Time series data is one of the types of the data along with panel data and cross-sectional data. As we all know that a time series data is a set of data listed on a regular interval over time. (Pls excuse me for the use of data as a singular word). So why we need to decompose a time series data and what is actually ‘decomposition’ means? are discussed here. Decomposition refers to breaking down of a time series data into its’ components. Components?! Yes! Components. The Components of a time series data are trend, seasonal, cyclical and irregular, some models also include a level component. (Irregular components are also called as noise or remainder components). The details on these different components are discussed here. Okay. Why do we need to do decomposition of time series data? The reasons are as follows,
To understand the presence and impact of each components,
To sort the method or model to be applied for forecasting.
Through decomposition, the influence of each of the components can be well recognised which leads to sort the appropriate forecasting model to be applied. Now, as we understood on the ‘What and Why’, lets’ move on to ‘How to do the forecasting?
Procedure
Before decomposing we need to assume the fashion of integration of different components. There are two assumptions behind how these four components are related in a time series data: additive and multiplicative models. In order to find the fashion of integration, plot the data over time.
The graph is linear and does not increase in proportion with time.
The graph is exponential and increase with time.
In an additive model, all the components are integrated together in an additive fashion. Consider that Yt is a time series data. Whereas, Tt, St, Ct and Rt are trend, seasonal, cyclical and irregular components, respectively. In the additive model Yt can be represented as follows, Yt= Tt + St + Ct + Rt. The additive model is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. An additive model is linear where changes over time are consistently made by the same amount. A linear trend is a straight line. Researchers usually decompose trend and cyclicality together and call it as ‘trend-cycle’ component. The steps involved in additive model are as follows,
Moving Average: Every other decomposition starts with plotting graphs and finding the duration of seasonality (m). If m is an even number, the researcher have to compute the trend-cycle component (). Hereafter a term with cap denotes calculated/estimated value. Trend-cycle component can be calculated through moving averages (MA). For this step if the m is an even number 2×m –MA should be carried out. This 2×m –MA is called centered moving average. If m is an odd number, compute the trend-cycle component using moving average (m-MA). Next step is to subtract the component from Yt so that we could obtain St and Rt components. Yt – = St + Rt
Once component is removed, the time series data is called as detrended series (Dt). From the detrended series the seasonality component have to be identified and removed using seasonality index. The general formula for seasonality index is the division of actual seasonal data by yearly average. However, for a time series data, we need to follow few more steps as follows.
Calculate the yearly average for each year in the data. That is, for a monthly data over 5 years, the yearly average for 5 years have to be calculated.
The next step is to divide the detrended data by respective yearly average.
Then the seasonal average is to be calculated over the resulting data of the previous step. The resulting seasonal average is called seasonality index.
The seasonality index can also be used to do forecasting of short range.
(Tips: Use pivot table to find the different averages)
Final step is to de-seasonalise the data. That is to remove the seasonal component from the Dt by subtraction. Once seasonal component is also removed, only irregular component is left out. Thus we have decomposed each of the components.
Multiplicative Model
In the multiplicative model Yt can be represented as follows, Yt = Tt x St x Ct x Rt. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative model is more appropriate. A multiplicative or compound model is nonlinear, such as quadratic or exponential. Changes increase or decrease over time. A classical multiplicative decomposition is similar, except that the subtractions are replaced by divisions.
Decomposition through tools: Following these simple steps listed above anyone can do classical decomposition in MsExcel. However, data analytic tools such as SPSS, Matlab, R allow to do decomposition.
Let's test your understanding? Try the objective type quiz on this topic now . 👇
Comments