# Welcome to deFit
Fitting Differential Equations to Time Series Data ( [deFit](https://github.com/yueqinhu/defit) ).
## Overview
### What is deFit?
Use numerical optimization to fit ordinary differential equations (ODEs) to time series data to examine the dynamic relationships between variables or the characteristics of a dynamical system. It can now be used to estimate the parameters of ODEs up to second order.
### Features
* Fit ordinary differential equation models to time series data
* Report model parameter estimations, standard errors, R-squared, and root mean standard error
* Plot raw data points and fitted lines
* Support ordinary differential equation models up to second order
* deFit can run in Python and R environments
### 1.2 First impression in Python
To get a first impression of how deFit works in simulation, consider the following example of a differential equational model. The figure below contains a graphical representation of the model that we want to fit.
```python
import defit
import pandas as pd
df1 = pd.read_csv('defit/data/example1.csv')
model1 = '''
x =~ myX
time =~ myTime
x(2) ~ x + x(1)
'''
result1 = defit.defit(data=df1,model=model1)
```
## 2 Navigation
- [Home](https://github.com/yueqinhu/defit)
- [User guide in R](https://github.com/yueqinhu/defit/blob/main/Documents/UserGuideR.md)
- [User guide in Python](https://github.com/yueqinhu/defit/blob/main/Documents/UserGuidePython.md)
- [issues](https://github.com/yueqinhu/defit/issues)
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