Time-series analysis
Peaks and troughs
Let’s start by creating a random walk.
import numpy as np
import pandas as pd
N = 10000
step_set = [-1, 0, 1]
origin = np.zeros((1, 1))
step_shape = (N, 1)
steps = np.random.choice(a=step_set, size=step_shape)
path = np.concatenate([origin, steps]).cumsum(0)
df = pd.DataFrame(path,
columns =['y'])
df.head()
from scipy.signal import find_peaks
subset = df.head(100)
peaks = find_peaks(subset["y"])
troughs = find_peaks(-subset["y"])
peaks
<AxesSubplot:xlabel='index', ylabel='y'>
Autocorrelation
Pandas provides an autocorrelation1 plot function.
figure(figsize=(14, 7), dpi=80)
pd.plotting.autocorrelation_plot(df["y"])
<AxesSubplot:xlabel='Lag', ylabel='Autocorrelation'>
Differencing
Calculating the difference between \(x_t\) and \(x_{t-1}\).
stationary = df['y'].diff()
figure(figsize=(14, 7), dpi=80)
plt.plot(stationary)
plt.show()
