mathematics

Seasonal subseries plot

Seasonal subseries plot is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Seasonal subseries plot rather than just read about it. In short: Seasonal subseries plots are a graphical tool to visualize and detect seasonality in a time series. Seasonal subseries plots involves the extraction of the seasons from a time series into a subseries.

Key takeaways

Seasonal subseries plot belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Seasonal subseries plot to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Seasonal subseries plot from memory before moving on to harder problems.

Reference excerpt

Seasonal subseries plots are a graphical tool to visualize and detect seasonality in a time series. Seasonal subseries plots involves the extraction of the seasons from a time series into a subseries. Based on a selected periodicity, it is an alternative plot that emphasizes the seasonal patterns are where the data for each season are collected together in separate mini time plots. Seasonal subseries plots enables the underlying seasonal pattern to be seen clearly, and also shows the changes in seasonality over time. Especially, it allows to detect changes between different seasons, changes within a particular season over time. However, 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.

Definition Seasonal sub-series plots are formed by

Vertical axis: response variable Horizontal axis: time of year; for example, with monthly data, all the January values are plotted (in chronological order), then all the February values, and so on. The horizontal line displays the mean value for each month over the time series. 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 outliers once seasonality has been accounted for? Is the seasonality changing over time? Practically, seasonal subseries plots are often inspected as a preliminary screening tool. They allow visual inferences to be drawn from data prior to modelling and forecasting.

Related techniques Autocorrelation plot Box plot Recurrence plot Run sequence plot Time series Seasonal plot

Software Seasonal subseries plots can be implemented in the R programming language using function monthplot(). Example The following R code results in the above seasonal deviation plot of antidiabetic drug sales; > monthplot(a10, ylab= "$ million" , xlab= "Month", xaxt= "n", main= "Seasonal deviation plot: antidiabetic drug sales") > axis(1, at=1:12, labels=month.abb, cex=0.8)

References

Further reading Cleveland, William (1993). Visualizing Data. Hobart Press. ISBN 9780963488404. Maindonald, Braun (2010). Data Analysis and Graphics Using R: An Example-Based Approach. 3rd ed. Cambridge, UK: Cambridge University Press. Hyndman, R.J.; Koehler, A.B. (2006). "Another look at measures of forecast accuracy". International Journal of Forecasting. 22 (4): 679–688. CiteSeerX 10.1.1.154.9771. doi:10.1016/j.ijforecast.2006.03.001. S2CID 15947215. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help)

External links Seasonal Subseries Plot This article incorporates public domain material from the National Institute of Standards and Technology

Worked examples

Example 1 — a first encounter with Seasonal subseries plot

Start with the simplest possible case. Write down what Seasonal subseries plot claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Seasonal subseries plot before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Seasonal subseries plot ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Seasonal subseries plot

In research: Seasonal subseries plot appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Seasonal subseries plot in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Seasonal subseries plot is common in secondary-school and first-year university syllabi. It links to neighbouring topics Statistical charts and diagrams, Time series, so understanding it makes those chapters shorter.
In everyday life: Look for Seasonal subseries plot outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Seasonal subseries plot in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Seasonal subseries plot means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Seasonal subseries plot out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Seasonal subseries plot in simple terms?

Why does Seasonal subseries plot matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Seasonal subseries plot?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Seasonal subseries plot.