Time Series Forecasting Models

ARIMA models vs ETS models

Time!

What is time series forecasting?

Time series forecasting is a technique for predicting future aspects of data, in which we translate past data into estimates of future data. This technique is commonly used in business, as companies need to account for the uncertainty of the future, and being able to forecast data over time offers them a way to prepare for this.

Through the analysis of historical data, we can observe patterns of the data over time and generate forecasts of future data points. These forecasts can be crucial for companies, as they impact both short-term and long-term decision-making and strategic outlook.

In time series forecasting, the measurement of time is used as the independent variable in our model. These measurements of time will appear in successive periods and in many different intervals, including hourly, daily, weekly, monthly, and yearly intervals. Our model will be trying to produce demand, in which if we can observe a consistent pattern in demand, we can get adequate predictions from our time series models.

Components of time series forecasting models

There are four general components that a time series forecasting model is comprised of:

• Trend component: the direction in which the data is trending over time
• Cyclical component: the observance of the data deviating over time due to fluctuation
• Seasonal component: captures the variability of the data over time, also due to fluctuation
• Irregular component: captures the random variation in data that cannot be predicted in advance and are generally caused by short-term, unanticipated and nonrecurring factors that occur over time

Time series data trending and fluctuating over time

Time series forecasting methods: ARIMA models vs ETS models

Two of the most commonly used time series forecasting methods are ARIMA (Auto Regressive Integrated Moving Average) and ETS (Error Trend and Seasonality, or exponential smoothing). These two methods will be the specific focus for the rest of this blog post.

There are a number of factors to consider when it comes to selecting which time series forecasting method to apply, including the following:

• what is the context of the forecast we want to do
• what is the availability of historical data
• the amount of accuracy/inaccuracy we can tolerate with our model
• what time period are we forecasting for
• what is the cost of this forecast to the company and how much value/benefit does it bring
• how much time do we have to complete this analysis

When taking all of these factors into consideration, we make the best decision that incorporates the best use of available data to suit our needs, just like we do in any other project.

There are some metrics that we can take a look at to help us make this decision of which times series forecasting method to use. Most of the time, we can use AIC and BIC values of our models to determine which method works better within our model. We can also notice these characteristics if we examine a time series plot of our data and that will typically reveal the components of our data and which method may be more favorable. While both methods share many similarities, below are some of the key difference between them:

ARIMA models

• some are stationary
• do not have exponential smoothing counterparts
• use if you see autocorrelation in the data, i.e. the past data explains the present data well

ETS models

• are not stationary
• use exponential smoothing
• use if there is a trend and/or seasonality in the data, as this model explicitly models these components

Example of a time series forecast

Examples of real-world time series forecasting models

Now, to put everything into perspective, we can discuss a few real world examples where we would use a time series forecasting model.

• Predicting future disease outbreak: This is a relevant example right now with the coronavirus taking the world by storm. We can predict future outbreak of the virus using time series forecasting models. Another example that I personally have completed in a previous project was predicting future dengue fever outbreak in tropical foreign countries where the disease was common and spreading rapidly. The disease spreads through mosquito bites and infection can cause fatalities.

Dengue Fever over time. We can predict future dengue fever outbreak.

• Predicting future company sales: All businesses, especially retail business, likely incorporate times series forecasting models, as they want to be able to project how much revenue they will generate from future sales projections.

Company sales over time. There is a dip in sales in November- we might want to know the answer as to why.

• Predicting stock market trends: We can use time series forecasting models to predict future stock market trends.

Stock Market trends over time.