Financial Time-Series Rebinning

Working with financial time-series, especially in trading and its following analysis of data trends or so on, we wish to rebin (resample) our data into a new time-series which would provide us with some sort of a new information on the average value of the underlying data records characterized by high volatility in time.

The following algorithm in Maltab does the job pretty well:

% Function rebins any time-series [x,y] where x is a time vector
%   and y stores time-series values from the current (regular or
%   irregular samping). A new time-series sampling is dt.
%
%  Input: x  : time vector [1xN]
%         y  : data vector [1xN]
%         dy : data error vector [1xN]
%         dt : new rebinning time (dt > current sampling)
%
% (c) 2013, QuantAtRisk.com, by Pawel Lachowicz
%
% Example: x=1:1:1001; % assume 1001 trading days
%          y=rand(1,1001); % simulate pseudo data
%          dy=0.1*rand(1,1001); % simulate pseudo data errors (if required)
%          dt=50; % rebin data from 1 day sampling down to 50 day intervals
%          [rx,ry]=rebin(x,y,dy,dt);
%      or  [rx,ry]=rebin(x,y,[],dt];
%          plot(x,y,'color',[0.7 0.7 0.7]); % plot original time-series
%          hold on; plot(rx,ry,'ro-'); % plot down-rebined time-series

function [rx,ry]=rebin(x,y,dy,dt)
    if(isempty(dy))
        dy=ones(1,length(y));
    end
    rdata=[];
    j=1;
    k=1;
    t2=x(1);
    while(j<=length(x))
        i=j;
        if((x(i)+dt)>x(end))
            break
        else
            t2=t2+dt;
        end
        i=j;
        sa=0;
        wa=0;
        ea=0;
        il=0;
        while(x(i)<t2)
            sa=sa+(y(i)/dy(i)^2);
            wa=wa+(1/dy(i)^2);
            i=i+1;
            il=il+1;
        end
        ry=sa/wa;
        rx=t2-dt;
        if(il>=1)
            rdata=[rdata; rx ry];
        end
        j=j+il;
    end
    rx=rdata(:,1);
    ry=rdata(:,2);
end

Example

As an example we will use the daily rate of returns in trading of AAPL (Apple Inc.) from Jan-1984 to Apr-2011 (download Matlab’s aaplr.mat M-file). Below, the short set of command lines allow us to execute the rebinning process of return series,

clear all; close all; clc;

load aaplr.mat
plot(aaplR)

x=1:length(aaplR); % 6855 days
y=aaplR;
plot(x,y,'color',[0.7 0.7 0.7]);

% rebin the data with dt=25 days step (one trading month)
dt=25;
dy=[]; % we have no information on data errors

[rx,ry]=rebin(x,y,dy,dt)

% overplot results and display first 500 days
hold on; plot(rx,ry,'ro-');
xlim([0 500]);
ylim([-0.125 0.15]);

and plot both time-series, original and rebinned with a new bin time of 25 days for the first 500 days of trading:

where a red line denotes a new rebinned data time-series with a binning time of 25 trading days. The function (the algorithm) computes a simple weighted mean based on data points falling into an interval of $\langle t,t+dt \rangle$. If we do not specify the input data error vector of $dy$ as in the example above, we should get a simple mean as a consequence.