Plotting 1D Conditional Distributions with kdensity stacked in a 3D figure.

Hi guys. It's my first time here and I am not a native English speaker. So, first of all, apologize.

Here is my problem: I have a T x 2 Matrix, where in the second column I have some daily financial returns and in the first column I have an indicator, which can assume integer values in the interval [1, 9].

I want to extract 9 different conditional distributions of my returns, conditioned on the values assumed by the indicator. At this point, I want to plot the conditional densities through a Gaussian smoothing with the function 'ksdensity' and plot them in the same 3D plot. The final output should be similar to this one:

Image

I tried to reach this result by adapting the answer I found at this thread: function.

Now suppose that x = axis of returns, y = axis of indicator possible values, z = smoothed conditional densities.

My problem is that, while the meshgrid requires for all the values of y to share the same values of x by construction, I have different values of x (the returns) because of the conditioning.

I hope I have been clear.

Thanks you guys in advance, and sorry for any mistake.

Answer 1

[Alan]

Hi Mishel,

The waterfall function requires grid data, and it might not be able to construct a grid using the Tx2 matrix you mention. To accomplish a waterfall plot, the following steps can be followed:

1. Filter the Tx2 based on the indicators to form separate arrays for a given indicator. These arrays could have different lengths (I have assumed each indicator to have a random number of returns)
2. Form ksdensity estimates from a fixed set of sample points for every indicator.
3. Stack the ksdensity estimates for each indicator and generate a grid using meshgrid.
4. Plot the data using the waterfal function.

I’ve created an example where the maximum returns is 1000 and the indicators are 1:9. Assume x to be analogous to the first column of T, containing the indicators, and returns to be analogous to the second column of T, containing the financial returns:

% Fix max returns as 1000 
x = randi([1 9], 1, 1000); 
returns = 1000.*rand(1000,1); 
% Using cell arrays due to different lengths of sub arrays 
returns_filtered = repmat({[]}, 1, 9); 
% Filter based on indicators 
for idx = 1:numel(x) 
    returns_filtered{x(idx)}(end+1) = returns(idx); 
end 
% Form pdf approximators evaluated at points 1 to max returns 
returns_distribution = zeros([9 1000], "double"); 
for idx=1:9 
    returns_distribution(idx, :) = ksdensity(returns_filtered{idx}, 1:1000); 
end 
[x_plot, y_plot] = meshgrid(1:1000, 1:9); 
p = waterfall(x_plot, y_plot, returns_distribution); 
p.FaceColor = 'none';

The individual lines shown in the waterfall plot are the conditional PDF approximations for each conditions in [1 9].

I hope this will help you to achieve your solution.