2. Definition of Time Series: An ordered sequence of values of a variable at equally spaced time intervals. The variable shall be time dependent.

3. The usage of time series models is twofold: Obtain an understanding of the underlying forces and structure that produced the observed data Fit a model and proceed to forecasting, monitoring or even feedback and feed forward control.

4. Applications of the Time Series Analysis Economic Forecasting Sales Forecasting Budgetary Analysis Stock Market Analysis Yield Projections Process and Quality Control Inventory Studies Workload Projections Utility Studies Census Analysis

5. Composition Time series data can be separated into 4 components.  Seculars or Long term Treand (T)  Cyclical fluctuation (C)  Seasonal Variations (S)  Random, Irregular variation (I)

6. Time series Models Additive Model Y=T+C+S+I Multiplicative Model Y=TxCxSxI

7. Calculation of Trend 1. Regression Line Y t =b 0 +b 1 X 2. Method of Moving average 3. Exponential Smoothing F t = F t-1 + a(A t-1 - F t-1 ) where: A t-1 is the actual value F t is the forecasted value a is the weighting factor, which ranges from 0 to 1 t is the current time period.

8. Ex.. The following table represents the annual sales of a firm which started its operations in 1995. The firm has estimated the regression function on its sales as, Y = 0.22 + 0.19 X You are required to: (a) Forecast the firm’s annual sales for the year 2010. (b) Determine the forecasted annual sales for the years 2001 to 2006 using the method of exponential smoothing, considering the actual annual sales in 1999 being Rs.1.1 Mn. as the forecasted value of 2000. (Apply a smoothing constant of α =0.2) Year (X) 199 5 199 6 199 7 19981999200 0 2001 2002 200320042005 Sales (Y) in Rs. Mn 0.20.40.51.91.11.51.31.11.71.9 2.3

9. Statistics to Business and Economics by J I T S Chandan