Filling in missing values of a rolling correlation matrix - sas

Question

This question partially relates to this question.
My datafile can be found here. I use a sample period from 01 Jan 2008 to 31 Dec 2013. The datafile has no missing values.
The following code generates the rolling correlation matrix on each day from 01 Jan 2008 to 31 Dec 2013 using a rolling window of the previous 1 year worth of values. E.g., the correlation between AUT and BEL on 01 Jan 2008 is calculated using the series of values from 01 Jan 2007 to 01 Jan 2008, and likewise for all other pairs.
data work.rolling;
set mm.rolling;
run;
%macro rollingCorrelations(inputDataset=, refDate=);
/*first get a list of unique dates on or after the reference date*/
proc freq data = &inputDataset. noprint;
where date >="&refDate."d;
table date/out = dates(keep = date);
run;
/*for each date calculate what the window range is, here using a year's length*/
data dateRanges(drop = date);
set dates end = endOfFile
nobs= numDates;
format toDate fromDate date9.;
toDate=date;
fromDate = intnx('year', toDate, -1, 's');
call symputx(compress("toDate"!!_n_), put(toDate,date9.));
call symputx(compress("fromDate"!!_n_), put(fromDate, date9.) );
/*find how many times(numberOfWindows) we need to iterate through*/
if endOfFile then do;
call symputx("numberOfWindows", numDates);
end;
run;
%do i = 1 %to &numberOfWindows.;
/*create a temporary view which has the filtered data that is passed to PROC CORR*/
data windowedDataview / view = windowedDataview;
set &inputDataset.;
where date between "&&fromDate&i."d and "&&toDate&i."d;
drop date;
run;
/*the output dataset from each PROC CORR run will be
correlation_DDMMMYYY<from date>_DDMMMYY<start date>*/
proc corr data = windowedDataview
outp = correlations_&&fromDate&i.._&&toDate&i. (where=(_type_ = 'CORR'))
noprint;
run;
%end;
/*append all datasets into a single table*/
data all_correlations;
format from to date9.;
set correlations_:
indsname = datasetname
;
from = input(substr(datasetname,19,9),date9.);
to = input(substr(datasetname,29,9), date9.);
run;
%mend rollingCorrelations;
%rollingCorrelations(inputDataset=rolling, refDate=01JAN2008)
An excerpt of the output can be found here.
As can be seen row 2 to row 53 presents the correlation matrix for the day 1 Apr 2008. However, a problem arises for the correlation matrix for the day 1 Apr 2009: there are missing values for correlation coefficients for ALPHA and its pairs. This is because if one looks at the datafile, the values for ALPHA from 1 Apr 2008 to 1 Apr 2009 are all zero, hence causing a division by zero. This situation happens with a few other data values too, for example, HSBC also has all values as 0 from 1 Apr 08 to 1 Apr 09.
To resolve this issue, I was wondering how the above code can be modified so that in cases where this situation happens (i.e., all values are 0 between 2 certain dates), then the correlation between the two pairs of data values are simply calculated using the WHOLE sample period. E.g., the correlation between ALPHA and AUT is missing on 1 Apr 09, thus this correlation should be calculated using the values from 1 JAN 2008 to 31 DEC 2013, rather than using the values from 1 Apr 08 to 1 Apr 09

Answer 1

Once you run the above macro and have got your all_correlations dataset, you would need to run another PROC CORR this time using all of the data i.e.,
/*first filter the data to be between "01JAN2008"d and "31DEC2013"d*/
data work.all_data_01JAN2008_31DEC2013;
set mm.rolling;
where date between "01JAN2008"d and "31DEC2013"d;
drop date ;
run;
Then pass the above dataset to PROC CORR:
proc corr data = work.all_data_01JAN2008_31DEC2013
outp = correlations_01JAN2008_31DEC2013
(where=(_type_ = 'CORR'))
noprint;
run;
data correlations_01JAN2008_31DEC2013;
length id 8;
set correlations_01JAN2008_31DEC2013;
/*add a column identifier to make sure the order of the correlation matrix is preserved when joined with other tables*/
id = _n_;
run;
You would get a dataset which is unique by the _name_ column.
Then you would have to join correlations_01JAN2008_31DEC2013 to all_correlations in such a way that if a value is missing in all_correlations then a corresponding value from correlations_01JAN2008_31DEC2013 is inserted in its place. For this we can use PROC SQL & the COALESCE function.
PROC SQL;
CREATE TABLE MISSING_VALUES_IMPUTED AS
SELECT
A.FROM
,A.TO
,b.id
,a._name_
,coalesce(a.AUT,b.AUT) as AUT
,coalesce(a.BEL,b.BEL) as BEL
,coalesce(a.DEN,b.DEN) as DEN
,coalesce(a.FRA,b.FRA) as FRA
,coalesce(a.GER,b.GER) as GER
,coalesce(a.GRE,b.GRE) as GRE
,coalesce(a.IRE,b.IRE) as IRE
,coalesce(a.ITA,b.ITA) as ITA
,coalesce(a.NOR,b.NOR) as NOR
,coalesce(a.POR,b.POR) as POR
,coalesce(a.SPA,b.SPA) as SPA
,coalesce(a.SWE,b.SWE) as SWE
,coalesce(a.NL,b.NL) as NL
,coalesce(a.ERS,b.ERS) as ERS
,coalesce(a.RZB,b.RZB) as RZB
,coalesce(a.DEX,b.DEX) as DEX
,coalesce(a.KBD,b.KBD) as KBD
,coalesce(a.DAB,b.DAB) as DAB
,coalesce(a.BNP,b.BNP) as BNP
,coalesce(a.CRDA,b.CRDA) as CRDA
,coalesce(a.KN,b.KN) as KN
,coalesce(a.SGE,b.SGE) as SGE
,coalesce(a.CBK,b.CBK) as CBK
,coalesce(a.DBK,b.DBK) as DBK
,coalesce(a.IKB,b.IKB) as IKB
,coalesce(a.ALPHA,b.ALPHA) as ALPHA
,coalesce(a.ALBK,b.ALBK) as ALBK
,coalesce(a.IPM,b.IPM) as IPM
,coalesce(a.BKIR,b.BKIR) as BKIR
,coalesce(a.BMPS,b.BMPS) as BMPS
,coalesce(a.PMI,b.PMI) as PMI
,coalesce(a.PLO,b.PLO) as PLO
,coalesce(a.BINS,b.BINS) as BINS
,coalesce(a.MB,b.MB) as MB
,coalesce(a.UC,b.UC) as UC
,coalesce(a.BCP,b.BCP) as BCP
,coalesce(a.BES,b.BES) as BES
,coalesce(a.BBV,b.BBV) as BBV
,coalesce(a.SCHSPS,b.SCHSPS) as SCHSPS
,coalesce(a.NDA,b.NDA) as NDA
,coalesce(a.SEA,b.SEA) as SEA
,coalesce(a.SVK,b.SVK) as SVK
,coalesce(a.SPAR,b.SPAR) as SPAR
,coalesce(a.CSGN,b.CSGN) as CSGN
,coalesce(a.UBSN,b.UBSN) as UBSN
,coalesce(a.ING,b.ING) as ING
,coalesce(a.SNS,b.SNS) as SNS
,coalesce(a.BARC,b.BARC) as BARC
,coalesce(a.HBOS,b.HBOS) as HBOS
,coalesce(a.HSBC,b.HSBC) as HSBC
,coalesce(a.LLOY,b.LLOY) as LLOY
,coalesce(a.STANBS,b.STANBS) as STANBS
from all_correlations as a
inner join correlations_01JAN2008_31DEC2013 as b
on a._name_ = b._name_
order by
A.FROM
,A.TO
,b.id
;
quit;
/*verify that no missing values are left. NMISS column should be 0 from all variables*/
proc means data = MISSING_VALUES_IMPUTED n nmiss;
run;