*The Business Professor*, updated May 5, 2019, last accessed July 11, 2020, https://thebusinessprofessor.com/lesson/seasonality-forecast-definition/.

**Seasonality Forecast Definition**

In time series data, seasonality refers to the presence of variations which occur at certain regular intervals either on a weekly basis, monthly basis, or even quarterly but never up to a year. Various factors may cause seasonality like a vacation, weather, and holidays and comprise repetitive, periodic, and generally regular and patterns that are predictable in a time series level.

**A Little More on What is Seasonality Predictions**

In a time series, seasonality fluctuations can be differentiated from cyclical patterns. Cyclical patterns take place when the data shows rises and falls which aren’t of a fixed timeframe. These non-seasonal fluctuations are majorly as a result of economic conditions and usually have relations with the “business cycle”; usually, their period go beyond a year, and these fluctuations usually span for a minimum of two years.

Organizations encounter seasonal variations like ice-cream vendors who are usually interested in knowing how they perform in relation to the normal seasonal variation. In the labor market, seasonal variations can be ascribed to the school leavers’ entry into the labor market as they aim at contributing to the workforce upon completing their schooling. Those who study employment data have less interest in these continuous changes unlike the interest shown in the variations which occur as a result of the economy’s underlying state. Their focus is centered on how change has occurred in unemployment in the workforce despite the effect of seasonal variations that occur regularly.

It is important for organizations to identify and also calculate seasonal variations within their market in order to assist them in planning for the future. This can ready them for the future. Furthermore, it can prepare them for the temporal increments or reductions in labor requirements, as well as, inventory as there are periodic fluctuations of demand for their product or service. This may require periodic maintenance, training, and other things which can be organized in advance. Asides these considerations, the organizations need to know if they have experienced more or less variation than the anticipated amount, greater than what is accounted for by the usual seasonal variations.

Seasonal variation is calculated in terms of an index known as a seasonal index. It refers to an average which can be used for comparing a real observation in relation to what it would be if no seasonal variation existed. Each period of the time series has an index value attached to it within a year. This means that twelve different seasonal indices exist when considering monthly data, one for each of the months. The methods below utilize seasonal indices for measuring seasonal variations of time-series data.

- Method of simple averages
- Ratio to trend method
- Ratio-to-moving-average method
- Link relatives method

Using the ratio-to-moving-average method too measure seasonal variation provides an index for measuring the seasonal variation degree in a time series. The index is based on a mean of 1oo, having the seasonality degree measured by variations far from the base. For instance, if the hotel rentals in a winter resort are observed, it is then discovered that the winter quarter index is 124. The value, 124, shows that 124% of the average quarterly rental takes place in winter. If for the whole of the previous year, the hotel management records 1,436 rentals, then 359 = (1436/4) would be the average quarterly rental. Since the winter-quarter is 123, the number of winter rentals is estimated as follows:

359 (124/100) = 445;

In this case, the average quarterly rental is 359 while the winter-quarter index is 124. The seasonal winter-quarter rental is 445.

This method is also referred to as percentage moving average method. Here, the original data values in the time-series are shown as moving average percentages. The step, as well as, tabulations are given below:

**Steps:**

- The first step is to find the twelve monthly or four quarterly moving averages of the real data values in the time-series.
- Next is expressing each time-series’ original data as a percentage of the equivalent centered moving average values gotten in the first step. This means that, in a multiplicative time-series model, we get (Original data values) / (Trend values) 100 = (T C S I) / (TC) 100 = (S I) 100. This means that the ratio-to-moving average represents the components that are seasonal and inconsistent.
- Arrange the percentages based on the months or quarters of given years. Then find the averages of overall months or quarters of the given years.
- If the summation of these indices isn’t 1,200, (or 400 for quarterly figures), multiply then by a correction factor = 1,200 / (monthly indices sum). Otherwise, the twelve monthly averages would be seen as seasonal indices.

### References for Seasonality Forecast

- http://www.businessdictionary.com/definition/seasonality-index.html
- https://en.wikipedia.org/wiki/Seasonality
- https://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/SeasonalTools.htm

### Academic Research on Seasonality index

Short-term electricity demand **forecasting **using double **seasonal **exponential smoothing, **Taylor, J. W. (2003). ***Journal of the Operational Research Society***, ***54***(8), 799-805.**

Neural network **forecasting **for **seasonal **and trend time series, **Zhang, G. P., & Qi, M. (2005). ***European journal of operational research***, ***160***(2), 501-514.**

Triple **seasonal **methods for short-term electricity demand **forecasting**, **Taylor, J. W. (2010). ***European Journal of Operational Research***, ***204***(1), 139-152.**

**Forecasting **with combined **seasonal indices**, **Withycombe, R. (1989). ***International Journal of Forecasting***, ***5***(4), 547-552.**

How to use aggregation and combined **forecasting **to improve **seasonal **demand **forecasts**, **Dekker, M., Van Donselaar, K., & Ouwehand, P. (2004). ***International Journal of Production Economics***, ***90***(2), 151-167.**

Short-term load **forecasting **methods: An evaluation based on european data, **Taylor, J. W., & McSharry, P. E. (2007). ***IEEE Transactions on Power Systems***, ***22***(4), 2213-2219.**

**Forecasting **trends in time series, **Gardner Jr, E. S., & McKenzie, E. D. (1985). ***Management Science***, ***31***(10), 1237-1246.**

Revisiting top-down versus bottom-up **forecasting**, **Kahn, K. B. (1998). ***The Journal of Business Forecasting***, ***17***(2), 14.**

Comparison of **seasonal **estimation methods in multi-item short-term **forecasting**, **Bunn, D. W., & Vassilopoulos, A. I. (1999). ***International Journal of Forecasting***, ***15***(4), 431-443.**

Using group **seasonal indices **in multi-item short-term **forecasting**, **Bunn, D. W., & Vassilopoulos, A. I. (1993). ***International Journal of Forecasting***, ***9***(4), 517-526.**

Short-term **forecasting **of anomalous load using rule-based triple **seasonal **methods, **Arora, S., & Taylor, J. W. (2013). ***IEEE transactions on Power Systems***, ***28***(3), 3235-3242.**