.5, 
62.5, 64.5, 63, 62, 65.5)), .Names = c("Year", "Month", "Day", 
"Hour", "temperature"), class = "data.frame", row.names = c(NA, 
-49L))

and I have to calculate standardized anomaly. The steps to calculate the anomalies are following:

1. Monthly premature departures from the long-term (1991-2007) average are obtained.
2. Then standardized by dividing by the standard deviation of monthly temperature.
3. The standardized monthly anomalies are then weighted by multiplying by the fraction of the average temperature for the given month.
4. These weighted anomalies are then summed over 3 month time period.

Can you please help me?