Seasonality in sales. Ratio-to-moving-average method

by gatekeeper on 21.10.2019

Sales and revelenues are a subject to significant swings throughout the year. Those moves follow sometimes a systematic pattern of seasonality. 

Retail sales have a peak every year before Christmas (religious festivals). The demand for ice cream is very high during the hot summer months (climate). They are a lot of examples for the presence of variations that occur at specific regular intervals in less than a year.

Sometimes, analysts have the problem, that time obervations deviate strongly from the previous sales figures and comparison of data points become difficult. In such cases, data can be seosonaly adjusted by employing moving average estimations. 

Here, we have the an example of the fictive Cupcake KING Company located in Grand Canaria. The cupecake cafe is located on a main street with tourists coming mainly from Germany and the rest of Europe. They love the mild summer and relatively hot months just before Christmas. The majority of them starts every new year back home. The cafe owner has been asking himself the question “My Q4 sales are very strong, but Q1 revenue is always weak — what is the general trend for my business?

The ratio-to-moving-average method would help the owner to better understand the topic of seasonality.
First, 4‑quarter moving average has been used to smooth the sales data of the company. Then moving averages are calculated for Q 2/3 and Q 3/4. The centered moving average corresponding to Q3 is the average of both numbers (Q2/3 and Q3/4). Deviding the centered moving average by the original data leads to the so-called seasonality ratio results. The formulas average afterwards the ratios separately for each quarter of the year to obtain unnormalized seasonal indices. The next step is to normalize the seasonal values by rescaling the indices to add up to 400% exactly.

Seasonally adjusted figures are found by dividing actual values by the seasonal indices.

Finally, the owner of Cupcake KING could be calm, that his business is not out of control. Over the last few years , there has been a significant trend towards increasing sales. His company is doing good job.

Other useful estimations such as linear trend calculations and forecasting (additive model) could be found the Excel file uploaded below. 

One Response to Seasonality in sales. Ratio-to-moving-average method

    FraB says:

    Hello, many thanks for the the topic seisonality. Could you please tell me, why should seasonality removed from a time series?

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