Time Series Analysis and Forecasting - Cengage

1 time Series Analysis and ForecastingCONTENTSSTATISTICS IN PRACTICE:NEVADA OCCUPATIONAL HEALTH Series PATTERNSH orizontal PatternTrend PatternSeasonal PatternTrend and Seasonal PatternCyclical PatternUsing Excel s Chart Tools to Construct a time Series PlotSelecting a Forecasting AVERAGES AND EXPONENTIALSMOOTHINGM oving AveragesUsing Excel s Moving Average ToolWeighted Moving AveragesExponential SmoothingUsing Excel s ExponentialSmoothing PROJECTIONL inear Trend RegressionUsing Excel s Regression Toolto Compute a LinearTrend EquationNonlinear Trend RegressionUsing Excel s Regression Toolto Compute a QuadraticTrend

2 EquationUsing Excel s Chart Tools forTrend AND TRENDS easonality Without TrendSeasonality and TrendModels Based on Monthly SERIESDECOMPOSITIONC alculating the Seasonal IndexesDeseasonalizing the time SeriesUsing the Deseasonalized TimeSeries to Identify TrendSeasonal AdjustmentsModels Based on Monthly DataCyclical ComponentCHAPTER15 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in 15 time Series Analysis and ForecastingNevada Occupational Health Clinic is a privately ownedmedical clinic in Sparks, Nevada.

3 The clinic specializesin industrial medicine. Operating at the same site formore than 20 years, the clinic had been in a rapid growthphase. Monthly billings increased from $57,000 to morethan $300,000 in 26 months, when the main clinic build-ing burned to the clinic s insurance policy covered physical prop-erty and equipment as well as loss of income due to theinterruption of regular business operations. Settling theproperty insurance claim was a relatively straightforwardmatter of determining the value of the physical propertyand equipment lost during the fire.

4 However, determiningthe value of the income lost during the seven months thatit took to rebuild the clinic was a complicated matterinvolving negotiations between the business owners and theinsurance company. No preestablished rules could helpcalculate what would have happened to the clinic sbillings if the fire had not occurred. To estimate the lost in-come, the clinic used a Forecasting method to project thegrowth in business that would have been realized duringthe seven-month lost-business period. The actual history ofbillings prior to the fire provided the basis for a forecastingmodel with linear trend and seasonal components asdiscussed in this chapter.

5 This Forecasting model enabledthe clinic to establish an accurate estimate of the loss,which was eventually accepted by the insurance OCCUPATIONAL HEALTH CLINIC*SPARKS, NEVADASTATISTICSinPRACTICE*The authors are indebted to Bard Betz, Director of Operations, andCurtis Brauer, Executive Administrative Assistant, Nevada OccupationalHealth Clinic, for providing this Statistics in purpose of this chapter is to provide an introduction to time Series Analysis and fore-casting. Suppose we are asked to provide quarterly forecasts of sales for one of our com-pany s products over the coming one-year period.

6 Production schedules, raw materialpurchasing, inventory policies, and sales quotas will all be affected by the quarterly fore-casts we provide. Consequently, poor forecasts may result in poor planning and increasedcosts for the company. How should we go about providing the quarterly sales forecasts?Good judgment, intuition, and an awareness of the state of the economy may give us a roughidea or feeling of what is likely to happen in the future, but converting that feeling into anumber that can be used as next year s sales forecast is methods can be classified as qualitative or quantitative.

7 Qualitative meth-ods generally involve the use of expert judgment to develop forecasts. Such methods areappropriate when historical data on the variable being forecast are either not applicable orunavailable. Quantitative Forecasting methods can be used when (1) past information aboutthe variable being forecast is available, (2) the information can be quantified, and (3) it isreasonable to assume that the pattern of the past will continue into the future. In such cases,A physician checks a patient s blood pressure at the Nevada Occupational Health Clinic. Bob Pardue Medical forecast is simply aprediction of what willhappen in the must learn toaccept that regardless ofthe technique used, theywill not be able to developperfect forecasts.

8 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in time Series Patterns15-3a forecast can be developed using a time Series method or a causal method. We will focusexclusively on quantitative Forecasting methods in this the historical data are restricted to past values of the variable to be forecast, the fore-casting procedure is called a time Series methodand the historical data are referred to as atime Series . The objective of time Series Analysis is to discover a pattern in the historicaldata or time Series and then extrapolate the pattern into the future; the forecast is basedsolely on past values of the variable and/or on past forecast errors.

9 Causal Forecasting methods are based on the assumption that the variable we are fore-casting has a cause-effect relationship with one or more other variables. In the discussionof regression Analysis in Chapters 12 and 13, we showed how one or more independent vari-ables could be used to predict the value of a single dependent variable. Looking atregression Analysis as a Forecasting tool, we can view the time Series value that we want toforecast as the dependent variable. Hence, if we can identify a good set of related indepen-dent, or explanatory, variables, we may be able to develop an estimated regression equationfor predicting or Forecasting the time Series .

10 For instance, the sales for many products areinfluenced by advertising expenditures, so regression Analysis may be used to develop anequation showing how sales and advertising expenditures are related. Once the advertisingbudget for the next period is determined, we could substitute this value into the equation todevelop a prediction or forecast of the sales volume for that period. Note that if a time se-ries method were used to develop the forecast, advertising expenditures would not be con-sidered; that is, a time Series method would base the forecast solely on past sales.