Cubic Spline Interpolation for given data not matching with target data

Question

Data:

data = pd.Series({
    '2005-01': 14.80,
    '2005-02': np.nan,
    '2005-03': np.nan,
    '2005-04': 14.83,
    '2005-05': np.nan,
    '2005-06': np.nan,
    '2005-07': 15.14,
    '2005-08': np.nan,
    '2005-09': np.nan,
    '2005-10': 15.03,
    '2005-11': np.nan,
    '2005-12': np.nan
})

Taget Data:

target_data = pd.Series({
    '2005-01': 14.85,
    '2005-02': 14.76,
    '2005-03': 14.79,
    '2005-04': 14.71,
    '2005-05': 14.83,
    '2005-06': 14.95,
    '2005-07': 15.16,
    '2005-08': 15.16,
    '2005-09': 15.11,
    '2005-10': 15.05,
    '2005-11': 15.02,
    '2005-12': 15.01
})

I'm using below function for interpolation but it's not matching with target, help me match it to it with max acceptable error being mismatch after 4 decimal point.

def interpolate(row):
    row = row.replace("nan", np.nan).astype(float)
    
    first_non_null_index = row.first_valid_index()
    if first_non_null_index is not None:
        non_null_values = row.loc[first_non_null_index:].dropna().values
        
        if len(non_null_values) > 1:
            original_quarterly_values = non_null_values
            quarterly_positions = np.arange(0, len(non_null_values) * 3, 3)
            original_length = len(row.loc[first_non_null_index:])
            interpolation_positions = np.arange(original_length)
            
            #used natural for boundry condition, could that be an issue?
            cs = CubicSpline(quarterly_positions, non_null_values, bc_type="natural")
            interpolated_values = cs(interpolation_positions)
            months)
            interpolated_quarterly_avgs = []
            for i in range(0, len(interpolated_values), 3):
                end_idx = min(i + 3, len(interpolated_values))
                quarterly_avg = np.mean(interpolated_values[i:end_idx])
                interpolated_quarterly_avgs.append(quarterly_avg)
            
            differences = original_quarterly_values - np.array(interpolated_quarterly_avgs)
            
            #making adjustments could this be an issue?
            adjusted_values = interpolated_values.copy()
            for i in range(len(differences)):
                start_idx = i * 3
                end_idx = min(start_idx + 3, len(interpolated_values))
                adjusted_values[start_idx:end_idx] += differences[i]
            
            adjusted_values = np.round(adjusted_values, 3)
            
            row.loc[first_non_null_index:] = adjusted_values
            return row
        else:
            print('Only one non-null value found - cannot interpolate')
            return row
    return row

Tried cubic spline for interpolation but not getting expected output, do I've to change adjustment or bc_type or even use different kind of interpolation techniques ?