---
template: overrides/main.html
title: AOLS - Visão Geral
---
# AOLS - Visão Geral
Exemplo criado por Wilson Rocha Lacerda Junior
> **Procurando mais detalhes sobre modelos NARMAX?**
> Para informações completas sobre modelos, métodos e uma ampla variedade de exemplos e benchmarks implementados no SysIdentPy, confira nosso livro:
> [*Nonlinear System Identification and Forecasting: Theory and Practice With SysIdentPy*](https://sysidentpy.org/book/0%20-%20Preface/)
>
> Este livro oferece orientação aprofundada para apoiar seu trabalho com o SysIdentPy.
```python
import pandas as pd
from sysidentpy.utils.generate_data import get_siso_data
from sysidentpy.metrics import root_relative_squared_error
from sysidentpy.basis_function import Polynomial
from sysidentpy.utils.display_results import results
from sysidentpy.utils.plotting import plot_residues_correlation, plot_results
from sysidentpy.residues.residues_correlation import (
compute_residues_autocorrelation,
compute_cross_correlation,
)
from sysidentpy.model_structure_selection import AOLS
# gerando dados simulados
x_train, x_test, y_train, y_test = get_siso_data(
n=1000, colored_noise=False, sigma=0.001, train_percentage=90
)
```
```python
basis_function = Polynomial(degree=2)
model = AOLS(xlag=3, ylag=3, k=5, L=1, basis_function=basis_function)
model.fit(X=x_train, y=y_train)
```
```python
yhat = model.predict(X=x_test, y=y_test)
rrse = root_relative_squared_error(y_test, yhat)
print(rrse)
r = pd.DataFrame(
results(
model.final_model,
model.theta,
model.err,
model.n_terms,
err_precision=8,
dtype="sci",
),
columns=["Regressors", "Parameters", "ERR"],
)
print(r)
```
0.0018996279285613828
Regressors Parameters ERR
0 y(k-1) 1.9999E-01 0.00000000E+00
1 x1(k-2) 9.0003E-01 0.00000000E+00
2 x1(k-1)y(k-1) 9.9954E-02 0.00000000E+00
3 x1(k-3)y(k-1) -2.1442E-04 0.00000000E+00
4 x1(k-1)^2 3.3714E-04 0.00000000E+00
```python
plot_results(y=y_test, yhat=yhat, n=1000)
ee = compute_residues_autocorrelation(y_test, yhat)
plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$")
x1e = compute_cross_correlation(y_test, yhat, x_test)
plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
```
