BUSINESS MATHEMATICS AND STATISTICSNishantha Palihawadana

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.

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.

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

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)

Time series Models

Additive ModelY=T+C+S+I

Multiplicative ModelY=TxCxSxI

Calculation of Trend1. Regression Line

Yt=b0+b1X2. Method of Moving average

3. Exponential SmoothingFt = 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.

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)

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

Sales (Y) inRs. Mn

0.2

0.4 0.5 1.9 1.1 1.5 1.3 1.1 1.7 1.9 2.3

Statistics to Business and Economics by J I T S Chandan