1.
Exploratory Data Analysis
1.3. EDA Techniques 1.3.3. Graphical Techniques: Alphabetic


Purpose: Check for randomness  A lag plot checks whether a data set or time series is random or not. Random data should not exhibit any identifiable structure in the lag plot. Nonrandom structure in the lag plot indicates that the underlying data are not random. Several common patterns for lag plots are shown in the examples below.  
Sample Plot 
This sample lag plot exhibits a linear pattern. This shows that the data are strongly nonrandom and further suggests that an autoregressive model might be appropriate. 

Definition 
A lag is a fixed time displacement. For example,
given a data set Y_{1}, Y_{2} ...,
Y_{n}, Y_{2} and
Y_{7} have lag 5 since 7  2 = 5. Lag plots can
be generated for any arbitrary lag, although the most commonly
used lag is 1.
A plot of lag 1 is a plot of the values of Y_{i} versus Y_{i1}


Questions 
Lag plots can provide answers to the following questions:


Importance  Inasmuch as randomness is an underlying assumption for most statistical estimation and testing techniques, the lag plot should be a routine tool for researchers.  
Examples  
Related Techniques 
Autocorrelation Plot Spectrum Runs Test 

Case Study  The lag plot is demonstrated in the beam deflection data case study.  
Software  Lag plots are not directly available in most general purpose statistical software programs. Since the lag plot is essentially a scatter plot with the 2 variables properly lagged, it should be feasible to write a macro for the lag plot in most statistical programs. 