timeseries (1)

What is a Time What is a Time Series?Series?

Set of evenly spaced numerical dataObtained by observing response variable at

regular time periods Forecast based only on past values

Assumes that factors influencing past, present, & future will continue

ExampleYear: 19951996199719981999Sales: 78.763.589.7 93.292.1

Time Series vs. Time Series vs. Cross Sectional DataCross Sectional Data Contrary to restrictions placed

on cross-sectional data, the major purpose of forecasting with time series is to extrapolate beyond the range of the explanatory variables.

Time Series Components


TrendTrend


TrendTrend CyclicalCyclical


TrendTrend

SeasonalSeasonal

CyclicalCyclical


TrendTrend

SeasonalSeasonal

CyclicalCyclical

IrregularIrregular

Trend Component Persistent, overall upward or downward

pattern Due to population, technology etc. Several years duration

Mo., Qtr., Yr.Mo., Qtr., Yr.

ResponseResponse

© 1984-1994 T/Maker Co.

Trend ComponentTrend Component Overall Upward or Downward Movement Data Taken Over a Period of Years

Sales

Time

Upward trend

Cyclical Component Repeating up & down movements Due to interactions of factors influencing

economy Usually 2-10 years duration

Mo., Qtr., Yr.Mo., Qtr., Yr.

ResponseResponseCycle

Cyclical Cyclical ComponentComponent

Upward or Downward Swings May Vary in Length Usually Lasts 2 - 10 Years

Sales

Time

Cycle

Seasonal Component Regular pattern of up & down

fluctuations Due to weather, customs etc. Occurs within one year

Mo., Qtr.Mo., Qtr.

ResponseResponseSummerSummer

© 1984-1994 T/Maker Co.

Seasonal Seasonal ComponentComponent

Upward or Downward Swings Regular Patterns Observed Within One Year

Sales

Time (Monthly or Quarterly)

Winter

Irregular Component Erratic, unsystematic, ‘residual’

fluctuations Due to random variation or unforeseen

eventsUnion strikeWar

Short duration & nonrepeating

© 1984-1994 T/Maker Co.

Random or Irregular Random or Irregular ComponentComponent

Erratic, Nonsystematic, Random, ‘Residual’ Fluctuations

Due to Random Variations of Nature

Accidents

Short Duration and Non-repeating

Time Series Forecasting


TimeSeries


TimeSeries

Trend?


TimeSeries

Trend?SmoothingMethods

No


TimeSeries


TrendModels

YesNo


TimeSeries


TrendModels

YesNo

ExponentialSmoothing

MovingAverage


Linear

TimeSeries


TrendModels

YesNo


Quadratic Exponential Auto-Regressive

MovingAverage

Time Series Time Series AnalysisAnalysis

Plotting Time Plotting Time Series DataSeries Data

09/83 07/86 05/89 03/92 01/95

Month/Year

0

2

4

6

8

10

12

Number of Passengers

(X 1000)Intra-Campus Bus Passengers

Data collected by Coop Student (10/6/95)

Time Series Time Series ForecastingForecasting

Linear

TimeSeries


TrendModels

YesNo



MovingAverage

Moving Average Method Series of arithmetic means Used only for smoothing

Provides overall impression of data over time

Moving Average Moving Average MethodMethod Series of arithmetic means Used only for smoothing

Provides overall impression of data over time

Used for elementary forecasting Used for elementary forecasting

Time Series Time Series ForecastingForecasting

Linear

TimeSeries


TrendModels

YesNo



MovingAverage

Exponential Exponential Smoothing MethodSmoothing Method Form of weighted moving average

Weights decline exponentiallyMost recent data weighted most

Requires smoothing constant (W)Ranges from 0 to 1Subjectively chosen

Involves little record keeping of past data

Time Series Plot [Revised]

01/93 01/94 01/95 01/96 01/97

Month/Year

183

185

187

189

191

193

Number of Surgeries

(X 100)

Revised Surgery Data(Time Sequence Plot)

Source: General Hospital, Metropolis

Seasonality Plot

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

99.7

99.9

100.1

100.3

100.5

Monthly Index

Revised Surgery Data(Seasonal Decomposition)


Trend Analysis

12/92 10/93 8/94 6/95 9/96 2/97 12/97

Month/Year

18

18.3

18.6

18.9

19.2

19.5

Number of Surgeries

(X 1000)

Revised Surgery Data(Trend Analysis)


Questions?

timeseries (1)

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