MARKET PROJECTIONS

COMMON METHODS USED IN MARKET PROJECTION

ARITHMETIC STRAIGHT LINE METHOD ARITHMETIC GEOMETRIC CURVE STATISTICAL STRAIGHT LINE STATISTICAL PARABOLIC CURVE

USING THE SAME HISTORICAL DATA, ONE MUST REMEMBER THAT EACH OF THESE METHODS YIELDS DIFFERENT PROJECTED FIGURES & TRENDS. WE MUST FIRST DETERMINE WHICH METHOD IS MOST APPROPRIATE FOR THE SET OF FIGURES ON HAND.

2 WAYS OF DETERMINING THE RIGHT METHOD OF PROJECTION

FIRST

DONE BY PLOTTING THE HISTORICAL DATA ALONG THE COORDINATES & VISUALLY DETERMINING THE TREND LINE. FROM THE SHAPE OF THE LINE, ONE CAN MORE OR LESS DETERMINE WHICH METHOD WILL DEVIATE FROM THE PAST TREND.

SECOND

IT INVOLVES MATHEMATICAL COMPUTATIONS. UNDER EACH OF THE METHODS, THE

REGRESSION LINES ARE DERIVED AND THE STANDARD DEVIATIONS OF EACH ARE COMPUTED FOR.

THE ONE WHICH YIELDS THE SMALLEST STANDARD DEVIATION IS MOST LIKELY TO GIVE THE MOST RELIABLE FORECAST.

1. GRAPHICAL METHOD

CURVE

Q

T

Fig. 1

-PROGRESSIVELY INCREASING- ARITHMETIC GEOMETRIC CURVE IS THE RECOMMENDED PROJECTION METHOD

CURVE

Q

T

Fig. 2

-INCREASING- STATISTICAL PARABOLIC IS THE RECOMMENDED PROJECTION METHOD

STRAIGHT

Q

T

Fig. 3

-

-CONSTANTLY INCREASING- ARITHMETIC STRAIGHT LINE IS THE RECOMMENDED PROJECTION METHOD

STRAIGHT

Q

T

Fig. 4

-INCONSISTENTLY INCREASING-STATISTICAL STRAIGHT LINE IS THE RECOMMENDED PROJECTION METHOD

MATHEMATICAL METHOD

T Q

2000 198.6

2001 214.9

2002 234.2

2003 353.7

2004 429.3

2005 340.8

2006 416.2

2007 351.6

2008 512.2

2009 471.2

GIVEN THE FF DATA, WE CAN DETERMINE THE TREND LINE W/C WILL BEST FIT THE HISTORICAL DATA THROUGH THE GIVEN STEPS ON THE NEXT SLIDE.

STEP 1.

COMPUTE THE EXPECTED VALUES USING THE FOUR METHODS: A. Arithmetic Straight Line: Yc = a + Yi

- 1 B. Arithmetic Geometric Curve: Yc = Yi + 1

1 + r C. Statistical Straight Line: Yc = a +

bx D. Statistical Parabolic: Yc = a +

bx +cX2

STEP 2.

COMPUTE FOR THE STANDARD DEVIATIONS OF EACH METHOD USING THE FORMULA: σ= √ ∑ (y –yc)2

THE METHOD WHICH YIELDS THE LEAST

STANDARD DEVIATION IS LIKELY TO COME UP WITH THE BEST ESTIMATES.

X

METHODS OF PROJECTION

1. ARITHMETIC STRAIGHT LINE Yc = a + Yi – 1

Where a = Yn – Yc = 471.2 – 198.6 = 30.29

N – 1 9

Yc = initial value (1st year)Yn = final value (last year)N = number of yearsYi = value for the year past

HISTORICAL VALUES

STEP 1 STEP 2

Y a + Yi - 1 = Yc Y - Yc (Y-Yc)2

2000 198.6 - - 0 0.00

2001 214.9 30.29 + 198.6 = 228.89 - 13.99 195.72

2002 234.2 30.29 + 288.89

= 259.18 - 24.98 624.00

2003 353.7 30.29 + 259.18

= 289.47 64.23 4,125.49

2004 429.3 30.29 + 289.47

= 319.76 109.05

11,999.01

2005 340.8 30.29 + 319.79

= 350.05 - 9.25 85.16

2006 416.2 30.29 + 350.05

= 380.24 35.86 1,285.94

2007 451.6 30.29 + 380.24

= 410.63 40.97 1,678.54

2008 512.2 30.29 + 410.63

= 440.92 71.28 5,080.94

2009 471.2 30.29 + 440.92

= 471.20 - 0.01 0.00

∑ =22,110.62

σ= 22,110.62 10

= 47

PROJECTED VALUES

a + Yi - 1 = Yc

2010 30.29 + 471.21 = 501.50

2011 30.29 + 501.50 = 531.79

2012 30.29 + 531.79 = 562.08

2013 30.29 + 562.08 = 592.37

2014 30.29 + 592.37 = 622.26

2015 30.29 + 622.66 = 652.95

2016 30.29 + 652.95 = 683.24

2017 30.29 + 683.24 = 713.53

2018 30.29 + 713.53 = 743.82

2019 30.29 + 743.81 = 774.11

2. ARITHMETIC GEOMETRIC CURVE Yc = Yi + 1 1 + r

Where: Yi + 1 = value for the year ahead

r = average rate of increases

HISTORICAL VALUES

STEP 1 STEP 2

Y % increase (decreas

e)

Yi + 1

+ (1 + r)

Yc Y - Yc (Y-Yc)2

2000

198.6

- 204.46

+ 1.11 = 184.20

14.40 207.36

2001

214.9

8 226.95

+ 1.11 = 204.46

10.44 108.99

2002

234.2

9 251.92

+ 1.11 = 226.95

7.25 52.56

2003

353.7

51 279.63

+ 1.11 = 251.92

101.78

10,359.17

2004

429.3

21 310.39

+ 1.11 = 279.63

149.67

22,401.11

2005

340.8

(21) 344.53

+ 1.11 = 310.39

30.41 924.77

2006

416.2

22 382.43

+ 1.11 = 344.53

71.69 5,136.59

2007

451.6

8 424.50

+ 1.11 = 382.43

69.17 4,754.49

2008

512.2

13 471.20

+ 1.11 = 424.50

87.70 7,691.29

2009

471.2

(8) 0

103

r = ∑ % increase = 103 = 11.44 N – 1 9

σ= 51,666.33 10

= 71.9

PROJECTED VALUES

Yi -1x(1+r)

= Yc

2010 471.20 X 1.11 = 523.03

2011 523.03 X 1.11 = 580.56

2012 580.56 X 1.11 = 644.42

2013 644.42 X 1.11 = 715.31

2014 715.31 X 1.11 = 793.99

2015 793.99 X 1.11 = 881.33

2016 881.33 X 1.11 = 978.28

2017 978.28 X 1.11 = 1,085.89

2018 1,085.89 X 1.11 = 1,205.34

2019 1,205.34 X 1.11 = 1,337.93

Yc = Yi – 1 (1 + r)

3. STATISTICAL STRAIGHT LINE Yc = a + bx Where: a = ∑Y - b ∑x n n

b = n ∑ XY - ∑X ∑Y n ∑ X2 – (∑ X)2

HISTORICAL VALUES

STEP 1

Y X X2 XY a + b (x)

2000 198.6 1 1 198.6 160.92 + 36.61 (1)

2001 214.9 2 4 429.8 160.92 + 36.61 (2)

2002 234.2 3 9 702.6 160.92 + 36.61 (3)

2003 353.7 4 16 1,414.8 160.92 + 36.61 (4)

2004 429.3 5 25 2,146.5 160.92 + 36.61 (5)

2005 340.8 6 36 2,044.8 160.92 + 36.61 (6)

2006 416.2 7 49 2,193.4 160.92 + 36.61 (7)

2007 451.6 8 64 3,612.8 160.92 + 36.61 (8)

2008 512.2 9 81 4,609.8 160.92 + 36.61 (9)

2009 471.2 10 100 4,712.0 160.92 + 36.61 (10)

3,622.7

55 386 22,785.1

HISTORICAL VALUES

STEP 2

Yc Y - Yc (Y-Yc)2

= 197.53 1.07 1.14

= 234.14 -19.24 370.80

= 270.75 -36.55 1,335.90

= 307.36 46.34 2,147.40

= 343.97 85.33 7,281.21

= 380.53 -9.78 95.65

= 417.19 -0.99 0.98

= 453.80 -2.20 4.84

= 490.41 21.79 474.80

527.02 -55.82 3,115.87

10 (22,785.1) – (55) (3,622.7) b = 10 (385) – (55)2 = 36.61

a = 3,622.7 – 36.61 (55) = 160.92 10 10

14,827.97

σ= 14,827.97 = 38.5 10

PROJECTED VALUES

a + b = Yc

2010 160.92 + 36.61 (11) = 563.63

2011 160.92 + 36.61 (12) = 600.24

2012 160.92 + 36.61 (13) = 636.85

2013 160.92 + 36.61 (14) = 673.46

2014 160.92 + 36.61 (15) = 710.07

2015 160.92 + 36.61 (16) = 746.68

2016 160.92 + 36.61 (17) = 783.29

2017 160.92 + 36.61 (18) = 819.90

2018 160.92 + 36.61 (19) = 856.51

2019 160.92 + 36.61 (20) = 893.12

Yc = Yi – 1 (1 + r)

4. STATISTICAL PARABOLIC Y = a + bx + cx2

Where: “a” = (∑X4) (∑Y) – (∑X2) (∑X2Y) n(∑X4) - (∑X2)2

“b” = ∑XY ∑X2

”c” = n(∑X2Y) - (∑X2) (∑Y) n(∑X4) - (∑X2)2

HISTORICAL VALUES

STEP 1

Y X X2 X4 XY X2Y

2000 198.6 -9 81 6,561 -1,787.4 16,086.6

2001 214.9 -7 49 2,401 -1,504.3 10,530.1

2002 234.2 -5 25 625 -1,171.0 5,855.0

2003 353.7 -3 9 81 -1,061.1 3,183.3

2004 429.3 -1 1 1 -429.3 429.3

2005 340.8 1 1 1 340.8 340.8

2006 416.2 3 9 81 1,284.6 3,745.8

2007 451.6 5 25 625 2,258.0 11,290.0

2008 512.2 7 49 2,401 3,585.8 25,097.8

2009 471.2 9 81 6,561 4,240.8 38,167.2

3,622.7 330 19,338 5,720.5 114,725.9

HISTORICAL VALUE

STEP 1 STEP 2

a + B x + c X2 = Yc Y - Yc (Y-Yc)2

381.11 + 17.33 (-9) + (-57) (-92) = 178.97

19.63 385.34

381.11 + 17.33 (-7) + (-57) (-72) = 231.87

-16.97

287.98

381.11 + 17.33 (-5) + (-57) (-52) = 280.21

-46.01

2,116.92

381.11 + 17.33 (-3) + (-57) (-32) = 323.99

29.71 882.68

381.11 + 17.33 (-1) + (-57) (-12) = 363.21

-66.09

4,367.89

381.11 + 17.33 (1) + (-57) (12) = 397.87

-57.07

3,256.98

381.11 + 17.33 (3) + (-57) (32) = 427.97

-11.77

138.53

381.11 + 17.33 (5) + (-57) (52) = 453.51

-1.91 3.65

381.11 + 17.33 (7) + (-57) (72) = 474.49

37.71 1,422.04

381.11 + 17.33 (9) + (-57) (92) 490.91

-19.71

388.48

13,250.49

σ= 13,250.49 10

= 36.3

PROJECTED VALUES

a + b X + c X2 = Yc

2010 381.11

+ 17.33 (11)

+ (-57) (112) = 502.77

2011 381.11

+ 17.33 (13)

+ (-57) (132) = 510.07

2012 381.11

+ 17.33 (15)

+ (-57) (152) = 512.81

2013 381.11

+ 17.33 (17)

+ (-57) (172) = 510.99

2014 381.11

+ 17.33 (19)

+ (-57) (192) = 504.61

2015 381.11

+ 17.33 (21)

+ (-57) (212) = 493.67

2016 381.11

+ 17.33 (23)

+ (-57) (232) = 478.17

2017 381.11

+ 17.33 (25)

+ (-57) (252) = 458.11

2018 381.11

+ 17.33 (27)

+ (-57) (272) = 433.49

2019 381.11

+ 17.33 (29)

+ (-57) (292) = 404.31

Yc = Yi – 1 (1 + r)

Remarks on the Mathematical Methods of Projection

1. Based on the standard deviations derived: A. Arithmetic straight line = 47 B. Arithmetic geometric curve = 71.9 C. Statistical Straight line = 38.5 D. Statistical Parabolic = 36.3

The statistical parabolic curve is bound to be favored by the statistician as the best method in projecting the future.

Remarks.. 2. However, it is advisable to reconsider the

projected trend the statistical parabolic would yield in the light of other factors which may or may not make the projection realistic. A. If, for instance, the historical data refer to demand for

heavy automobiles, then the down-sloping curve of the statistical parabolic method would be logical since continually increasing oil prices will presumably cause demand to taper off or even decline in the future.

B. However, if the data refer to the demand for cement which has not been doing well lately, but is expected to fare much better in the future, then the downward-sloping curve would seem unrealistic. In this case, the statistical straight line method, which also gives a small standard deviation, might give a more realistic approximation of the future demand.

Remarks..

3. In general, if the method yielding the smallest standard deviation appears to be unrealistic, then the one which yields the next smallest deviation may be favored.

DATA GATHERING & DERIVATION A PROBLEM COMMONLY ENCOUNTERED BY THE

RESEARCHER IN UNDERTAKING THE MARKET STUDY IS THE UNAVAILABILITY OF THE DATA REQUIRED.

VERY OFTEN, HE WILL RESORT TO DIFFERENT METHODOLOGIES TO DETERMINE THE FIGURES NEEDED TO ESTABLISH A PARTICULAR ASPECT OF HIS STUDY.

MAKING USE OF OTHER DATA WHICH ARE AVAILABLE AND SIGNIFICANTLY CORRELATED WITH THE DESIRED BUT UNAVAILABLE ONES, HE CAN DERIVE FIGURES WITH WHICH, HE CAN WORK ON.

SAMPLE CASES & REMEDIES

CASE 1. PROBLEM: THE PROJECT INVOLVES

PRODUCTION AND SALE OF HOGS. A PROJECTION OF THE SUPPLY OF HOGS IS NEEDED AS PART OF THE MARKET STUDY.

SOLUTION: THE BUREAU OF AGRICULTURAL ECONOMICS CAN PROVIDE A CENSUS ON THE HOG POPULATION WHICH COVERS THE PERIOD 2000-2009.

SAMPLE CASES

CASE 2. PROBLEM: THE PROJECT PROPOSES TO PRODUCE HOG

FEEDS, BUT NO CENSUS RECORDING THE DEMAND FOR THE PRODUCT IS AVAILABLE.

SOLUTION: HERE, THE DEMAND FIGURES WILL REPRESENT THE ESTIMATED TOTAL HOG FEED REQUIREMENTS. SINCE, THE QUANTITY OF HOG FEEDS AND THE NUMBER OF HOGS ARE HIGHLY CORRELATED, THE DEMAND FOR HOG FEEDS CAN BE DERIVED THROUGH THE FOLLOWING DATA GATHERED BY THE BUREAU OF AGRI’L ECONOMICS: AN ANNUAL HOG POPULATION CENSUS COVERING AT

LEAST 10 YEARS. AN ESTIMATED ANNUAL CONSUMPTION, 298 KG, OG HOG

FEEDS BY THE AVERAGE HOG.

SAMPLE CASES

CASE 3. THE PROJECT CONCERNS THE PLANTING OF SOYBEANS TO

MEET THE PROTEIN REQUIREMENTS OF THE HOG POPULATION. FOR SOME REASONS, NO RECORD OF PAST SOYBEAN PURCHASES BY FEED MILLERS IS AT HAND.

SOLUTION: BASED ON THE CORRELATIONS: 1. BETWEEN THE QUANTITY OF SOYBEANS AND HOG FEEDS

REQUIRED. BETWEEN THE QUANTITY OF HOG FEEDS REQUIRED AND THE

HOG POPULATION, THE DEMAND FOR SOYBEANS BY THE HOG FEED INDUSTRY CAN BE ESTABLISHED BY MAKING USE OF THE FOLLOWING AVAILABLE DATA: AN ANNUAL HOG POPULATION CENSUS COVERING AT LEAST 10

YEARS AN ESTIMATED ANNUAL CONSUMPTION, 298 KG, OF HOG FEEDS BY

THE AVERAGE HOG. THE QUANTITY, 5.6 KG OF SOYBEANS, A 40 KG BAG OF HOG MASH

CONTAINS:

LET’S TWIST YOUR MINDS A LITTLE BIT

Pulsing Vortex

If you stare at this one long enough you’ll notice a fast and pulsing multicolored vortex.

Waves

The blue almond-shaped objects look as if they’re all passing over three separate columns.

Hypnosis

Although this image is comprised of simple purple and green squares outlined in black, it looks like it is bulging out in the center

Kaleidoscopes

Wormhole

The black and white circular lines make this illusion seem as if there are various depths in the image, creating different entryways and tunnels.

Bull’s-Eye

If you stare at the center of the image, it looks as if the outer rings are rotating in alternating directions—an effect meant to mesmerize the viewer.

Starbursts

These bright purple and green star-like shapes appear to be moving, which can be a little nauseating if you stare at it for too long.

WARNING!!!

The phenomena on this page rely on your eye movements. You will be moving them anyway (you can never keep your eyes really still), but the demonstrations are aided by moving your display (if possible), or by scrolling the page in small steps.

The sample on the right is the “Ouchi Illusion” (Ouchi 1977, Spillmann et al 1986). When you shake your head rapidly, or better shake the display, a central disk will segregate as a distinct object, which in addition seems to be floating atop the background.

Akiyoshi Kitaoka’s image on the left is called “Out of Focus”. It also leads to a seeming shift of the central disk with respect to the surroundings. It is very effectively provoked by the eye movements occurring during reading. So, while you are reading this cast your “inner eye” to the left and watch for a seeming decoupling of disk and background. You may also observe that the disk floats above the background. (Image reproduced with kind permission.)

This sample called “Floating Motion” from Pinna & Spillmann (2002) also often appears very strong to me. I do not need to shake the screen, or the saccades from reading, just by exploratory eye movements over the image the centre square “decouples”. Here the background seems to move, while the central square remains in place, and seems to float on top. (Image redrawn with kind permission.)

JOKES LANG… FVR: ERAP, may gift ako for you.

Galing sa India and it's a 10 feet snake.

ERAP: Ows, niloloko mo naman ako eh! 10 feet? Hoy, di ako ganoon katanga, snake walang feet.

di ba??

JOKES LANG… Stewardess: Sir, chewing gum po

para di sumakit ang tenga nyo during d flight.Pasahero: Tenk u!(aftr 1 hr)Pasahero: Ms. pano ba tanggalin tong chewing gum sa tenga ko?

JOKES LANG… Secretary: IDEDEMANDA KO ANG

BOSS KO NG SEXUAL HARASSMENTAttorney: Bakit anong ginawa sa iyo?Secretary: Kasi sabi nya na mabango daw ang buhok ko e.Attorney: Para ganoon lang ay magdedemanda ka na, Bakit?Secretary: Kasi unano siya e...

JOKES LANG… Mrs. Tanoy is a very kuripot Ilocana (no offense meant to all

Ilocanos.

When her husband died, she inquired with the newspaper, asking the price for the obituary.

The ad taker said: "300 pesos for 5 words.

She said: "Pwede ba 2 words lang? Eto lang naman yun... "Tanoy Dead"

Ad taker said: "No mam. 5 words is the minimum."

After thinking for a while,

Mrs. Tanoy said: "Ok, para sulit, ilagay mo,

"TANOY DEAD, TOYOTA FOR SALE " ...

JOKES LANG… Pablo: Father, patawarin po ninyo

ako.Pari: Ano ang kasalanan mo?Pablo: Nagnakaw ako ng limang manok.Pari: Magdasal ka ng limang Ama Namin.Pablo: Father, walong Ama Namin na po ang dadasalin ko. Babalikan ko pan yung naiwan kong tatlong manok.

JOKES LANG… Pari: Iho, nakita ko ang kuya mo na naglalaro ng

tong-its sa kanto. Pinapabayaan na niya ang kanyang pag-aaral. Sana di mo siya tularan at pagbutihin mo ang pag-aaral mo.Juan: Wag po kayong mag-alala father, di ko naman po pinapabayaan ang pag-aaral ko eh.Pari: Talaga! Alam mo bang magbilang?Juan: Opo!Pari: Umpisahan mo ngaJuan: One…Two…Three…Four…Five…Six…Seven…Eight…Nine…Ten!Pari: Magaling! Kaya mo bang ituloy?Juan: Opo!Pari: Very Good! Sige nga. (Tuwang-tuwa)Juan: Jack…Queen..King!!!!

JOKES LANG… Quiapo Church :

MRS: Lord, bigyan ninyo ako ng P1,000 kasi anak ko nasa hospital.Narinig ng pulis, naawa, binigyan ng P500.MRS: Lord, next time huwag padaan sa pulis, nabawasan agad

Thank you