2.3 Goals of Time Series Analysis

What do people want from time series analysis? What questions are being answered?

2.3.1 Forecasting

Given the past and the present, what will the future look like (and its uncertainty)?

  • Given the past 10 years of quarterly earnings per share, what will next quarter’s earnings per share be for Apple, Inc.?

  • Given global average temperatures for the past 200 years, what will global average temperatures be in the next 100 years?

2.3.2 Filtering

Given the past and the present observation, how should I update my estimate of the true state of nature?

  • Given my current estimate of my spacecraft’s position and velocity, how should I update my estimate of position and velocity based on new gyroscope and radar measurements?

  • Given the history of monthly unemployment data in the U.S. and my estimate of the current unemployment level, how should I revised my estimate based on the Bureau of Labor Statistics’ latest data release?

  • Given the history of endowment returns, the current year return, and the need for spending a target percentage of the endowment value every year, how much should a University spend from the endowment in the following fiscal year?

2.3.3 Time Scale Analysis

Given an observed set of data, what time scales of variation dominate or account for the majority of temporal variation in the data.

  • Is there a strong seasonal cycle in the observations of temperature in Baltimore, MD?

  • Is the association between ambient air pollution and mortality primarily driven by large annual changes in pollution levels or by short-term spikes?

2.3.4 Regression Modeling

Given a time series of two phenomena, what is the association between them?

  • What is the association between daily levels of air pollution and daily values of cardiac hospitalizations?

  • What is the lag (in months) between a change in a country’s unemployment rate and a change in the gross domestic product?

  • What is the cumulative number of excess deaths that occurs in the 2 weeks following a major hurricane?

2.3.5 Smoothing

Given a complete (noisy) dataset, what can I infer about the true state of nature in the past?

  • Given a noisily measured signal, can I reconstruct the true signal from the data?

  • Now that my spacecraft has flown around the moon, what the distance of its closest approach to the moon?