This is a very basic of time series forecasting and modelling which makes this topic even more important. Let's understand the basic structure of time series data. A time series data is referenced by its index. That is you may have a monthly time series data from May, 2000 to May, 2020. But, the data points will be referenced by the index. In the given data we have 120 data points and the index of the data from May, 2020 is 120. Coming to the components, a time series data can have trend, seasonality, cyclicality and irregular component. Except Irregular component, all the other are systematic components. Irregular is a non-systematic component. One last component of time series is level component, which describes the average value in the series.
Trend Component
Trend is the direction of data movement (either up or down) over the years. If the data moves up, it has upward trend. If it moves down, it has downward trend. If the data moves horizondally, then the data has no trend. Look at the Figure 1 below, the data is a semi-annual data. That is there are two data points for a year. S1 and S2 are two seasons in a year. It could be clearly visible that the data is moving upward, which means that the data is having an upwards trend. For convenience, the trend line is also plotted here in dotted lines.
Seasonality Component
It is the regular or periodic fluctiations of data around the trend. Seasonal time series is also called as periodic time series. Seasonality is the fluctuation in data due to seasonal factors. Look at the Figure 1. The data at S2 is always higher and falls down in S1. Thus the data is seasonal.
Consider, a weekly sales data, where the quantity of sales is presented for every week. So for every month there may be four or five data values. In the start of the month there is a peak (influenced by salary) which declines through the end of month. Again the sales quantity increases in the first of the month and these fluctuations repeats itself. When you consider a monthly rainfall data, the rainfall goes up to peak during the monsoonal seasons and drops down in non-monsoonal season. This pattern repeats itself.
Check this Figure 2 Below
Cyclicality Component
Cyclicality is that fluctations in data around the trend which does not repeats itself in a regular or fixed patterns and duaration or intervals. The most common example of cyclicality is business cycle. Often, cyclicality is confused with seasonality. The magnitude of fluctuations is highly variable in cyclicality and the duration can even be upto two years.
Irregular Component
Irregularity is the left over component whose presence could not be explained.
The components other than cyclicality affects the stationarity of the time series data.
The presence of trend and seasonal components renders the data non-stationary. For a time series to be stationary, the mean and variance of the data generating process should be constant over time as well as the seasonality effect should be less. In the presence of trend, this mean value is not constant. Intrestingly, Cyclicality does not affect stationarity. Based on the presence and dominance of each component, suitable forecasting model is sorted out. A classical decomposition divides the time series data into its components. Some of the other forecasting models are Moving Average, Exponential Smoothing, Double and Triple Exponential Smoothing, ARMA and ARIMA. In case of stronger seasonality, Seasonal ARIMA (SARIMA) can be used to forecast.
What is additive and Multplicative Model? Is discussed in next article on classical decomposition.
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