Fourier Transform

[paulb]

Good morning

I have acquired eviews a few months ago and started to use it for real only recently. I have seen that a series could be frequency filtered but have not found a way to get its Fourier transform. Is there any such way ?

Thanks in advance

Paul

[paulb]

Hello

Anyone knows how to do a spectral analysis of à time series with eviews ?

Thanks for any answer.

Paul

[EViews Chris]

I'm afraid EViews doesn't have any built in procedures that calculate the fourier transform of a series.

The problem is at least partially that EViews doesn't currently support complex numbers, so it's not clear how we would return the results to the user.

If you're interested in the fourier transform mainly for looking at the power spectrum of a series rather than for more general use, one way to do this is to estimate an ARMA model and plot the theoertical power spectrum of the ARMA process.

The following program shows the general idea (although the axis labelling could certainly be improved upon):

Code: Select all

'create some test data create u 2000 series z= nrnd series x = 0 smpl @first+4 @last series x = .6*x(-3) + z 'generate a series with a non-flat spectrum smpl @all 'estimate an arma(4,1) model on the data series x ls x c ar(1) ar(2) ar(3) ar(4) ma(1) 'extract arma coefs into car and cma vectors Vector(4) car 'ar coefs car(1) = c(2) car(2) = c(3) car(3) = c(4) car(4) = c(5) Vector(1) cma 'ma coefs cma(1) = c(6) 'calculate spectrum Vector(100) f 'vector for output !n = @rows(f)-1 !pi = 4 * @atan(1) !step = !pi / !n 'numerator is PI for !i = 0 to !n !omega = !step * !i 'evaluate ma polynomial for complex value e^(-i * omega) !ma_r = 1.0 !ma_i = 0.0 for !j=1 to @rows(cma) !temp = !omega * !j !ma_r = !ma_r + cma(!j) * cos(!temp) !ma_i = !ma_i + cma(!j) * sin(!temp) next !ma_i = -!ma_i 'change e^(i omega) to e^(-i omega) 'evaluate ar polynomial for complex value e^(-i * omega) !ar_r = 1.0 !ar_i = 0.0 for !j = 1 to @rows(car) !temp = !omega * !j !ar_r = !ar_r - car(!j) * cos(!temp) !ar_i = !ar_i - car(!j) * sin(!temp) next !ar_i = -!ar_i 'change e^(i omega) to e^(-i omega) 'do complex divide: ma(e^(-i omega)) / ar(e^(-i * omega)) !s = @abs(!ar_r) + @abs(!ar_i) if(!s <> 0.0) then 'normal case !one_on_s = 1.0 / !s !ma_r = !ma_r * !one_on_s !ma_i = !ma_i * !one_on_s !ar_r = !ar_r * !one_on_s !ar_i = !ar_i * !one_on_s !denom = !ar_r*!ar_r + !ar_i*!ar_i !f_r = (!ma_r * !ar_r + !ma_i * !ar_i) / !denom !f_i = (!ma_i * !ar_r - !ma_r * !ar_i) / !denom else 'we've hit a 'pole' (root in ar) !f_r = !ma_r / 0 !f_i = !ma_i / 0 endif 'take squared norm of complex f and scale for final spectrum f(!i+1) = !f_r*!f_r + !f_i*!f_i next 'show the results show f f.line

[paulb]

Thanks a lot Chris

I'll try yout program.

Regards

Paul