## 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?