How to estimate the summation equation quickly in Matlab?

I have to estimate PCi for 6 series. I have a dataset with daily data for 2 months which has DATE in format yyyy-mm-dd and 6 return series P1,P2,P3,P4,P5,P6 for day t.

I need to estimate the equation given as image for each month. I have to estimate PC1 to PC6 for all 6 series. Kindly guide how to code it fast.

In this equation t is day and T is month ; i is 6 prices series.

[NS]

any help on this?

[NS]

Kindly reply?

[Guillaume]

In this equation t is day and T is month

I doubt that. normally means sum from t=1 up to t=T.

Of course, we have absolutely no idea what and stand for (and in particular why some r have two indices and others only one), nor what the X symbol stands for.

It's also not clear what you mean by estimate (as opposed to just calculate)

[NS]

Dear Sir

1. You are right t= 1 day and t is from 1 to T. This capital T means number of days in a month.
2. r i,t is the return for series i as I have 6 return series so i is from 1 to 6 in six. (Basically it is return for 6 different hours in a day)
3. r t is return for all the 6 series combined (It is the close to close return for entire day)
4. X symbol is multiplication sign
5. I meant to calculate

Kindly suggest how to code the same efficiently.

[Guillaume]

r t is return for all the 6 series combined (It is the close to close return for entire day)

I have no idea what that means, so don't know how to calculate from the data you have.

Also specify how the input data is currently stored in matlab (a timetable ideally)

[NS]

Sir I have uploaded a dataset that matched my input data file from which i need to calculate PC for each hour.Kindly see.

[NS]

Since i have R2016a i dont have access to timetable feature.

[Guillaume]

As I've written:

r t is return for all the 6 series combined (It is the close to close return for entire day)

I have no idea what that means, so don't know how to calculate from the data you have.

[NS]

Sir in data file rt is given as ReturnforDay.

[NS]

We just have to calculate the sum of absolute return for the month for denominator of second part of the above equation.

If you break this equation into two parts first part gives the contribution of return of Hour i to Return of the day t. The second part of the equation is contribution of absolute Return of Day t to Sum of absolute Return of the Month i.e. (weighting factor for day in a month) .

Answer 1

[Guillaume]

If I've understood your formula correctly:

returns = readtable('PC Example.xlsx');   %read the data
[year, month] = ymd(returns.DATE);        %extract year and month
[bin, binyear, binmonth] = findgroups(year, month);  %bin all days of the same year/month combination together

%pcifun is a function that applies to a monthly matrix of 7 columns (returns)
%the first column (returns(:, 1)) is rt, column 2:7 (returns(:, 2:end) are rit.
%the function returns a 1x6 vector according to the given formula
pcifun = @(returns) sum(returns(:, 2:end) ./ returns(:, 1).* abs(returns(:, 1)) / sum(abs(returns(:, 1))), 1);

pcis = splitapply(pcifun, returns{:, 2:end}, bin);  %apply the function to each bin (month)
result = array2table([binyear, binmonth, pcis], 'VariableNames', {'year', 'month', 'pci1', 'pci2', 'pci3', 'pci4', 'pci5', 'pci6'})  %convert to table for better display

Note: I've done my best to use functions that exist in R2016a, I may have got it wrong.

[NS]

Thank you sir. Let me check with my data. Thanks for all the help.