Python periodogram Examples

Example #1

File: solution_estspec_ex1.py Project: YixiaoZhou/quant-econ

import numpy as np
import matplotlib.pyplot as plt
from linproc import linearProcess
from estspec import periodogram

## Data
n = 400
phi = 0.5
theta = 0, -0.8
lp = linearProcess(phi, theta)
X = lp.simulation(ts_length=n)

fig, ax = plt.subplots(3, 1)

for i, wl in enumerate((15, 55, 175)):  # window lengths
    
    x, y = periodogram(X)
    ax[i].plot(x, y, 'b-', lw=2, alpha=0.5, label='periodogram')

    x_sd, y_sd = lp.spectral_density(two_pi=False, resolution=120)
    ax[i].plot(x_sd, y_sd, 'r-', lw=2, alpha=0.8, label='spectral density')

    x, y_smoothed = periodogram(X, window='hamming', window_len=wl)
    ax[i].plot(x, y_smoothed, 'k-', lw=2, label='smoothed periodogram')

    ax[i].legend()
    ax[i].set_title('window length = {}'.format(wl))

fig.show()

Example #2

import numpy as np
import matplotlib.pyplot as plt
from linproc import linearProcess
from estspec import periodogram

## Data
n = 400
phi = 0.5
theta = 0, -0.8
lp = linearProcess(phi, theta)
X = lp.simulation(ts_length=n)

fig, ax = plt.subplots(3, 1)

for i, wl in enumerate((15, 55, 175)):  # window lengths

    x, y = periodogram(X)
    ax[i].plot(x, y, 'b-', lw=2, alpha=0.5, label='periodogram')

    x_sd, y_sd = lp.spectral_density(two_pi=False, resolution=120)
    ax[i].plot(x_sd, y_sd, 'r-', lw=2, alpha=0.8, label='spectral density')

    x, y_smoothed = periodogram(X, window='hamming', window_len=wl)
    ax[i].plot(x, y_smoothed, 'k-', lw=2, label='smoothed periodogram')

    ax[i].legend()
    ax[i].set_title('window length = {}'.format(wl))

plt.show()

Example #3

fig, ax = plt.subplots(3, 1)

for i in range(3):
    X = lp.simulation(ts_length=150)
    ax[i].set_xlim(0, np.pi)

    x_sd, y_sd = lp.spectral_density(two_pi=False, resolution=180)
    ax[i].semilogy(x_sd,
                   y_sd,
                   'r-',
                   lw=2,
                   alpha=0.75,
                   label='spectral density')

    x, y_smoothed = estspec.periodogram(X, window='hamming', window_len=wl)
    ax[i].semilogy(x,
                   y_smoothed,
                   'k-',
                   lw=2,
                   alpha=0.75,
                   label='standard smoothed periodogram')

    x, y_ar = estspec.ar_periodogram(X, window='hamming', window_len=wl)
    ax[i].semilogy(x,
                   y_ar,
                   'b-',
                   lw=2,
                   alpha=0.75,
                   label='AR smoothed periodogram')

Example #4

File: solution_estspec_ex2.py Project: YixiaoZhou/quant-econ

import numpy as np
import matplotlib.pyplot as plt
from linproc import linearProcess
import estspec

lp = linearProcess(-0.9)
wl = 65


fig, ax = plt.subplots(3, 1)

for i in range(3):
    X = lp.simulation(ts_length=150)
    ax[i].set_xlim(0, np.pi)

    x_sd, y_sd = lp.spectral_density(two_pi=False, resolution=180)
    ax[i].semilogy(x_sd, y_sd, 'r-', lw=2, alpha=0.75, label='spectral density')

    x, y_smoothed = estspec.periodogram(X, window='hamming', window_len=wl)
    ax[i].semilogy(x, y_smoothed, 'k-', lw=2, alpha=0.75, label='standard smoothed periodogram')

    x, y_ar = estspec.ar_periodogram(X, window='hamming', window_len=wl)
    ax[i].semilogy(x, y_ar, 'b-', lw=2, alpha=0.75, label='AR smoothed periodogram')

    ax[i].legend(loc='upper left')
fig.show()