Seasonal adjustment

Key takeaways

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

Reference excerpt

Seasonal adjustment or deseasonalization is a statistical method for removing the seasonal component of a time series. It is usually done when wanting to analyse the trend, and cyclical deviations from trend, of a time series independently of the seasonal components. Many economic phenomena have seasonal cycles, such as agricultural production, (crop yields fluctuate with the seasons) and consumer consumption (increased personal spending leading up to Christmas). It is necessary to adjust for this component in order to understand underlying trends in the economy, so official statistics are often adjusted to remove seasonal components. Typically, seasonally adjusted data is reported for unemployment rates to reveal the underlying trends and cycles in labor markets.

Time series components

The investigation of many economic time series becomes problematic due to seasonal fluctuations. Time series are made up of four components:

S t {\displaystyle S_{t}} : The seasonal component

T t {\displaystyle T_{t}} : The trend component

C t {\displaystyle C_{t}} : The cyclical component

E t {\displaystyle E_{t}} : The error, or irregular component. The difference between seasonal and cyclic patterns:

Seasonal patterns have a fixed and known length, while cyclic patterns have variable and unknown length. Cyclic pattern exists when data exhibit rises and falls that are not of fixed period (duration usually of at least 2 years). The average length of a cycle is usually longer than that of seasonality. The magnitude of cyclic variation is usually more variable than that of seasonal variation. The relation between decomposition of time series components

Additive decomposition: Y t = S t + T t + C t + E t {\displaystyle Y_{t}=S_{t}+T_{t}+C_{t}+E_{t}} , where Y t {\displaystyle Y_{t}} is the data at time t {\displaystyle t} . Multiplicative decomposition: Y t = S t ⋅ T t ⋅ C t ⋅ E t {\displaystyle Y_{t}=S_{t}\cdot T_{t}\cdot C_{t}\cdot E_{t}} . Logs turn multiplicative relationship into an additive relationship: Y t = S t ⋅ T t ⋅ C t ⋅ E t → log ⁡ Y t = log ⁡ S t + log ⁡ T t + log ⁡ C t + log ⁡ E t {\displaystyle Y_{t}=S_{t}\cdot T_{t}\cdot C_{t}\cdot E_{t}\rightarrow \log Y_{t}=\log S_{t}+\log T_{t}+\log C_{t}+\log E_{t}} : An additive model is appropriate if the magnitude of seasonal fluctuations does not vary with level. If seasonal fluctuations are proportional to the level of the series, then a multiplicative model is appropriate. Multiplicative decomposition is more prevalent with economic series.

Adjustment methods Unlike the trend and cyclical components, seasonal components, theoretically, happen with similar magnitude during the same time period each year. The seasonal components of a series are sometimes considered to be uninteresting and to hinder the interpretation of a series. Removing the seasonal component directs focus on other components and will allow better analysis. Different statistical research groups have developed different methods of seasonal adjustment, for example X-13-ARIMA and X-12-ARIMA developed by the United States Census Bureau; TRAMO/SEATS developed by the Bank of Spain; MoveReg (for weekly data) developed by the United States Bureau of Labor Statistics; STAMP developed by a group led by S. J. Koopman; and “Seasonal and Trend decomposition using Loess” (STL) developed by Cleveland et al. (1990). While X-12/13-ARIMA can only be applied to monthly or quarterly data, STL decomposition can be used on data with any type of seasonality. Furthermore, unlike X-12-ARIMA, STL allows the user to control the degree of smoothness of the trend cycle and how much the seasonal component changes over time. X-12-ARIMA can handle both additive and multiplicative decomposition whereas STL can only be used for additive decomposition. In order to achieve a multiplicative decomposition using STL, the user can take the log of the data before decomposing, and then back-transform after the decomposition.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Seasonal adjustment

Start with the simplest possible case. Write down what Seasonal adjustment claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 adjustment 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 adjustment 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 adjustment

In research: Seasonal adjustment appears in science 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 adjustment 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 adjustment is common in secondary-school and first-year university syllabi. It links to neighbouring topics Seasonality, Time series, so understanding it makes those chapters shorter.
In everyday life: Look for Seasonal adjustment 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.

How to study Seasonal adjustment in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Seasonal adjustment 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 adjustment out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Seasonal adjustment in simple terms?

Seasonal adjustment or deseasonalization is a statistical method for removing the seasonal component of a time series. It is usually done when wanting to analyse the trend, and cyclical deviations from trend, of a time series independently of the seasonal components.

Why does Seasonal adjustment matter?

Because it connects several science 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 adjustment?

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 adjustment.