auto correlation time in matlab

in my assignment, i am asked to "State the autocorrelation time for each variable" (of which i have 2). I have just created 2 time series graphs for 2 datasets for context. I am very confused as to what this means. Please help?

load("RiverData50.mat")

x = RiverData(:,1); % daily discharge of riverdata

x2 = x(1:365); % first 365 days of daily discharge

y = RiverData(:,2); % daily rainfall of riverdata

y2 = y(1:365); % first 365 days of daily rainfall

ts1 = timeseries(x2,1:365);

ts1.Name = 'Daily Discharge (M^3/s)';

ts1.TimeInfo.Units = 'Days';

ts1.TimeInfo.StartDate = '1-Oct-1990'; % start date.

ts1.TimeInfo.Format = 'mmm dd, yy'; % Set format for display on x-axis.

ts1.Time = ts1.Time - ts1.Time(1); % Express time relative to the start date.

ts2 = timeseries(y2,1:365);

ts2.Name = 'Daily Rainfall (mm)';

ts2.TimeInfo.Units = 'Days';

ts2.TimeInfo.StartDate = '1-Oct-1990'; % Setting start date.

ts2.TimeInfo.Format = 'mmm dd, yy'; % Setting format for display on x-axis.

ts2.Time = ts2.Time - ts2.Time(1); % Express time relative to the start date.

subplot(2,1,1)

plot(ts1)

subplot(2,1,2)

plot(ts2)

(my code, if that helps with context at all)

Answer 1

[Bora Eryilmaz]

"Autocorrelation time" most likely means the lag (in days, in your case) where the autocorrelation sequence of your data it at a maximum. See this documentation for additional info: https://www.mathworks.com/help/signal/ug/find-periodicity-using-autocorrelation.html.

The locations of the maxima of the autocorrelation sequence indicate the periodicities in a signal. In this context, the autocorrelation time is the same as the period (in days) of the most prominent periodic component in a signal.