Statistical Graphics for Forecasting
Zhenhao Gong University of Connecticut
Welcome 2
This course is designed to be:
1. Introductory
2. Leading by interesting questions and applications 3. Less math, useful, and fun!
Most important:
Feel free to ask any questions!
Enjoy!
The Power of Statistical Graphics 3
Graphical data analysis usually is the best start point for any forecasting project:
Helps us summarize and reveal patterns in data
Helps us identify anomalies in data
Facilitates and encourages comparison of different pieces of data
Enables us to present a huge amount of data in a small space
Example: Anscombe’s Quartet
Regression results 5
Regression results 6
Question 7
Are the relationship between y and x is the same in each dataset and the specific data differ is due to random influence?
Pairwise scatterplots, or bivariate scatterplots
Anomalous data point
Simple Graphical Techniques 10
Graphics useful for modeling and forecasting time series. We will segment our discussion into two parts:
Univariate Graphics Multivariate Graphics
Univariate Graphics 11
The series of interest is graphed against time line. It’s very useful and popular since:
Reveal the patterns in time series data such as trend, seasonality and cycles.
Reveal the nature and location of any unusual or aberrant observations, structural breaks, etc.
Assess distribution shape by histogram: a simple estimate of the probability density of a r.v.
1-Year Treasury Bond Rate, 1960.01-2005.03.
Change in 1-Year Treasury Bond Rate, 1960.01-2005.03.
U.S. liquor sales, 1960.01-2001.03.
Histogram for the change in the 1-year T-Bond rate with related diagnostic information
Multivariate Graphics 16
When two or more variables are available, the possibility of relations between the variables becomes important, and we use graphics to uncover the existence and nature of such relationships.
1-Year versus 10-year Treasury Bond Rate
Remark 18
The regression line that we superimpose on a scatterplot of y vs. x summarizes how E(y|x) varies with x.
Under certain conditions, this conditional mean is the best point forecast of y.
That is, the regression line summarizes how our best point forecast y varies with x.
Scatterplot Matrix: 1-, 10-, 20-, and 30-Year Treasury Bond Rates
Elements of Graphical Style 20
There are at least three keys to good graphics:
Know your audience, and know your goals.
Understand and follow two fundamental principles: Show the data, and appeal to the viewer.
Revise and edit, again and again.
Show the data 21
We can use a number of devices to show the data.
Avoid distorting the data or misleading the viewer. (For example, avoid changing scales in midstream, use common scales in comparisons.)
Minimize, within reason, nondata ink.
(Avoid chartjunk such as elaborate shadings and grids, decoration, and related nonsense.)
Appeal to the viewer 22
Some guidelines help us appeal to the viewer:
Use clear and modest type, avoid mnemonics and abbreviations, and use labels rather then legends when possible.
Make graphics self-contained; a knowledgeable reader should be able to understand your graphics without reading pages of accompanying text.
Graph’s aspect ratio 23
The aspect ratio is the ratio of the graph’s height, h, to its width, w, and it should be selected such that the graph reveals patterns in the data and is visually appealing.
Golden ratio:
h=a= w w h+w
⇒a2 +a−1=0⇒a=0.618.
⇒
a= 1 a+1