Consider the following example:
% RANDOM DATA
startDate = datetime(2018,01,01);
endDate = datetime(2018,04,01);
xTimeSpan = startDate:days(1):endDate;
yData = rand(1,length(xTimeSpan)).*randi([25,75],1,length(xTimeSpan));
% calculationg moving mean
wSize = 10; % window size
mMean = movmean(yData,wSize,'omitnan','Endpoints','shrink');
% find the specific start-end dates (in your case beginning/end of year)
% i.e
StartRangeDate = datetime(2018,01,15);
EndRangeDate = datetime(2018,02,15);
% condition vector
cond = (xTimeSpan == StartRangeDate) | (xTimeSpan == EndRangeDate);
% values for moving mean in your range
yStartEndRange = mMean(cond);
figure
plot(xTimeSpan,yData);
hold on
plot(xTimeSpan,mMean);
plot(xTimeSpan(cond),yStartEndRange,'or')
The output:
You'll see that some of the functions that you need (i.e moving average ) if not all are already available in Matlab so all you have to do is read up the documentation to understand how to use them.
