What Is Time Series Forecasting

Time series forecasting is an important area of machine learning that is often neglected. It is important because there are so many prediction problems that involve a time component. These problems are neglected because it is this time component that makes time series problems more

difficult to handle. In this lesson, you will discover time series forecasting. 

After reading this lesson, you will know:

• Standard definitions of time series, time series analysis, and time series forecasting.
• The important components to consider in time series data.
• Examples of time series to make your understanding concrete.

A. Time Series

A normal machine learning dataset is a collection of observations. 

For example:

                    observation #1

                    observation #2

                    observation #3

Time does play a role in normal machine learning datasets. Predictions are made for new data when the actual outcome may not be known until some future date. The future is being predicted, but all prior observations are treated equally. 

Perhaps with some very minor temporal dynamics to overcome the idea of concept drift such as only using the last year of observations rather than all data available.

A time series dataset is different. Time series adds an explicit order dependence between observations: a time dimension. This additional dimension is both a constraint and a structure that provides a source of additional information.

A time series is a sequence of observations taken sequentially in time.

For example:

                Time #1, observation

                Time #2, observation

                Time #3, observation

B. Time Series Nomenclature

Before we move on, it is important to quickly establish the standard terms used when describing time series data. The current time is defined as t, an observation at the current time is defined as obs(t).

We are often interested in the observations made at prior times, called lag times or lags. Times in the past are negative relative to the current time. For example the previous time is t-1 and the time before that is t-2. The observations at these times are obs(t-1) and obs(t-2) respectively. Times in the future are what we are interested in forecasting and are positive relative to the current time. For example the next time is t+1 and the time after that is t+2. The observations at these times are obs(t+1) and obs(t+2) respectively. For simplicity, we often drop the obs(t) notation and use t+1 instead and assume we are talking about observations at times rather than the time indexes themselves. Additionally, we can refer to an observation at a lag by shorthand such as a lag of 10 or lag=10 which would be the same as t-10.

To summarize:

• t-n: A prior or lag time (e.g. t-1 for the previous time).
• t: A current time and point of reference.
• t+n: A future or forecast time (e.g. t+1 for the next time).

C. Describing vs. Predicting

In descriptive modeling, or time series analysis, a time series is modeled to determine its components in terms of seasonal patterns, trends, relation to external factors, and the like. 

In contrast, time series forecasting uses the information in a time series (perhaps with additional information) to forecast future values of that series.

1. Time Series Analysis

The primary objective of time series analysis is to develop mathematical models that provide plausible descriptions from sample data.

2. Time Series Forecasting

The skill of a time series forecasting model is determined by its performance at predicting the future. This is often at the expense of being able to explain why a specific prediction was made, confidence intervals and even better understanding the underlying causes behind the problem.

D. Components of Time Series

Time series analysis provides a body of techniques to better understand a dataset. Perhaps the most useful of these is the decomposition of a time series into 4 constituent parts:

• Level. The baseline value for the series if it were a straight line.
• Trend. The optional and often linear increasing or decreasing behavior of the series over time.
• Seasonality. The optional repeating patterns or cycles of behavior over time.
• Noise. The optional variability in the observations that cannot be explained by the model.

All time series have a level, most have noise, and the trend and seasonality are optional.

E. Concerns of Forecasting

When forecasting, it is important to understand your goal. Use the Socratic method and ask lots of questions to help zoom in on the specifics of your predictive modeling problem. 

For example:

• How much data do you have available and are you able to gather it all together? More data is often more helpful, offering greater opportunity for exploratory data analysis, model testing and tuning, and model fidelity.
• What is the time horizon of predictions that is required? Short, medium or long term? Shorter time horizons are often easier to predict with higher confidence.
• Can forecasts be updated frequently over time or must they be made once and remain static? Updating forecasts as new information becomes available often results in more accurate predictions.
• At what temporal frequency are forecasts required? Often forecasts can be made at a lower or higher frequencies, allowing you to harness down-sampling, and up-sampling of data, which in turn can offer benefits while modeling.

Time series data often requires cleaning, scaling, and even transformation. 

For example:

• Frequency. Perhaps data is provided at a frequency that is too high to model or is unevenly spaced through time requiring resampling for use in some models.
• Outliers. Perhaps there are corrupt or extreme outlier values that need to be identified and handled.
• Missing. Perhaps there are gaps or missing data that need to be interpolated or imputed.

F. Examples of Time Series Forecasting

10 examples from a range of industries to make the notions of time series analysis and forecasting more concrete.

• Forecasting the corn yield in tons by state each year.
• Forecasting whether an EEG trace in seconds indicates a patient is having a seizure or not.
• Forecasting the closing price of a stock each day.
• Forecasting the birth rate at all hospitals in a city each year.
• Forecasting product sales in units sold each day for a store.
• Forecasting the number of passengers through a train station each day.
• Forecasting unemployment for a state each quarter.
• Forecasting utilization demand on a server each hour.
• Forecasting the size of the rabbit population in a state each breeding season.
• Forecasting the average price of gasoline in a city each day.