QMBU 301QMBU 301

FORECASTING YEARLY AREA SOWN FORECASTING YEARLY AREA SOWN IN TURKEYIN TURKEY

Ceren SekbanCeren SekbanÖzge ŞahlananÖzge Şahlanan

Tutku ÖzmenTutku ÖzmenBurcu KurtBurcu Kurt

Beste YılmayanBeste Yılmayan

Year

Are

a so

wn

2000199219841976196819601952

19000

18000

17000

16000

15000

14000

13000

12000

11000

Time Series Plot of Area sown

OBSERVED PATTERNSOBSERVED PATTERNS• Increasing trend.Increasing trend.• Trend component Trend component

increased significantly increased significantly after 1980after 1980

• Not randomNot random• Consequtive years Consequtive years

have similar areas have similar areas sownsown

• Decreasing trend after Decreasing trend after 19901990

Lag

Auto

corr

elat

ion

121110987654321

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Autocorrelation Function for Area sown(with 5% significance limits for the autocorrelations)

Year

Are

a so

wn

2000199219841976196819601952

19000

18000

17000

16000

15000

14000

13000

12000

11000

Time Series Plot of Area sown

CANDIDATECANDIDATE METHODSMETHODS

• RegressionRegression• Single exponential smoothingSingle exponential smoothing• Double exponential smoothingDouble exponential smoothing• Moving averageMoving average• Trend analysis (linear trend)Trend analysis (linear trend)

REGRESSIONREGRESSION

Potential DriversPotential Drivers

• Employed population in agricultureEmployed population in agriculture• The percentage of area that is fallowed each yearThe percentage of area that is fallowed each year• The amount of forest fires that is done to open The amount of forest fires that is done to open

new agricultural areasnew agricultural areas• Number of equipment and machinery used for Number of equipment and machinery used for

agricultural purposesagricultural purposes• The value of agricultural output in a yearThe value of agricultural output in a year• Observed technological development in Observed technological development in

agriculture; development of new machinery with agriculture; development of new machinery with the capability of cultivating a land which was hard the capability of cultivating a land which was hard to cultivate with previous methodsto cultivate with previous methods

• Regression Analysis: Area sown versus total agricu; Forest area ; ... Regression Analysis: Area sown versus total agricu; Forest area ; ...

• The regression equation isThe regression equation is• Area sown = 20283 - 0,000683 total agricultural creditsArea sown = 20283 - 0,000683 total agricultural credits• + 0,0289 Forest area burned(hectares)+ 0,0289 Forest area burned(hectares)• - 0,000049 Fertilizer used(tons)- 0,000049 Fertilizer used(tons)

• Predictor Coef SE Coef T PPredictor Coef SE Coef T P• Constant 20282,9 108,0 187,80 0,003Constant 20282,9 108,0 187,80 0,003• total agricultural credits -0,00068339 0,00001841 -37,12 0,017total agricultural credits -0,00068339 0,00001841 -37,12 0,017• Forest area burned(hectares) 0,028945 0,001202 24,08 0,026Forest area burned(hectares) 0,028945 0,001202 24,08 0,026• Fertilizer used(tons) -0,00004892 0,00000833 -5,87 0,107Fertilizer used(tons) -0,00004892 0,00000833 -5,87 0,107

• S = 16,4593 R-Sq = 99,9% R-Sq(adj) = 99,7%S = 16,4593 R-Sq = 99,9% R-Sq(adj) = 99,7%

• Analysis of VarianceAnalysis of Variance

• Source DF SS MS F PSource DF SS MS F P• Regression 3 421765 140588 518,95 0,032Regression 3 421765 140588 518,95 0,032• Residual Error 1 271 271Residual Error 1 271 271• Total 4 422036Total 4 422036

• • Residual Plots for Area sown Residual Plots for Area sown

Regression AnalysisRegression Analysis

Residual

Perc

ent

20100-10-20

99

90

50

10

1

Fitted Value

Resid

ual

1850018250180001775017500

10

50

-5-10

Residual

Freq

uenc

y

1050-5-10

3

2

1

0

Observation Order

Resid

ual

54321

10

5

0

-5

-10

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Area sown

OBSERVED PATTERNS AVAILABLE OBSERVED PATTERNS AVAILABLE DATADATA

• Consequtive years Consequtive years have similar areas have similar areas sownsown

• Trend component Trend component increased increased significantly after significantly after 1980 due to 1980 due to existence of free existence of free tradetrade

• Lag 1 Lag 1

• Economic Policy Economic Policy (Free Trade)( Free (Free Trade)( Free trade years trade years expressed in a expressed in a duumy variable)duumy variable)

Correlations: Area sown; free trade; Correlations: Area sown; free trade; lag1lag1

Area sown free tradeArea sown free trade

free trade 0,834free trade 0,834 0,0000,000

lag1 0,987 lag1 0,987 0,8280,828 0,000 0,0000,000 0,000

Cell Contents: Pearson correlationCell Contents: Pearson correlation P-ValueP-Value

Regression Analysis: Area sown versus free trade; Regression Analysis: Area sown versus free trade; lag1lag1

The regression equation isThe regression equation isArea sown = 2904 + 429 free trade + 0,821 lag1Area sown = 2904 + 429 free trade + 0,821 lag1

48 cases used, 1 cases contain missing values48 cases used, 1 cases contain missing values

Predictor Coef SE Coef T PPredictor Coef SE Coef T PConstant 2903,9 531,2 5,47 0,000Constant 2903,9 531,2 5,47 0,000free trade 429,2 124,8 3,44 0,001free trade 429,2 124,8 3,44 0,001lag1 0,82052 0,03486 23,54 0,000lag1 0,82052 0,03486 23,54 0,000

S = 240,376 R-Sq = 98,0% R-Sq(adj) = 97,9%S = 240,376 R-Sq = 98,0% R-Sq(adj) = 97,9%

Analysis of VarianceAnalysis of Variance

Source DF SS MS F PSource DF SS MS F PRegression 2 128717224 64358612 1113,84 0,000Regression 2 128717224 64358612 1113,84 0,000Residual Error 45 2600132 57781Residual Error 45 2600132 57781Total 47 131317356Total 47 131317356

Durbin-Watson statistic = 2,19863Durbin-Watson statistic = 2,19863

Residual

Per

cent

5002500-250-500

99

90

50

10

1

Fitted Value

Res

idua

l

1800016500150001350012000

500

250

0

-250

-500

Residual

Freq

uenc

y

6003000-300-600

16

12

8

4

0

Observ ation Order

Res

idua

l

454035302520151051

500

250

0

-250

-500

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Area sown

SINGLE EXPONENTIAL SINGLE EXPONENTIAL SMOOTHINGSMOOTHING

Single Exponential Single Exponential SmoothingSmoothing

Year

Area

sow

n

199719881979197019611952

20000

19000

18000

17000

16000

15000

14000

13000

12000

11000

Smoothing ConstantAlpha 1.15764

Accuracy MeasuresMAPE 1MAD 227MSD 100983

Variable

Forecasts95,0% PI

ActualFits

Single Exponential Smoothing Plot for Area sown

Single Exponential Single Exponential SmoothingSmoothing

Residual

Perc

ent

10005000-500

99

90

50

10

1

Fitted Value

Resi

dual

2000018000160001400012000

1000

500

0

-500

Residual

Freq

uenc

y

12008004000-400

16

12

8

4

0

Observ ation Order

Resi

dual

454035302520151051

1000

500

0

-500

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Area sown

DOUBLE EXPONENTIAL DOUBLE EXPONENTIAL SMOOTHINGSMOOTHING

Double Exponentioal Double Exponentioal SmoothingSmoothing

Year

Area

sow

n

199719881979197019611952

20000

19000

18000

17000

16000

15000

14000

13000

12000

11000

Smoothing ConstantsAlpha (level) 0.555794Gamma (trend) 0.890040

Accuracy MeasuresMAPE 1.4MAD 217.3MSD 73662.8

Variable

Forecasts95,0% PI

ActualFits

Double Exponential Smoothing Plot for Area sown

Double Exponentioal Double Exponentioal SmoothingSmoothing

Residual

Perc

ent

5000-500-1000

99

90

50

10

1

Fitted Value

Resi

dual

2000018000160001400012000

500

0

-500

-1000

Residual

Freq

uenc

y

4002000-200-400-600-800

10.0

7.5

5.0

2.5

0.0

Observ ation Order

Resi

dual

454035302520151051

500

0

-500

-1000

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Area sown

MOVING AVERAGEMOVING AVERAGE (k=3) (k=3)

Moving Average, k=3Moving Average, k=3

Year

Area

sow

n

199719881979197019611952

20000

19000

18000

17000

16000

15000

14000

13000

12000

11000

Moving AverageLength 3

Accuracy MeasuresMAPE 2MAD 312MSD 188862

Variable

Forecasts95,0% PI

ActualFits

Moving Average Plot for Area sown

Moving Average, k=3Moving Average, k=3

Residual

Perc

ent

150010005000-500

99

90

50

10

1

Fitted Value

Resi

dual

1800016500150001350012000

1500

1000

500

0

-500

Residual

Freq

uenc

y

150010005000-500

12

9

6

3

0

Observ ation Order

Resi

dual

454035302520151051

1500

1000

500

0

-500

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Area sown

TREND ANALYSISTREND ANALYSIS(LINEAR TREND MODEL)(LINEAR TREND MODEL)

Trend Analysis (Linear Trend Trend Analysis (Linear Trend Model)Model)

Year

Area

sow

n

199719881979197019611952

20000

19000

18000

17000

16000

15000

14000

13000

12000

11000

MAPE 3MAD 404MSD 286367

Accuracy Measures

ActualFitsForecasts

Variable

Trend Analysis Plot for Area sownLinear Trend Model

Yt = 13524,4 + 119,616*t

Trend Analysis (Linear Trend Trend Analysis (Linear Trend Model)Model)

Residual

Perc

ent

10000-1000-2000

99

90

50

10

1

Fitted Value

Resi

dual

20000180001600014000

1000

0

-1000

-2000

Residual

Freq

uenc

y

8004000-400-800-1200-1600

10,0

7,5

5,0

2,5

0,0

Observ ation Order

Resi

dual

454035302520151051

1000

0

-1000

-2000

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Area sown

AdequacyAdequacy MAPEMAPE MADMAD MSDMSDRegressioRegressio

nn √√ -- -- 5778157781Single Single

ExponentiaExponential l

SmoothingSmoothing

√√ 11 227227 100983100983

Double Double ExponentiaExponentia

l l SmoothingSmoothing

√√ 1.41.4 217.3217.3 73662.873662.8

Moving Moving average average

(k=3)(k=3)xx 22 312312 188862188862

Linear Linear TrendTrend xx 33 404404 286367286367

Forecast 1Forecast 1 Forecast 2Forecast 2 Forecast 3Forecast 3

RegressioRegressionn

18280,9518280,95 18280,9518280,95 18280,9518280,95

Double Double Ex. Ex. SmoothinSmoothingg

18133.918133.9 17913.117913.1 17692.417692.4