递归ewma计算和比较

Question

I have data which contains two column (Time , Result). For every second , I have different value for 'Result'. I want to check the value of 'Result' in every second if it's exceeded a given condition. The condition is changing for every value of 'Result' based on the previous mean. The previous mean is calculated based on the exponentially weighted moving average (EWMA) from the following :

μn = μn−1 + (1 − lambda)Xn , 

lambda is the EWMA factor (for this example use 0.2) 
μn−1 is the mean value calculated from measurements prior to record n.
μn   is the mean. 
Xn   is the value of 'Result' in the nth record.
n    is number of records in the df

The condition is :

g is variable that incremented for each time the condition is true.

if (Xn > (1.5)μn−1) {
  g<-g+1
}

This logic has to be carried out over all of the records in the data.

Here is MWE:

readFile<- read.table("data.tr",header=F, stringsAsFactor=F)
colnames(readFile)<-c("time","Results")
df<-data.frame(Time=readFile$time,Results=readFile$Results)

#The data looks like (df);
 Time Results
   1     10
   2     15
   3     15
   4     10
   5     10
   6     30
   7     15
   8     25
   9     40
  10     22
  11     48
  12     50
  13     30
  14     40
  15     64
  16     46
  17     30
  18     10
  19     17
  20     53
  #define variables
  g<-0
  result<-0
  previousAverage<-0

  for(i in df){
   result<-df&Results[i]
   # Here I'm confused how to make the recursive call !!
   #I'm assuming the average should be returned from a separate method 
   #(i.e AverageCalculation) and use in the condition

   condition <- (1.5) * previousAverage
   if ( result > condition){
       g<-g+1
    }
  }

I found that "qcc" package calculates the EWMA which should simplify the calculation. However, I want to use the equation above. The difficult part for me is how to calculate the mean from the first record to the n-1 th record and keep shifting? how I can hold the current record value.

Any suggestions?!!!

Answer 1

outside your loop, initalize mu and a column for the lag.

mu = 0
df$prevmu <- 0

then loop over the rows,

for(i in 1:nrow(df)) {
  df$prevmu[i] <- mu
  mu <- mu + (1 - lambda) * df$Result[i]
}

Now you can calculate g:

g <- with(df, sum(Results > 1.5 * prevmu))