2.2 Autocorrelation and Partial Correlation.ipynb

Kernel: Python 3 (ipykernel)

1. Autocorrelation Definition:

Autocorrelation, also called serial correlation, is the correlation of a signal with a delayed copy of itself. It measures how a time series is related to its own previous values.

It seems the dataset size [1, 2, 3, 4, 5, 6, 7, 8] is too small to compute the Partial Autocorrelation Function (PACF) for 7 lags because PACF can only be computed for lags up to 50% of the sample size.

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from statsmodels.graphics.tsaplots import plot_acf

# Generate a sample time series data
np.random.seed(0)
n = 100
time_series_data = pd.Series(np.random.randn(n))

# Plot Autocorrelation
plt.figure(figsize=(15, 0))
plot_acf(time_series_data, lags=20)
plt.show()

<Figure size 1080x0 with 0 Axes>

2. Partial Autocorrelation

• ACF Plot shows how each value in the series is correlated with its lagged values.

• PACF Plot shows the direct correlation between the values and their lagged counterparts after removing the effects of intermediate lags.

from statsmodels.graphics.tsaplots import plot_pacf

# Plot Partial Autocorrelation
plt.figure(figsize=(10, 5))
plot_pacf(time_series_data, lags=30)
plt.show()

<Figure size 720x360 with 0 Axes>

Difference Between Autocorrelation and Partial Autocorrelation:

1- Autocorrelation

• Measure the correlation between a time series and its lagged Values

• ACF plots the Correlation values values against different lasgs

2- Partial

• Measure the corrlation between a time series and its lagged values controlling the effects of intermediate lags.

• PACF curve

Visualizing and Interpreting the Results

Visualizing and Interpreting the Results: The autocorrelation plot (ACF) usually starts at 1 (since a series is perfectly correlated with itself at lag 0) and then decreases as the lag increases. The partial autocorrelation plot (PACF) typically drops sharply after a certain lag, especially in autoregressive processes

Xt   Xt-6