# [R] Filling a covariance matrix

emorway emorway at usgs.gov
Tue Oct 23 17:59:09 CEST 2012

```useRs –
I’m working with the attached data that contains one year’s worth of
sub-daily observations of flow (“Q”) and specific conductance (“SC”, a
surrogate for concentration) at a point in a stream.  The R code posted
below shows the extent of data processing thus far.  My goal is to create a
covariance matrix that takes on the following form:
Q1 Q2 … Q365  SC1 SC2 … SC365
Q1
Q2
…
Q365
SC1
SC2
...
SC365

Where the covariance between Q1 (flow on day 1) & Q2 (flow on day 2) is
determined using the sub-daily data contained in the variable ‘x’ of the R
code below.  Similarly, the covariance between Q1 & SC1 (specific
conductance on day 1) would be made using the sub-daily observations of flow
and specific conductance.  Covariance between observations that are more
than 5 days distant from one another are likely meaningless.  Thus, the
covariance matrix should reflect this limitation with zeros.  For example,
the covariance between Q1 & Q6, or between Q1 & SC6, or between SC359
(specific conductance on day 359) & SC365 (specific conductance on day 365)
would be zero as these observations are more than 5 days apart.  Here is the
R code that reads the attached files containing Q and SC and puts the
processed data into ‘x’:

07130500_BelowJM_q_2004.txt
<http://r.789695.n4.nabble.com/file/n4647170/07130500_BelowJM_q_2004.txt>
07130500_BelowJM_2004.txt
<http://r.789695.n4.nabble.com/file/n4647170/07130500_BelowJM_2004.txt>

library(xts)

Q_subDaily\$datetime.str <- paste(Q_subDaily\$date, Q_subDaily\$time)
SC_subDaily\$datetime.str <- paste(SC_subDaily\$date, SC_subDaily\$time)

fmt <- "%Y%m%d %H%M%S"
xQ <- xts(as.matrix(Q_subDaily["Q"]), as.POSIXct(Q_subDaily\$datetime.str,
format=fmt))
xSC <- xts(as.matrix(SC_subDaily["SC"]),
as.POSIXct(SC_subDaily\$datetime.str, format=fmt))

x <- merge(xQ,xSC)

And here’s where I’m stuck, I’m not sure how to create the covariance matrix
I’ve described above?  I would appreciate and greatly benefit from the sort
of help often found in the useR community.

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