What is a Seasonality Forecast?

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. They comprise repetitive, periodic, and generally regular patterns that are predictable in a time series level.

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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 are not in a fixed timeframe. These non-seasonal fluctuations are generally a result of economic conditions and usually relate to the business cycle. Also, cyclical patterns usually span a minimum of two years. 

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 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:

1. The first step is to find the twelve monthly or four quarterly moving averages of the real data values in the time-series.
2. 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.
3. 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.
4. If the summation of these indices isnt 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.

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.