Business Mathematics and Statistics

1. Business Mathematics and Statistics NishanthaPalihawadana

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

3. Applications: 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 Yt=b0+b1X 2. Method of Moving average 3. Exponential Smoothing Ft = Ft-1 + a(At-1 - Ft-1 ) where: At-1 is the actual value Ft 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)

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