These are accidently changes which are purely random or unpredictable. Normally they are short-term variations, but its occurrence sometimes has its effect so intense that they may give rise to new cyclic or other movements of variations. For example floods, wars, earthquakes, Tsunami, strikes, lockouts etc… Mathematical Model for a Time Series There are two common models used for decomposition of a time series into its components, namely additive and multiplicative model. (i) Additive Model: This model assumes that the observed value is the sum of all the four components of time series.
(i.e) Y= T+S+C+I where Y = Original value, T = Trend Value, S = Seasonal component, C = Cyclic component, I = Irregular component The additive model assumes that all the four components operate independently. It also assumes that the behavior of components is of an additive character. (ii) Multiplicative Model: This model assumes that the observed value is obtained by multiplying the trend (T) by the rates of other three components. Y = T × S × C × I where Y = Original value , T = Trend Value, S = Seasonal component, C = Cyclic component, I = Irregular component This model assumes that the components due to different causes are not necessarily independent and they can affect one another.
It also assumes that the behavior of components is of a multiplicative character. . . Measurements of Trends Following are the methods by which we can measure the trend.
(i) Freehand or Graphic Method. (ii) Method of Semi-Averages. (iii) Method of Moving Averages. (iv) Method of Least Squares.
(i) Freehand or Graphic Method. It is the simplest and most flexible method for estimating a trend. We will see the working procedure of this method. Procedure: (a) Plot the time series data on a graph.
(b) Draw a freehand smooth curve joining the plotted points. (c) Examine the direction of the trend based on the plotted points. (d) Draw a straight line which will pass through the maximum number of plotted points. XII Std - Business Maths & Stat EM Chapter - -