Time Series Indexing and Averaging

Outputs windowed means of a continuous set of data given a vector of labels and time stamps

Doing stimulus triggered averaging? Continuous EEG analysis? Want to know what the average hourly barometric pressures were for the last 30 years, but you need individual results for each month?
A common problem in time series analysis is trying to get the average signal that follows (or precedes) a set of time points. This function will output means for an arbitrary set of indices. The function takes as its inputs the time series itself, a vector of labels, and matching time stamps. The output will be an array with mean signal in the rows with a column for each unique label.
Important: the time stamps must be in samples at the sample rate of the time series.

TIMESERIES_INDEXER windows and sums timeseries given time and labels
[mean_data,label_counts] = TIMESERIES_INDEXER(labels,timestamps,win,data)
Given a time series (vector), a set of grouping labels, time stamps,
and an analysis window this function will output an array of mean data.

This is useful for instances where you know when each particular
stimulus type occurred and you wish to find the average response
following (or preceding) these stimuli.

Input args:
labels (int) an array of labels
time (samples) stamps associated with the stimulus labels
win (samples) beginning and end of the analysis window, e.g.,[-10 40]
data (float, int) the time series to analyze

Example:
data = rand(88200,1)+sin(2*pi*5*linspace(0,2,88200)');
labels = [1 2 1 2 1 2 1 2 1 2];
timestamps = linspace(0,44099-4410,10);
win = [-441 4410];
mean_data = TIMESERIES_INDEXER(labels,timestamps,win,data);
plot(mean_data)

Full output can include the pre-meaned data array:
[~,~,full_array] = timeseries_indexer(labels,timestamps,win,data);

Note: The function will return means even if the total counts for each
label are not the same. Care should be taken as the variance in the
means will be higher for labels with fewer instances (this is
unavoidable).

Author: Owen Brimijoin - MRC/CSO Institute of Hearing Research
Date: 03/07/14