04 Time Series Analysis

ForecastingВ

Forecasting

ItВ wouldВ beВ veryВ helpfulВ toВ decisionВ­makersВ ifВ theyВ hadВ anВ ideaВ ofВ whatВ isВ likelyВ toВ happenВ inВ theВ future. В ItВ isВ possibleВ toВ forecastВ usingВ historicalВ numericalВ data, В e. g. В salesВ figuresВ

ThisВ isВ knownВ asВ TIMEВ­SERIESВ ANALYSIS

© BusinessВ StudiesВ Online: В SlideВ 1В

Time-Series AnalysisВ

Analysis

ThereВ areВ 4В stagesВ involvedВ inВ carryingВ outВ timeВ­В seriesВ analysis: В

1)В IdentifyingВ theВ trendВ

ThisВ isВ theВ mostВ importantВ aspect, В andВ requiresВ businessesВ toВ identifyВ whatВ hasВ beenВ happening. В

2)В IdentifyingВ variationsВ

RecessionsВ andВ boomsВ withinВ theВ economyВ willВ affectВ manyВ typesВ ofВ businessВ data, В andВ thusВ mustВ beВ accountedВ for. В

3)В IdentifyingВ seasonal/cyclicalВ variationsВ

SomeВ businessesВ areВ seasonalВ inВ nature, В ieВ salesВ areВ higherВ inВ summer. В В TheseВ mustВ alsoВ beВ accountedВ for. В

4)В AcceptingВ randomВ variationsВ

" freak” events do occur,  and will affect businesses.  E. g.  September 11th 2001.

© BusinessВ StudiesВ Online: В SlideВ 2В

1) Discovering The TrendВ

Trend

TimeВ­seriesВ analysisВ isВ basedВ onВ historicalВ dataВ

ManagersВ mustВ identifyВ whetherВ theВ dataВ showsВ aВ

generallyВ upward, В downward, В orВ constantВ trendВ

RawВ data, В though, В mayВ makeВ thisВ veryВ difficultВ

e. g. В canВ youВ identifyВ theВ trendВ inВ theВ salesВ figuresВ givenВ below? В 1993В 1994В 1995В 1996В 1997В 1998В 1999В 2000В 2001В 2002В 2003В 2004В 2005В YearВ

SalesВ (ВЈm)В 67В 70В 64В 61В 59В 66В 73В 69В 64В 63В 69В 75В 72

ToВ helpВ themВ toВ doВ thisВ businessesВ willВ " smoothВ out” theВ rawВ dataВ byВ usingВ MOVINGВ AVERAGESВ

TheВ movingВ averageВ isВ usuallyВ eitherВ 3В­periodВ orВ 4В­period, В dependingВ howВ oftenВ theВ averageВ isВ taken. В

© BusinessВ StudiesВ Online: В SlideВ 3В

An Example a few Period Moving AverageВ

Normal

TheВ 3В periodВ movingВ averageВ isВ foundВ byВ addingВ upВ everyВ 3В piecesВ ofВ data, В andВ dividingВ byВ 3В toВ findВ theВ average. В UsingВ theВ previousВ data, В weВ wouldВ calculateВ asВ follows: В YearВ

1993В

1994В

1995В

1996В

1997В

1998В

1999В

2000В

2001В

2002В

2003В

2004В

2005В

SalesВ

(ВЈm)В

67В

70В

64В

61В

59В

66В

73В

69В

64В

63В

69В

75В

72

3В PointВ

TotalВ

3В PointВ

MovingВ

AverageВ

201В

195В

184В

186В

198В

208В

206В

196В

196В

207В

216В

67. 00В

65. 00В

61. 33В

62. 00В

66. 00В

69. 33В

68. 67В

65. 33В

65. 33В

69. 00В

72. 00В

© BusinessВ StudiesВ Online: В SlideВ 4В

A Visual RepresentationВ

Rendering

ItВ isВ thenВ possibleВ toВ plotВ bothВ theВ originalВ andВ trendВ data, В toВ seeВ howВ theВ dataВ hasВ beenВ " smoothedВ out”: В

85. 00В

3В PointВ

MovingВ

AverageВ

SalesВ

(ВЈm)

70. 00В

60. 00В

05

twenty

03

twenty

01

20

99

nineteen

97

nineteen

95

nineteen

93

60. 00В

nineteen

SalesВ (ВЈm)В

TimeВ SeriesВ Analysis: В

3В PointВ MovingВ AverageВ

YearВ

© BusinessВ StudiesВ Online: В SlideВ 5В

A good example 4 Period Moving AverageВ

Average

AВ 4В periodВ movingВ averageВ isВ oftenВ usedВ becauseВ itВ " smoothes” theВ dataВ outВ furtherВ

TheВ 4В periodВ movingВ averageВ isВ moreВ complex, В sinceВ noВ oneВ periodВ isВ theВ centreВ period. В

TheВ solutionВ isВ toВ useВ CENTRINGВ

CentringВ requiresВ theВ calculationВ ofВ theВ 4В andВ 8В yearВ movingВ totalsВ inВ orderВ toВ findВ aВ midВ­point. В

ItВ isВ thenВ necessaryВ toВ findВ theВ averageВ byВ dividingВ theВ totalsВ byВ 8В

UsingВ theВ previousВ data, В weВ wouldВ calculateВ theВ 4В periodВ movingВ averageВ asВ follows:

© BusinessВ StudiesВ Online: В SlideВ 6В

YearВ

1993В

SalesВ

(ВЈm)В

67В

1994В

70В

4В PointВ

TotalВ

8В PointВ

TotalВ

4В PointВ

MovingВ

AverageВ

516В

sixty four. 50В

504В

63. 00В

509В

63. 63В

526В

65. 75В

539В

67. 38В

541В

67. 63В

534В

66. 75В

536В

67. 00В

550В

68. 75В

262В

1995В

64В

254В

1996В

61В

250В

1997В

59В

259В

1998В

66В

267В

1999В

73В

272В

2000В

69В

269В

2001В

64В

265В

2002В

63В

An illustration

4 Period

Moving

AverageВ

Average

IfВ requiredВ thisВ dataВ

couldВ alsoВ beВ

shownВ graphicallyВ

271В

2003В

69В

279В

2004В

75В

2005В

72...

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