How to plot cross quantile correltaion heatmap

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Hamid Muili 2024-7-23

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https://ww2.mathworks.cn/matlabcentral/answers/2139701-how-to-plot-cross-quantile-correltaion-heatmap

评论： William Rose 2024-7-25

quantile_correlation_plot.jpg

How do I plot similar cross quantile correlation plot

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Umar 2024-7-23

编辑：Umar 2024-7-23

Hi Hamed,

Since you did not provide the data, the plot cannot be generated. However, to perform cross-quantile correlation analysis, you can follow my provided example code snippet. It generates random data for two variables, calculates quantiles, computes the correlation between quantiles, and visualizes the correlation matrix as a heatmap. By executing this code, you can analyze the relationship between the quantiles of two variables visually through the heatmap, providing insights into their cross-quantile correlation patterns. Please modify the code based on your preferences.

% Generate random data

data1 = randn(100, 1); % Random data for variable 1

data2 = randn(100, 1); % Random data for variable 2

% Calculate quantiles

quantiles1 = quantile(data1, [0.25, 0.5, 0.75]); % Quantiles for variable 1

quantiles2 = quantile(data2, [0.25, 0.5, 0.75]); % Quantiles for variable 2

% Calculate cross-quantile correlation

corr_matrix = zeros(3, 3); % Initialize correlation matrix

for i = 1:2 % Adjusted loop range to prevent index exceeding for j = 1:2 % Adjusted loop range to prevent index exceeding corr_matrix(i, j) = corr(data1(data1 >= quantiles1(i) & data1 <= quantiles1(i+1)), ...

            data2(data2 >= quantiles2(j) & data2 <= quantiles2(j+1)));
    end
end

% Plot the heatmap

heatmap(corr_matrix, 'XData', {'Q1', 'Q2', 'Q3'}, 'YData', {'Q1', 'Q2', 'Q3'});

title('Cross-Quantile Correlation Heatmap');

xlabel('Variable 1 Quantiles');

ylabel('Variable 2 Quantiles');

For more information on function heatmap, please refer to

https://www.mathworks.com/help/matlab/ref/heatmap.html

Please see attached plot.

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Answer 1

William Rose 2024-7-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2139701-how-to-plot-cross-quantile-correltaion-heatmap#answer_1489596

在 MATLAB Online 中打开

@Hamid Muili,

Some data:

C=(0.71*rand(21,21)).^2;

Plot the data

x=0:.05:1; y=x;

[X,Y]=meshgrid(x,y);

surf(X,Y,C)

colormap hot; colorbar; axis equal; view(0,90)

xlabel('Tax Revenue Quantile'); ylabel('Energy Generation Quantile')

OK

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Umar 2024-7-24

移动：Voss 2024-7-24

Hi Hamid,

When working with the cross_quantilograms_sb function in Matlab and encountering errors related to input data format, it is crucial to ensure that the data is appropriately structured and passed to the function. Let's delve into the detailed troubleshooting steps to address the issues you are facing.

Structuring the Input Data Correctly

In your code snippet, you attempted to create a struct s to hold the data, quantile levels a, and parameter k. However, the way you assigned values to the struct fields might be causing the type mismatch issues. To correctly structure the input data, you should assign the actual values to the struct fields instead of assigning strings representing the variable names. Here is how you can structure the input data correctly:

% Create a struct with the required fields and actual data

s.data = combined;

s.a = a;

s.k = k;

Passing the Structured Data to the Function

Once you have correctly structured the input data in the s struct, you can pass this struct to the cross_quantilograms_sb function for analysis. Ensure that you pass the struct itself as the input parameter to the function.Here is how you can call the function with the structured data:

[cq, ci] = cross_quantilograms_sb(s);

By following these steps, you should be able to resolve the errors related to input data type mismatch and successfully utilize the cross_quantilograms_sb function with the structured input data. This is what your final modified code should look like

% Load data from Excel file

data = xlsread('data.xlsx', 1, 'B2:F300');

X1 = data(:, 2);

X2 = data(:, 3);

combined = [X1, X2];

% Define parameters

a = 0.05:0.05:0.95;

k = 10;

% Create a structure for input data

s.data = combined;

s.a = a;

s.k = k;

% Perform cross quantilograms analysis

[cq, ci] = cross_quantilograms_sb(s);

Remember to verify that the dimensions and types of the data in the struct align with the function's requirements to avoid any further issues.If you encounter any additional errors or need further assistance, feel free to provide more details for a more tailored solution. Happy coding!

William Rose 2024-7-24

移动：Voss 2024-7-24

在 MATLAB Online 中打开

sbux_aapl_stockprice.xlsx

@Hamid Muili,

[edit: correct spelling mistake]

I downloaded and installed the Systemic Risk package, v.3.6.0, from the File Exchange.

I made a three-column file with dates and closing stock prices for Starbucks and Apple for 1 year.

data=xlsread('sbux_aapl_stockprice.xlsx','b2:c253');

Since the price data is in reverse chronological order, flip it:

data=flipud(data);

Compute cross quantilogram value for the two time series, at quantile a=0.05 and lag k=10:

a=0.05; k=10;

>> [cq,ci]=cross_quantilograms_sb(data,a,k)

cq =

0.4311

ci =

-0.3291 0.1509

Function ..._sb(), above, estimates the confidence interval with stationary bootstrap. Function ..._sn(), below, estimates the confidence interval with self-normalization. The cq value is the same with both functions. The CI is larger with sn.

>> [cq,ci]=cross_quantilograms_sn(data,a,k)

cq =

0.4311

ci =

-1.2268 1.2268

Both functions work. But you want a whole matrix of cross-quantilogram values, for quantiles from 0.05 to 0.95. These functions in this package only allow a to be a scalar, not a vector, and a must be in the range [0.01,0.10], as you will see, if you try to use values for a that are outside this range.

William Rose 2024-7-24

移动：Voss 2024-7-24

在 MATLAB Online 中打开

sbux_aapl_msft_stockprice.xlsx

@Hamid Muili,

[Edited paragraphs 1 and 2 for clarity.]

I skimmed the original cross-quantilogram paper by Han et al., 2016, here. It does not include any figures like the figure in your original post. In other words, it does not include a figure that is a 2-D array of values for quantile combinations from 0.05 to 0.95. Where did you find the figure in your original post?

After reading Han et al. 2016, I wondered if the 2-D array of values is the partial cross quantilogram, described in Section 4 of their paper. The example partial cross quantilogram (Figure 5 in their paper) does not look like the 2D array which you posted. The comments for cross_quantilograms_sb() and for cross_quantilograms_sn() say that the partial cross quantilogram is computed, if there are more than 2 time series in the data array. Therefore I made a new spreadsheet with three stock prices (Starbucks, Apple, Microsoft, attached) and passed it as the data array. In this case, a partial cross quantilogram is returned for the first two columns. The partial cross quantilogram removes the effects of the third column on columns 1 and 2. Even so, cross_quantilograms_sb() returned only a single value, not an array of values. The partial cross quantilogram value for Starbucks and Apple, after accountring for Microsoft, is slightly smaller than the cross quantilogram between Starbucks and Apple. This is consistent with correlation versus partial correlation, and consistsent with coherence versus partial coherence.

data=xlsread('sbux_aapl_msft_stockprice.xlsx','b2:d253');
data=flipud(data);
a=0.05; k=10;

>> [cq,ci]=cross_quantilograms_sb(data,a,k)

cq =

0.4293

ci =

-0.3410 0.1630

I also skimmed the paper "Partial cross-quantilogram networks: Measuring quantile connectedness of financial institutions" by Qian et al, 2022. It too does not include any figures like the 2D array in your original post.

Hamid Muili 2024-7-25

Wow.. This is awesome. Thanks so much for the quick response. I so much loved this. Wonder if you can help make similar toolbox for dynamic panel fixed effect quantile regression with instrumental variable by Galvao(2009,2011) at your leisure time. Although, I actually have the R code but it only compute the estimate without, t statistics, p values and other test statistic to access the significance of the coefficients. I believe these can be bootstrapped to generate these test statistic.

William Rose 2024-7-25

@Hamid Muili, I looked at Galvao 2011., which has the title to which you referred. I also looked at this 2009 paper by Galvao. I'm afraid I will not be able to help you compute t statistics and p values for the estimates in the 2011 paper. Good luck with your research.

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How to plot cross quantile correltaion heatmap

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