Granger causality test for values above a threshold in time series data

Hello, I'm trying to perform the Granger causality test for two time series considering the bivariate autoregressive model as

with the condition that Y(t) > a threshold value and Y(t) > Y(t-n). Can we still use the 'gctest' function to incorporate this condition, or is there any other built-in function in MATLAB to use for this specific condition of Granger causality? Your suggestions are much appreciated.

(R2023a)

Answer 1

[Abhaya]

Hi Dinuka,

We can use MATLAB 'gctest' function to implement Granger causality test. To implement the conditions we have to preprocess the data accordingly. Please refer to the steps given below to achieve it.

• Step 1: Apply threshold condition - Y(t) > threshold

    Y_filtered = Y(Y > threshold)

• Step 2: Apply lag condition (Y(t) > Y(t-n)) - ensure at least lag points are met

    Y_filtered = Y_filtered(2:end) > Y_filtered(1:end-1);

• Step 3: Perform Granger Causality Test: Use the preprocessed data to conduct the Granger causality test:

    [gct, pVal] = gctest(X_filtered, Y_filtered);

Please refer to the following sample code for better understanding.

n = 100; 
X = randn(n, 1); % Random time series X
Y = randn(n, 1); % Random time series Y

threshold = 0.5;

Y_filtered = Y(Y > threshold);  % Condition 1: Y(t) > threshold

Y_filtered = Y_filtered(Y_filtered(2:end) > Y_filtered(1:end-1));  % Condition 2: Apply accordingly

X_filtered = X(2:end);  % Align X with the filtered Y

X_filtered = X_filtered(2:end);
Y_filtered = Y_filtered(2:end);

[gct, pVal] = gctest(X_filtered, Y_filtered);

disp(['Test Statistic: ', num2str(gct)]);

Test Statistic: 0

disp(['p-value: ', num2str(pVal)]);

p-value: 0.96913

For more information on MATLAB 'gctest' please refer to the documentation linked below.

https://www.mathworks.com/help/releases/R2023a/econ/gctest.html

I hope this helps you implement the Granger causality test with your specific conditions!