Table of Contents
- Introduction
- Prerequisites
- Installing Required Packages
- Overview of Time Series Forecasting
- ARIMA
- SARIMA
- Prophet
- Conclusion
Introduction
In this tutorial, we will learn about time series forecasting using three popular methods in Python: ARIMA, SARIMA, and Prophet. Time series forecasting is a technique used to predict future values based on historical data. By the end of this tutorial, you will have a good understanding of how to use these models to make accurate predictions.
Prerequisites
To follow along with this tutorial, you should have a basic understanding of Python programming and familiarity with the following libraries:
- NumPy
- Pandas
- Matplotlib
Installing Required Packages
Before we begin, let’s make sure we have all the necessary packages installed. Open your terminal or command prompt and execute the following command:
pip install numpy pandas matplotlib statsmodels pystan fbprophet
This will install the required packages for this tutorial.
Overview of Time Series Forecasting
Time series forecasting involves analyzing patterns and trends in the historical data to predict future values. The key components of time series forecasting are:
- Trend: The long-term increase or decrease in the data points.
- Seasonality: Periodic patterns that repeat at fixed intervals (e.g., yearly, monthly, weekly).
- Autocorrelation: The relationship between the current value and previous values in the series.
ARIMA, SARIMA, and Prophet are powerful algorithms that take these components into account and provide accurate predictions based on historical data.
ARIMA
ARIMA stands for AutoRegressive Integrated Moving Average. It is a popular method for time series forecasting, particularly for non-seasonal data. ARIMA models involve three parameters:
- AR (Autoregressive): The dependence between an observation and a certain number of lagged observations.
- I (Integrated): The number of times the raw observations are differenced to make the time series stationary.
- MA (Moving Average): The dependency between an observation and a residual error from a moving average model.
Understanding the AR, MA, and I Terms
The AR parameter captures the relationship between each observation and a certain number of lagged observations. For example, an AR(2) model uses the two previous observations to predict the current one.
The I parameter represents the number of times the data needs to be differenced to make it stationary. Stationary data has a constant mean and variance over time, which simplifies the forecasting process.
The MA term accounts for the dependency between an observation and a residual error from a moving average model. It helps to capture the short-term fluctuations in the data.
Model Order Selection
To determine the order of the ARIMA model, we need to consider the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots. These plots help identify the optimal values for the AR, I, and MA parameters.
To illustrate this, let’s consider an example of forecasting stock prices. We can use the pandas library to load the dataset:
```python
import pandas as pd
data = pd.read_csv('stock_prices.csv')
``` ### Model Fitting and Forecasting
Once we have determined the order of the ARIMA model, we can fit the model to the data and make predictions. We can use the statsmodels library to perform these tasks.
```python
from statsmodels.tsa.arima.model import ARIMA
# Define the order of the ARIMA model
order = (2, 1, 1)
# Fit the ARIMA model
model = ARIMA(data, order=order)
model_fit = model.fit()
# Make predictions
forecast = model_fit.forecast(steps=10)
``` ## SARIMA
SARIMA (Seasonal AutoRegressive Integrated Moving Average) is an extension of the ARIMA model that considers seasonality in the data. It can handle both non-seasonal and seasonal time series.
Seasonal Differencing
Before applying SARIMA, we need to identify and remove the seasonality in the data. Seasonal differencing involves subtracting the observation from the same time in the previous season. ```python from statsmodels.tsa.statespace.sarimax import SARIMAX
# Perform seasonal differencing
data['Seasonal Difference'] = data['Price'] - data['Price'].shift(12)
``` ### Model Order Selection with Seasonality
Similar to the ARIMA model, we need to determine the order of the SARIMA model. A seasonal ARIMA model has additional parameters for the seasonal components.
python
# Determine the order of the SARIMA model
order = (2, 1, 1)
seasonal_order = (1, 1, 1, 12)
Model Fitting and Forecasting with Seasonality
Once we have determined the order and seasonal order of the SARIMA model, we can fit the model to the data and make predictions. ```python # Fit the SARIMA model model = SARIMAX(data, order=order, seasonal_order=seasonal_order) model_fit = model.fit()
# Make predictions
forecast = model_fit.forecast(steps=10)
``` ## Prophet
Prophet is an open-source library developed by Facebook for time series forecasting. It handles multiple seasonality and provides a straightforward interface to use.
Model Fitting and Forecasting with Prophet
To use Prophet, we need to create a DataFrame with the columns ds (the timestamps) and y (the target variable).
```python
from fbprophet import Prophet
# Prepare the data for Prophet
prophet_data = pd.DataFrame({'ds': data.index, 'y': data['Price']})
# Fit the Prophet model
model = Prophet()
model.fit(prophet_data)
# Create future dates for forecasting
future_dates = model.make_future_dataframe(periods=10)
# Make predictions
forecast = model.predict(future_dates)
``` ## Conclusion
In this tutorial, we have learned three popular methods for time series forecasting: ARIMA, SARIMA, and Prophet. These techniques provide accurate predictions by considering different aspects of the time series data. By understanding the underlying concepts and following the step-by-step instructions, you can now apply these models to your own time series forecasting tasks.