# 14 Descriptive Analysis

Time Series Data is

• Numerical data ordered over time
• The time intervals can be annually, quarterly, daily, hourly, etc.
• The sequence of the observations is important

Example:

Year 2001 2002 2003 2004 2005 2006 2007
Sales 75.3 74.2 78.5 79.7 80.2 82.3 85.8

A time-series plot is a two-dimensional plot of time series data:

• the vertical axis measures the variable of interest
• the horizontal axis corresponds to the time periods

Some important questions to first consider when first looking at a time series are:

• Is there a trend, meaning that, on average, the measurements tend to increase (or decrease) over time?
• Is there seasonality, meaning that there is a regularly repeating pattern of highs and lows related to calendar time such as seasons, quarters, months, days of the week, and so on?
• Are there outliers? In regression, outliers are far away from your line. With time series data, your outliers are far away from your other data.
• Is there a long-run cycle or period unrelated to seasonality factors?
• Is there constant variance over time, or is the variance non-constant?
• Are there any abrupt changes to either the level of the series or the variance?

Time-Series Components

A time series has three components:

• Trend: long-term direction
• Seasonality: periodic behavior
• Cyclical:
• Residual: irregular fluctuations