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Triple exponential smoothing applies exponential smoothing three times, which is commonly used when there are three high frequency signals to be removed from a time series under study. There are different types of seasonality: 'multiplicative' and 'additive' in nature, much like addition and multiplication are basic operations in mathematics.
An additive model would be used when the variations around the trend do not vary with the level of the time series whereas a multiplicative model would be appropriate if the trend is proportional to the level of the time series. [3] Sometimes the trend and cyclical components are grouped into one, called the trend-cycle component.
1. In an additive time-series model, the seasonal component is estimated as: S = Y – (T + C + I) where S : Seasonal values Y : Actual data values of the time-series T : Trend values C : Cyclical values I : Irregular values. 2. In a multiplicative time-series model, the seasonal component is expressed in terms of ratio and percentage as
X-13ARIMA-SEATS, successor to X-12-ARIMA and X-11, is a set of statistical methods for seasonal adjustment and other descriptive analysis of time series data that are implemented in the U.S. Census Bureau's software package. [3]
Time series: random data plus trend, with best-fit line and different applied filters. In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time.
An additive model is appropriate if the magnitude of seasonal fluctuations does not vary with level. If seasonal fluctuations are proportional to the level of the series, then a multiplicative model is appropriate. Multiplicative decomposition is more prevalent with economic series.
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The GAM model class is quite broad, given that smooth function is a rather broad category. For example, a covariate may be multivariate and the corresponding a smooth function of several variables, or might be the function mapping the level of a factor to the value of a random effect.