Time series analysis provides an insight into the nature of the phenomenon represented by the series of observations and suggests how to forecast or to prediction future values.

Time series generally have three components forming observations:

- the
**trend** – the long-term direction of the time series
- the
**seasonality** – the tendency of observations to change together within months, quarters
- the
**irregular component** – unsystematic, short-term, random fluctuations

In order to assess the time series, the data should be decomposed into these components. When doing decomposition the time series should be checked if they fit the additive, pseudo-additive or multiplicative models.

To choose an appropriate decomposition model … examine a graph of the original series and try a range of models, selecting the one which yields the most stable seasonal component. If the magnitude of the seasonal component is relatively constant regardless of changes in the trend, an additive model is suitable. If it varies with changes in the trend, a multiplicative model is the most likely candidate. However if the series contains values close or equal to zero, and the magnitude of seasonal component appears to be dependent upon the trend level, then pseudo-additive model is most appropriate. *Australian Bureau of Statistics, 2008*

Once the model type is known, the forecast can be produced.

- In case of additive model, simple exponential smoothing can do the work.
- For multiplicative and pseudo-additive models, further selection of the appropriate technique might be needed.

Information sources:

- Applied time series analysis, Alexander Aue, University of California, Davis (link)
- Australian Bureau of Statistics (link)
- Information paper: An Introductory Course on Time Series Analysis, Australian Bureau of Statistics, May 2001
- Time Series Analysis – Statistics Textbook (link)
- Using R for Time Series Analysis (link)

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