What is the best metric to compute the error for complex time series data?

I have a complex number time series of data for ground truth and estimated values.

I am currently using Mean square error metric to check the quality of my method:

Howver, mean square error obtains only 1 value.

1. Is this correct way to calculate MSE for complex data?
2. Is there any other metric to see instantenous error at every sample of complex valued time series?

Answer 1

[Walter Roberson]

No, that could give you complex numbers, but MSE should be real and non-negative.

https://dsp.stackexchange.com/questions/35808/matlab-what-is-the-proper-way-to-calculate-mean-square-error-for-complex-number shows

mse(abs(h_e-h_true))

[Kalasagarreddi Kottakota]

Hi @Walter Roberson,

With the equation, you suggested and from stackexchnage, I get error using mse function.

h_true = [ 0.7071 + 0.7071i
            0.4243 + 0.4243i
            0.2121 + 0.2121i ];

 h_e = [ 0.8100 + 0.8100i  
         0.5100 + 0.5100i  
        0.1200 + 0.1200i ];

 g= mean(abs(h_e-h_true).^2);

 e = mse(abs(h_e-h_true));