Time-Series Analysis Using Auto ARIMA

Conducting a Univariate Time-Series analysis to forecast the number of airline passengers (from Kaggle) and discuss through the traditional ARIMA implementation versus the more efficient, auto_arima way. All code can be found in Time_Series.ipynb and all images can be found in the Images folder.

What is Time-Series Analysis?

One of the key concepts in data science is time-series analysis which involves the process of using a statistical model to predict future values of a time series (i.e. financial prices, weather, COVID-19 positive cases/deaths) based on past results. Some components that might be seen in a time-series analysis are:

• Trend : Shows a general direction of time series data over a period of time — trends can be increasing (upward), decreasing (downward), or horizontal (stationary).
• Seasonality : This component exhibits a trend that repeats with respect to timing, magnitude, and direction — such as the increase in ice cream sales during the summer months or increase in subway riders during colder months.
• Cyclical Component : A trend that has no set repetition over a certain time period. A cycle can be a period of ups and downs, mostly seen in business cycles — cycles do not exhibit a seasonality trend.
• Irregular Variation : Fluctuations in time-series data that is erratic, unpredictable and may/may not be random. When conducting time-series analysis, there are either Univariate Time-Series analysis or Multivariate Time-Series analysis. Univariate is utilized when only one variable is being observed against time, whereas Multivariate is utilized if there are two or more variables being observed against time.

What is ARIMA? Why Use Pmdarima?

ARIMA is an acronym which stands for Auto Regressive Integrated Moving Average and is a way of modeling time-series data for forecasting and is specified by three order parameters (p,d,q):

• AR(p): pattern of growth/decline in the data is accounted for
• I (d): rate of change of the growth/decline is accounted for
• MA (q): noise between time points is accounted for There are three types of ARIMA models, ARIMA, SARIMA, and SARIMAX which differ depending on seasonality and/or use of exogenous variables. Pmdarima‘s auto_arima function is extremely useful when building an ARIMA model as it helps us identify the most optimal p,d,q parameters and return a fitted ARIMA model.

The general steps to implement an ARIMA model:

1. Load and prepare data
2. Check for stationarity (make data stationary if necessary) and determine d value
3. Create ACF and PACF plots to determine p and q values
4. Fit ARIMA model
5. Predict values on test set
6. Calculate r²

Traditional Implementation of an ARIMA Model

Determining p,d,q values by conducting a Dickey-Fuller test, and using ACF/PACF plots resulted in a r^2 value of -1.52. These results indicate that our model does not follow the trend of the data very well.

Using pmdarima for Auto ARIMA model

In the previous method, checking for stationarity, making data stationary if necessary, and determining the values of p and q using the ACF/PACF plots can be time-consuming and less efficient. Using pmdarima’s auto_arima() function makes this task easier for us by eliminating steps 2 and 3 for implementing an ARIMA model. Let’s try it with the current dataset.

 model=auto_arima(train,start_p=0,d=1,start_q=0,
          max_p=5,max_d=5,max_q=5, start_P=0,
          D=1, start_Q=0, max_P=5,max_D=5,
          max_Q=5, m=12, seasonal=True,
          error_action='warn',trace=True,
          supress_warnings=True,stepwise=True,
          random_state=20,n_fits=50)

Using the trained model to forecast the number of airline passengers on the test set resulted in a r^2 value of 0.65 -- this model did a much better job at capturing the trend in the data compared to my first implementation of the ARIMA model.

Summary

Here we demonstrated the traditional implementation of an ARIMA model compared to the Auto ARIMA model using auto_arima(). While the traditional ARIMA implementation requires one to perform differencing and plotting ACF and PACF plots, the Auto ARIMA model using pmdarima’s auto_arima() function is more efficient in determining the optimal p,d,q values.