Superposed Epoch Analysis (SEA)

SEA.m function for Superposed Epoch Analysis (SEA) with confidence intervals estimated using block bootstrap procedure, the method is freely inspired from Adams et al. (2003), for an example of using SEA in palaeoecology see Blarquez and Carcaillet (2010). For details please refer to included help.

Example:

Create a random time serie with noise, define some events and plot them along with the time series:

t=1:500;
d=2.5*sin(2*pi*t/100)+1.5*sin(2*pi*t/41)+1*sin(2*pi*t/21);
T=(d+2*randn(size(d))).';
figure()
plot(t,T,'g')
ev=[50,93,131,175,214,257,297,337,381,428,470].';
hold on
plot(ev,repmat(4,length(ev),1),'v')

Screen Shot 2014-02-09 at 11.49.50 AM

Then we perform a SEA using a time window of 20 years before and 20 years after each event. ‘nbboot’ argument is used to define the number of circular block bootsrtap replicates with an automatically calculated block length (‘b’ equal 0) following Adams et al. (2003) procedure.


[SEA_means,SEA_prctiles]=SEA(T,ev,20,20,'prctilesIN',[5,95],'nbboot',9999,'b',0)

Screen Shot 2014-02-09 at 11.54.30 AM

Proxy response to the randomly generated events appears significant at the 95% confidence levels during events occurrence (at a lag close to zero).

Paleofire frequencies

KDffreq.m function calculates palaeo-fire frequency using a Gaussian kernel and computes bootstrapped confidence intervals arround fire frequency. Require the date of fire events as input variable. Associated with this function analyst may use cvKD.mfunction to estimate optimal kernel bandwidth by max log likelihood. Here’s an example:

Generate some fire dates for the last 8000 years:

x=randi(8000,40,1);
plot(x,1,'+','col','red')
set(gca,'xdir','reverse')
xlabel('Time (cal yrs. BP)')

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Use the cvKD.m function to calculate the optimal bandwidth for the kernel:

cvKD(x)
ans = 724.3434

Then we estimate the long term fire frequency using the Gaussian kernel density procedure:

 [ffreq]=KDffreq(x,'up',0,'lo',8000,'bandwidth',700,'nbboot',100,'alpha',0.05 );
 

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