FORECAST

Forecast



Forecast

Introduction

Quarterly house sales data for time span from the starting of 2005 until the middle of 2010 were investigated by time-series methods. Autocorrelation and partial autocorrelation purposes were calculated for the data. Appropriate Box-Jenkins autoregressive incorporated going mean model was fitted. Validity of the model was checked utilising benchmark statistical techniques. The forecasting power of autoregressive incorporated going mean model was utilised to forecast house sales for three premier years.

Sales are the lifeblood of a business. It's what assists businesses to yield workers, cover functioning costs, purchase more inventory, market new goods and appeal more investors. Sales forecasting is a vital part of the economic designing of a business. It's a self-assessment device that values past and present sales statistics to intelligently forecast future performance.

Data set of Scooter Production

Trend of data

Seasonal Decomposition

Series Name:Scooter

Case Number

Original Series

Moving Average Series

Ratio of initial sequence to moving Average (%)

Seasonal Factor (%)

Seasonally Adjusted Series

Smoothed Trend-Cycle Series

Irregular (Error) Component

1

3361.000

.

.

120.7

2785.047

2781.724

1.001

2

2822.000

.

.

103.1

2737.978

2767.806

.989

3

2268.000

2754.5000

82.3

81.6

2780.392

2739.970

1.015

4

2567.000

2709.2500

94.7

94.7

2711.243

2698.697

1.005

5

3180.000

2670.0000

119.1

120.7

2635.064

2658.869

.991

6

2665.000

2643.5000

100.8

103.1

2585.652

2620.867

.987

7

2162.000

2605.0000

83.0

81.6

2650.444

2594.710

1.021

8

2413.000

2563.5000

94.1

94.7

2548.589

2553.987

.998

9

3014.000

2530.7500

119.1

120.7

2497.510

2504.631

.997

10

2534.000

2476.5000

102.3

103.1

2458.553

2448.095

1.004

11

1945.000

2428.2500

80.1

81.6

2384.419

2399.438

.994

12

2220.000

2380.0000

93.3

94.7

2344.745

2359.150

.994

13

2821.000

2338.0000

120.7

120.7

2337.584

2323.897

1.006

14

2366.000

2308.0000

102.5

103.1

2295.555

2281.641

1.006

15

1825.000

2262.7500

80.7

81.6

2237.308

2237.447

1.000

16

2039.000

2218.0000

91.9

94.7

2153.574

2192.258

.982

17

2642.000

2173.0000

121.6

120.7

2189.258

2155.433

1.016

18

2186.000

2133.7500

102.4

103.1

2120.914

2121.055

1.000

19

1668.000

2122.2500

78.6

81.6

2044.839

2091.092

.978

20

1993.000

2078.5000

95.9

94.7

2104.989

2064.691

1.020

21

2467.000

.

.

120.7

2044.246

2051.491

.996

Model Description

Model Name

MOD_1

Series or Sequence

1

Scooter

Transformation

None

Non-Seasonal Differencing

0

Seasonal Differencing

0

Length of Seasonal Period

4

Horizontal Axis Labels

Date_

Intervention Onsets

None

Reference Lines

None

Area Below the Curve

Not filled

Applying the form specifications from MOD_1

Case Processing Summary

Scooter

Series or Sequence Length

21

Number of Missing places in the Plot

User-Missing

0

System-Missing

0

Above grahs shows seasonality and decreasing trend.

After applying seasonal difference of 4.

Model Description

Model Name

MOD_6

Series or Sequence

1

Scooter

Transformation

None

Non-Seasonal Differencing

0

Seasonal Differencing

4

Length of Seasonal Period

4

Horizontal Axis Labels

Date_

Intervention Onsets

None

Reference Lines

None

Area Below the Curve

Not filled

Applying the form specifications from MOD_6

Case Processing Summary

Scooter

Series or Sequence Length

21

Number of Missing values in the Plot

User-Missing

0

System-Missing

0

Model Description

Model Name

MOD_2

Series Name

1

Scooter

Transformation

None

Non-Seasonal Differencing

0

Seasonal Differencing

4

Length of Seasonal Period

4

Maximum Number of Quarterly differences

16

Process Assumed for Calculating the Standard Errors of the Autocorrelations

Independence(white noise)a

Display and Plot

All quarterly differences

Applying the form specifications from MOD_2

a. Not applicable for calculating the benchmark errors of the partial autocorrelations.

Case Processing Summary

Scooter

Series Length

21

Number of Missing Values

User-Missing

0

System-Missing

0

Number of Valid Values

21

Number of standards Lost Due to Differencing

16

Number of Computable First Quarterly differences After Differencing

4

Autocorrelations

Series:Scooter

Quarterly difference

Autocorrelation

Std. Errora

Box-Ljung Statistic

Value

df

Sig.b

1

-.426

.338

1.587

1

.208

2

-.124

.293

1.765

2

.414

3

.067

.239

1.844

3

.605

a. The underlying process assumed is self-reliance (white noise).

b. Based on the asymptotic chi-square approximation.

Partial Autocorrelations

Series:Scooter

Quarterly difference

Partial Autocorrelation

Std. Error

1

-.426

.447

2

-.373

.447

3

-.232

.447

Regression and Correlation Analysis

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.677a

.459

.430

334.98500

a. Predictors: (Constant), YEAR, not periodic

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

1806953.716

1

1806953.716

16.103

.001a

Residual

2132084.093

19

112214.952

Total

3939037.810

20

a. Predictors: (Constant), YEAR, not periodic

b. Dependent Variable: Scooter

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

380506.411

94215.978

4.039

.001

YEAR, not periodic

-188.318

46.929

-.677

-4.013

.001

a. Dependent Variable: Scooter

Correlations

Scooter

YEAR, not periodic

Scooter

Pearson Correlation

1

-.677**

Sig. (2-tailed)

.001

N

21

21

YEAR, not periodic

Pearson Correlation

-.677**

1

Sig. (2-tailed)

.001

N

21

21

**. Correlation is important at the 0.01 level (2-tailed).

Forecast Values

2499.92

Q3 2010

2779.331

Q4 2010

2044.711

Q1 2011

2296.449

Q2 2011

2510.78

Q3 2011

2803.617

Q4 2011

2061.912

Q1 2012

2306.016

Q2 2012

2520.74

Q3 2012

2823.88

Q4 2012

2097.127

Q1 2013

2318.006

Q2 2013

2532.32

Q3 2013

2849.867

Q4 2013

2116.601

Q1 2014

2329.251

Q2 2014

2543.06

Q3 2014

2877.71

Q4 2014

2142.079

Q1 2015

2332.108

Q2 2015

2553.56

Q3 2015

Manufacturing Cost

Trend of data

Seasonal Decomposition

Series Name:manufactureCost

DATE_

Original Series

Moving Average Series

Ratio of Original Series to Moving Average Series (%)

Seasonal Factor (%)

Seasonally Adjusted Series

Smoothed Trend-Cycle Series

Irregular (Error) Component

Q3 2005

5105.000

.

.

113.8

4487.245

4387.025

1.023

Q4 2005

4583.000

.

.

103.7

4419.790

4319.309

1.023

Q1 2006

3480.000

4273.7500

81.4

85.9

4050.891

4183.875

.968

Q2 2006

3927.000

4148.7500

94.7

96.6

4063.814

4085.366

.995

Q3 2006

4605.000

4029.5000

114.3

113.8

4047.750

3998.323

1.012

Q4 2006

4106.000

3963.5000

103.6

103.7

3959.777

3913.584

1.012

Q1 2007

3216.000

3874.7500

83.0

85.9

3743.582

3794.735

.987

Q2 2007

3572.000

3736.5000

95.6

96.6

3696.446

3693.591

1.001

Q3 2007

4052.000

3638.7500

111.4

113.8

3561.668

3599.339

.990

Q4 2007

3715.000

3566.5000

104.2

103.7

3582.702

3521.294

1.017

Q1 2008

2927.000

3473.0000

84.3

85.9

3407.172

3426.363

.994

Q2 2008

3198.000

3390.0000

94.3

96.6

3309.416

3337.000

.992

Q3 2008

3720.000

3282.5000

113.3

113.8

3269.843

3267.772

1.001

Q4 2008

3285.000

3246.2500

101.2

103.7

3168.015

3211.718

.986

Q1 2009

2782.000

3189.7500

87.2

85.9

3238.385

3156.633

1.026

Q2 2009

2972.000

3095.2500

96.0

96.6

3075.543

3072.905

1.001

Q3 2009

3342.000

3028.2500

110.4

113.8

2937.585

3012.821

.975

Q4 2009

3017.000

2997.2500

100.7

103.7

2909.559

2972.167

.979

Q1 2010

2658.000

2950.5000

90.1

85.9

3094.043

2939.715

1.052

Q2 2010

2785.000

2870.0000

97.0

96.6

2882.028

2876.873

1.002

Q3 2010

3020.000

.

.

113.8

2654.550

2845.453

.933

Model Description

Model Name

MOD_3

Series or Sequence

1

manufactureCost

Transformation

None

Non-Seasonal Differencing

0

Seasonal Differencing

0

Length of Seasonal Period

4

Horizontal Axis Labels

Date_

Intervention Onsets

None

Reference Lines

None

Area Below the Curve

Not filled

Applying the form specifications from MOD_3

Case Processing Summary

manufactureCost

Series or Sequence Length

21

Number of Missing Values in the Plot

User-Missing

0

System-Missing

0

Above grahs shows seasonality and decreasing trend.

After applying difference of 4.

Model Description

Model Name

MOD_4

Series or Sequence

1

manufactureCost

Transformation

None

Non-Seasonal Differencing

0

Seasonal Differencing

4

Length of Seasonal Period

4

Horizontal Axis Labels

Date_

Intervention Onsets

None

Reference Lines

None

Area Below the Curve

Not filled

Applying the form specifications from MOD_4

Case Processing Summary

manufactureCost

Series ...