Ex.No: 07 -- AUTO REGRESSIVE MODEL...

Date:

AIM :

To Implement an Auto Regressive Model using Python.

ALGORITHM :

Step 1 :

Import necessary libraries.

Step 2 :

Read the CSV file into a DataFrame.

Step 3 :

Perform Augmented Dickey-Fuller test.

Step 4 :

Split the data into training and testing sets.Fit an AutoRegressive (AR) model with 13 lags.

Step 5 :

Plot Partial Autocorrelation Function (PACF) and Autocorrelation Function (ACF).

Step 6 :

Make predictions using the AR model.Compare the predictions with the test data.

Step 7 :

Calculate Mean Squared Error (MSE).Plot the test data and predictions.

PROGRAM :

Import necessary libraries :

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import adfuller
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.ar_model import AutoReg
from sklearn.metrics import mean_squared_error

Read the CSV file into a DataFrame :

data = pd.read_csv("/content/Temperature.csv")  
data['date'] = pd.to_datetime(data['date'])
data.set_index('date', inplace=True)

Perform Augmented Dickey-Fuller test :

result = adfuller(data['temp']) 
print('ADF Statistic:', result[0])
print('p-value:', result[1])

Split the data into training and testing sets :

train_data = data.iloc[:int(0.8*len(data))]
test_data = data.iloc[int(0.8*len(data)):]

Fit an AutoRegressive (AR) model with 13 lags :

lag_order = 13
model = AutoReg(train_data['temp'], lags=lag_order)
model_fit = model.fit()

Plot Partial Autocorrelation Function (PACF) and Autocorrelation Function (ACF) :

plot_acf(data['temp'])
plt.title('Autocorrelation Function (ACF)')
plt.show()
plot_pacf(data['temp'])
plt.title('Partial Autocorrelation Function (PACF)')
plt.show()

Make predictions using the AR model :

predictions = model_fit.predict(start=len(train_data), end=len(train_data)+len(test_data)-1)

Compare the predictions with the test data :

mse = mean_squared_error(test_data['temp'], predictions)
print('Mean Squared Error (MSE):', mse)

Plot the test data and predictions :

plt.plot(test_data.index, test_data['temp'], label='Test Data')
plt.plot(test_data.index, predictions, label='Predictions')
plt.xlabel('Date')
plt.ylabel('Temperature')
plt.title('AR Model Predictions vs Test Data')
plt.legend()
plt.show()

OUTPUT :

GIVEN DATA :

Augmented Dickey-Fuller test :

PACF - ACF :

Mean Squared Error :

PREDICTION :

RESULT :

Thus, we have successfully implemented the auto regression function using python.

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