# Logistic in Time Series Data

I want to use logistic regression, but my data are time series data. Every observation is a different day, and I have days consecutively for 20 years. I have three variables(the predictors) that are daily measurements in these 20 years. My dependent variable is if it snows or not that day. I cannot use Logistic regression because the data are not independent. I was thinking of generalized estimating equations, but the data are neither clustered nor longitudinal. Any idea?

• A good place for a Markov logistic model. See last chapter of hbiostat.org/doc/rms.pdf Aug 14, 2022 at 12:02

I'm not sure if that's legit but you can still use GEE. If I were you I would define an autoregressive working dependence structure (use the PACF and confirm which lags is any are significantly different from zero), covariance type as robust and I would treat all observations as one cluster.

Here's Python code for that:

import statsmodels.api as sm
import statsmodels.formula.api as smf

# Define the GEE model formula
formula = 'target ~ X1 + X2 + X3'

# Define the correlation structure - note that this statsmodels class allows only for a first-order autoregressive working dependence structure. Grid will become default argument in the future release, so to suppress warnings I set this argument to True.
cov_struct = sm.cov_struct.Autoregressive(grid=True)

# Define the GEE model with binary target variable and logistic link function
model = smf.gee(
formula=formula,
data=df,
groups=np.ones(len(df)),
family=sm.families.Binomial(),
cov_struct=cov_struct,
)

# Fit the GEE model
result = model.fit(
maxiter=100,
cov_type='robust',
)

# Print the summary of the model
print(result.summary())