How To Convert A Variable Into Stationariy
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Publicado: 24 de mayo de 2012
HOW TO CONVERT A VARIABLE INTO STATIONARIY
Most time series patterns can be described in terms of two basic classes of components: trend and seasonality. The former represents a generalsystematic linear or (most often) nonlinear component that changes over time and does not repeat or at least does not repeat within the time range captured by our data (e.g., a plateau followed by a period ofexponential growth). The latter may have a formally similar nature (e.g., a plateau followed by a period of exponential growth), however, it repeats itself in systematic intervals over time. Thosetwo general classes of time series components may coexist in real-life data. For example, sales of a company can rapidly grow over years but they still follow consistent seasonal patterns (e.g., as muchas 25% of yearly sales each year are made in December, whereas only 4% in August).
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his general pattern is well illustrated in a "classic" Series G data set (Box and Jenkins, 1976, p. 531)representing monthly international airline passenger totals (measured in thousands) in twelve consecutive years from 1949 to 1960 (see example data file G.sta and graph above). If you plot thesuccessive observations (months) of airline passenger totals, a clear, almost linear trend emerges, indicating that the airline industry enjoyed a steady growth over the years (approximately 4 times morepassengers traveled in 1960 than in 1949). At the same time, the monthly figures will follow an almost identical pattern each year (e.g., more people travel during holidays than during any other time ofthe year). This example data file also illustrates a very common general type of pattern in time series data, where the amplitude of the seasonal changes increases with the overall trend (i.e., thevariance is correlated with the mean over the segments of the series). This pattern which is called multiplicative seasonality indicates that the relative amplitude of seasonal changes is constant...
Most time series patterns can be described in terms of two basic classes of components: trend and seasonality. The former represents a generalsystematic linear or (most often) nonlinear component that changes over time and does not repeat or at least does not repeat within the time range captured by our data (e.g., a plateau followed by a period ofexponential growth). The latter may have a formally similar nature (e.g., a plateau followed by a period of exponential growth), however, it repeats itself in systematic intervals over time. Thosetwo general classes of time series components may coexist in real-life data. For example, sales of a company can rapidly grow over years but they still follow consistent seasonal patterns (e.g., as muchas 25% of yearly sales each year are made in December, whereas only 4% in August).
[pic]
his general pattern is well illustrated in a "classic" Series G data set (Box and Jenkins, 1976, p. 531)representing monthly international airline passenger totals (measured in thousands) in twelve consecutive years from 1949 to 1960 (see example data file G.sta and graph above). If you plot thesuccessive observations (months) of airline passenger totals, a clear, almost linear trend emerges, indicating that the airline industry enjoyed a steady growth over the years (approximately 4 times morepassengers traveled in 1960 than in 1949). At the same time, the monthly figures will follow an almost identical pattern each year (e.g., more people travel during holidays than during any other time ofthe year). This example data file also illustrates a very common general type of pattern in time series data, where the amplitude of the seasonal changes increases with the overall trend (i.e., thevariance is correlated with the mean over the segments of the series). This pattern which is called multiplicative seasonality indicates that the relative amplitude of seasonal changes is constant...
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