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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _generate_noise_temporal_autoregression(timepoints, noise_dict, dimensions, mask, ):
 """Generate the autoregression noise Make a slowly drifting timecourse with the given autoregression parameters. This can take in both AR and MA components Parameters timepoints : 1 Dimensional array What time points are sampled by a TR noise_dict : dict A dictionary specifying the types of noise in this experiment. The noise types interact in important ways. First, all noise types ending with sigma (e.g. motion sigma) are mixed together in _generate_temporal_noise. The sigma values describe the proportion of mixing of these elements. However critically, SFNR is the parameter that describes how much noise these components contribute to the brain. If you set the noise dict to matched then it will fit the parameters to match the participant as best as possible. dimensions : 3 length array, int What is the shape of the volume to be generated mask : 3 dimensional array, binary The masked brain, thresholded to distinguish brain and non-brain Returns noise_autoregression : one dimensional array, float Generates the autoregression noise timecourse """


    # Pull out the relevant noise parameters
    auto_reg_rho = noise_dict['auto_reg_rho']
    ma_rho = noise_dict['ma_rho']

    # Specify the order based on the number of rho supplied
    auto_reg_order = len(auto_reg_rho)
    ma_order = len(ma_rho)

    # This code assumes that the AR order is higher than the MA order
    if ma_order > auto_reg_order:
        msg = 'MA order (%d) is greater than AR order (%d). Cannot run.' % (
            ma_order, auto_reg_order)
        raise ValueError(msg)

    # Generate a random variable at each time point that is a decayed value
    # of the previous time points
    noise_autoregression = np.zeros((dimensions[0], dimensions[1],
                                     dimensions[2], len(timepoints)))
    err_vols = np.zeros((dimensions[0], dimensions[1], dimensions[2],
                         len(timepoints)))
    for tr_counter in range(len(timepoints)):

        # Create a brain shaped volume with appropriate smoothing properties
        noise = _generate_noise_spatial(dimensions=dimensions,
                                        mask=mask,
                                        fwhm=noise_dict['fwhm'],
                                        )

        # Store all of the noise volumes
        err_vols[:, :, :, tr_counter] = noise

        if tr_counter == 0:
            noise_autoregression[:, :, :, tr_counter] = noise

        else:

            # Preset the volume to collect the AR estimated process
            AR_vol = np.zeros((dimensions[0], dimensions[1], dimensions[2]))

            # Iterate through both the AR and MA values
            for pCounter in list(range(1, auto_reg_order + 1)):
                past_TR = int(tr_counter - pCounter)

                if tr_counter - pCounter >= 0:

                    # Pull out a previous TR
                    past_vols = noise_autoregression[:, :, :, past_TR]

                    # Add the discounted previous volume
                    AR_vol += past_vols * auto_reg_rho[pCounter - 1]

                    # If the MA order has at least this many coefficients
                    # then consider the error terms
                    if ma_order >= pCounter:

                        # Pull out a previous TR
                        past_noise = err_vols[:, :, :, past_TR]

                        # Add the discounted previous noise
                        AR_vol += past_noise * ma_rho[pCounter - 1]

            noise_autoregression[:, :, :, tr_counter] = AR_vol + noise

    # Z score the data so that all of the standard deviations of the voxels
    # are one (but the ARMA coefs are unchanged)
    noise_autoregression = stats.zscore(noise_autoregression, 3)

    return noise_autoregression