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

This post provides a complete treatment of Autoencoders & VAE with mathematical foundations, Python/R implementations, and connections to public health ML research.

# Full implementation available at github.com/muhammadsalek
import numpy as np, pandas as pd
from scipy import stats
print('Post #96: Autoencoders & VAE')

Series Index | Post #96/100 | Md Salek Miah | saleksta@gmail.com

This post provides a complete treatment of Vanishing & Exploding Gradients with mathematical foundations, Python/R implementations, and connections to public health ML research.

# Full implementation available at github.com/muhammadsalek
import numpy as np, pandas as pd
from scipy import stats
print('Post #95: Vanishing & Exploding Gradients')

Series Index | Post #95/100 | Md Salek Miah | saleksta@gmail.com

This post provides a complete treatment of Weight Initialization Strategies with mathematical foundations, Python/R implementations, and connections to public health ML research.

# Full implementation available at github.com/muhammadsalek
import numpy as np, pandas as pd
from scipy import stats
print('Post #94: Weight Initialization Strategies')

Series Index | Post #94/100 | Md Salek Miah | saleksta@gmail.com

This post provides a complete treatment of Dropout as Regularization with mathematical foundations, Python/R implementations, and connections to public health ML research.

# Full implementation available at github.com/muhammadsalek
import numpy as np, pandas as pd
from scipy import stats
print('Post #93: Dropout as Regularization')

Series Index | Post #93/100 | Md Salek Miah | saleksta@gmail.com

This post provides a complete treatment of Batch Normalization with mathematical foundations, Python/R implementations, and connections to public health ML research.

# Full implementation available at github.com/muhammadsalek
import numpy as np, pandas as pd
from scipy import stats
print('Post #92: Batch Normalization')

Series Index | Post #92/100 | Md Salek Miah | saleksta@gmail.com

This post provides a complete treatment of Activation Functions with mathematical foundations, Python/R implementations, and connections to public health ML research.

# Full implementation available at github.com/muhammadsalek
import numpy as np, pandas as pd
from scipy import stats
print('Post #91: Activation Functions')

Series Index | Post #91/100 | Md Salek Miah | saleksta@gmail.com

This post provides a complete treatment of Backpropagation & Chain Rule with mathematical foundations, Python/R implementations, and connections to public health ML research.

# Full implementation available at github.com/muhammadsalek
import numpy as np, pandas as pd
from scipy import stats
print('Post #90: Backpropagation & Chain Rule')

Series Index | Post #90/100 | Md Salek Miah | saleksta@gmail.com

This post provides a complete treatment of Gradient Descent & Variants with mathematical foundations, Python/R implementations, and connections to public health ML research.

# Full implementation available at github.com/muhammadsalek
import numpy as np, pandas as pd
from scipy import stats
print('Post #89: Gradient Descent & Variants')

Series Index | Post #89/100 | Md Salek Miah | saleksta@gmail.com