## Time series models, Mathematics

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Time Series Models

Time series value = T +S +C +R

Whereas S, C and R are expressed in absolute value

Additive Model model is best suited where the component factors are independent for example where the seasonal variation is unaffected by trend.

Multiplicative Model:

Time series value = T × S× C × R

Whereas S, C and are expressed as proportions or percentage

Multiplicative model is best applied where characteristics interact for example where high trends increase seasonal variations. Multiplicative model is more generally used in practice. Of the four elements of time series the most significant are trend and seasonal variation. The given demonstration shows how the trend (T) and seasonal variation (S) are separated out from a time series and how the computed T and S values are used to prepare forecast. The process of separating out the trend and seasonal variation is termed as deseasonalizing the data. There are two approaches to such process: one is based on regression by the actual data points and the other calculates the regression line by moving average trend points. The method by using the actual data is verified first followed by the moving average method.

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