population variance (Equivalent of var.p command in excel in Matlab)

I have a time series data of 5 variables ( data is attached) and I grouped them based on month and year and take variance of each month by following code:

% reading daily data

data1=csvread('ffm.csv',1,0);

% extracting data into a MATLAB Table variable

T=table();

T.year=floor(data1(:,1)/10000);

T.mm=floor((data1(:,1)-T.year*10000)/100);

T.dd=data1(:,1)-T.year*10000-T.mm*100;

T.value=data1(:,2:6);

% compute monthly variance from daily data

v=[];

v=grpstats(T,{'year','mm'},'var');

However, this code by simply 'var' command in the last line of the code, gives the sample variance, but I need to obtain the population variance . The difference between population and sample variance is explained in the below link:

https://www.automateexcel.com/stats/var-p-vs-var-s/#:~:text=The%20VAR.,a%20sample%20of%20a%20populate.

Answer 1

[Star Strider]

Try something like this —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1165263/ffm.csv', 'VariableNamingRule','preserve')

T1 = 8393×6 table
       Var1       Mkt-RF     SMB      HML      RMW      CMA 
    __________    ______    _____    _____    _____    _____

    1.9901e+07     0.99         0    -0.56     0.43    -0.25
    1.9901e+07     0.33     -0.09        0     0.02     0.28
    1.9901e+07     0.24      0.03    -0.19    -0.09     0.23
    1.9901e+07    -0.64      0.22     0.08    -0.36     0.07
    1.9901e+07     0.07     -0.24     0.13     0.02     0.11
    1.9901e+07     0.49      0.01    -0.25     0.08    -0.19
    1.9901e+07     0.01       0.3    -0.41     0.12     -0.2
    1.9901e+07    -0.34     -0.43    -0.06      0.1     0.25
    1.9901e+07     0.62     -0.18    -0.01     0.21    -0.17
    1.9901e+07     0.48     -0.54     0.01      0.2      0.7
    1.9901e+07      0.3     -0.25    -0.24     0.02    -0.11
    1.9901e+07     0.56      0.11     0.28    -0.17    -0.29
    1.9901e+07     0.11     -0.07    -0.03    -0.28     0.02
    1.9901e+07    -0.15      0.33    -0.17     0.01     0.15
    1.9901e+07     0.34     -0.09     0.11    -0.05     0.03
    1.9901e+07    -0.07      0.63    -0.04    -0.19      0.1

T1.Var1 = datetime(string(T1.Var1), 'InputFormat',"yyyyMMdd");      % Create 'daterime' Array
TT1 = table2timetable(T1);                                          % Convert To 'timetable'
popvar = @(x) sum((x - mean(x)).^2)/numel(x);                       % Population Variance
TT1 = retime(TT1, 'monthly', @(x)popvar(x))                         % Monthly Variances For Each VAriable

TT1 = 386×5 timetable
       Var1        Mkt-RF       SMB         HML         RMW         CMA   
    ___________    _______    ________    ________    ________    ________

    01-Jul-1990    0.20209    0.079785    0.040261    0.028357    0.052715
    01-Aug-1990     1.5774     0.54992     0.11199     0.11584     0.10348
    01-Sep-1990    0.72235     0.18843    0.025233    0.034739      0.1206
    01-Oct-1990     1.2826     0.45467    0.033234     0.13269     0.26636
    01-Nov-1990     0.4126      0.1588    0.016932    0.034206    0.062261
    01-Dec-1990     1.1286     0.18742     0.03072    0.034776    0.035376
    01-Jan-1991       2.29     0.47251    0.024327     0.02668    0.051712
    01-Feb-1991    0.45675     0.22646    0.054133    0.020523    0.038269
    01-Mar-1991     1.2407      0.2562    0.027485    0.034653    0.081138
    01-Apr-1991     1.4353     0.15142    0.021445     0.02436    0.060899
    01-May-1991    0.61361    0.089571    0.013503    0.011822    0.042876
    01-Jun-1991    0.42029     0.17484    0.018303    0.019004    0.019435
    01-Jul-1991     0.6321     0.11613    0.031678    0.020199    0.021445
    01-Aug-1991     4.3165     0.28642    0.091536    0.042631    0.046931
    01-Sep-1991     0.2568    0.035454    0.017548    0.013641    0.025187
    01-Oct-1991    0.44615    0.077477    0.014712    0.029558    0.012857

NOTE — MATLAB calculates the ‘sample variance’ referred to in that link by default, as noted in the var documentation section on More About. So, this (using ‘popvar’) will produce the correct result.

.

[neda fathi]

Many thanks!

[Star Strider]

As always, my pleasure!