Seasonal subseries plot
Encyclopedia
Seasonal subseries plots are a tool for detecting seasonality
in a time series
. This plot allows one to detect both between-group and within-group patterns. This plot is only useful if the period of the seasonality is already known. In many cases, this will in fact be known. For example, monthly data typically has a period of 12. If the period is not known, an autocorrelation plot or spectral plot can be used to determine it. If there is a large number of observations, then a box plot
may be preferable.
In addition, a reference line is drawn at the group means.
The analyst must specify the length of the seasonal pattern before generating this plot. In most cases, the analyst will know this from the context of the problem and data collection.
function monthplot.
Seasonality
In statistics, many time series exhibit cyclic variation known as seasonality, periodic variation, or periodic fluctuations. This variation can be either regular or semi regular....
in a time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
. This plot allows one to detect both between-group and within-group patterns. This plot is only useful if the period of the seasonality is already known. In many cases, this will in fact be known. For example, monthly data typically has a period of 12. If the period is not known, an autocorrelation plot or spectral plot can be used to determine it. If there is a large number of observations, then a box plot
Box plot
In descriptive statistics, a box plot or boxplot is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation , lower quartile , median , upper quartile , and largest observation...
may be preferable.
Definition
Seasonal subseries plots are formed by- Vertical axis: response variable
- Horizontal axis: time ordered by season. For example, with monthly data, all the January values are plotted (in chronological order), then all the February values, and so on.
In addition, a reference line is drawn at the group means.
The analyst must specify the length of the seasonal pattern before generating this plot. In most cases, the analyst will know this from the context of the problem and data collection.
Importance
It is important to know when analyzing a time series if there is a significant seasonality effect. The seasonal subseries plot is an excellent tool for determining if there is a seasonal pattern. The seasonal subseries plot can provide answers to the following questions:- Do the data exhibit a seasonal pattern?
- What is the nature of the seasonality?
- Is there a within-group pattern (e.g., do January and July exhibit similar patterns)?
- Are there any outlierOutlierIn statistics, an outlier is an observation that is numerically distant from the rest of the data. Grubbs defined an outlier as: An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs....
s once seasonality has been accounted for?
Related techniques
- Autocorrelation plot
- Box plotBox plotIn descriptive statistics, a box plot or boxplot is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation , lower quartile , median , upper quartile , and largest observation...
- Recurrence plotRecurrence plotIn descriptive statistics and chaos theory, a recurrence plot is a plot showing, for a given moment in time, the times at which a phase space trajectory visits roughly the same area in the phase space...
- Run sequence plot
Software
Seasonal subseries plots are implemented in the RR (programming language)
R is a programming language and software environment for statistical computing and graphics. The R language is widely used among statisticians for developing statistical software, and R is widely used for statistical software development and data analysis....
function monthplot.