Statistics for ML #97 — Time Series Analysis: ARIMA, ACF, PACF

Time Series Analysis: ARIMA, ACF, PACF

Time Series Analysis models data collected over time, capturing trends, seasonality, and autocorrelation.

Key Concepts

• Stationarity: Mean, variance, autocorrelation constant over time
• ACF (Autocorrelation Function): Correlation of series with its own lags
• PACF (Partial ACF): Direct correlation at lag k, controlling for shorter lags
• ARIMA(p,d,q): p=AR order, d=differencing, q=MA order

Public Health Application

Trend analysis of water quality index in the Buriganga River (our published research):

import pandas as pd
from statsmodels.tsa.statespace.sarimax import SARIMAX
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

# Our Buriganga WQI trend analysis
wqi_data = pd.read_csv('buriganga_wqi.csv', index_col='date', parse_dates=True)

fig, (ax1, ax2) = plt.subplots(2,1, figsize=(12,8))
plot_acf(wqi_data['WQI'].dropna(), lags=24, ax=ax1)
plot_pacf(wqi_data['WQI'].dropna(), lags=24, ax=ax2)

# Fit SARIMA
model = SARIMAX(wqi_data['WQI'], order=(1,1,1), seasonal_order=(1,1,1,12))
result = model.fit()
print(result.summary())

Series Index | Post #97/100 | Md Salek Miah | saleksta@gmail.com