# Time Series for Apple, Inc

The required Apple Inc sales data in attached Excel document.

You will therefore be required to collect historical unadjusted (i.e. should not be adjusted for seasonality) data for eight years, that will be used for these time series.

TIME SERIES PARTICULARS

You must perform a complete time series analysis, making use of the following guidelines:

Double check that your data is NOT seasonally adjusted and that you have 8 years (must be either quarterly or monthly) of data in total.

Seasonal Variation

Trend Analysis

Based on the time series (original data) graph, describe the time series (i.e. before de-seasonalizing).

On the same graph as (a) graph the de-seasonalized time series.

Write out the Trend line equation provided by your computer (or manual) output and explain the meaning of the components (b0, b1) as they apply to your dependent variable. (De-seasonalize your data before finding the Trend Line).

Cyclical-Irregular variation

Forecasting

Show all detailed calculations.

Plot the actual and predicted values against time on the same graph.

Copy of the data.

Calculation of seasonal indices.

Calculation of Trend Line

Graph of original data and the trend line

Graph of Seasonal indices

Graph of Predicted and actual values vs. time.

https://brainmass.com/statistics/regression-analysis/time-series-apple-inc-446371

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the attached files.

Time Series for Apple Inc

Need urgent help with Time Series. Will add 50% additional credits if this is done in one day. The required Apple Inc sales data in attached document.

"You will therefore be required to collect historical unadjusted (i.e. should not be adjusted for seasonality) data for eight years, that will be used for these time series

TIME SERIES PARTICULARS

You must perform a complete time series analysis, making use of the following guidelines:

Double check that your data is NOT seasonally adjusted and that you have 8 years (must be either quarterly or monthly) of data in total.

Seasonal Variation

Trend Analysis

Based on the time series (original data) graph, describe the time series (i.e. before de-seasonalizing).

On the same graph as (a) graph the de-seasonalized time series.

Write out the Trend line equation provided by your computer (or manual) output and explain the meaning of the components (b0, b1) as they apply to your dependent variable. (De-seasonalize your data before finding the Trend Line).

Cyclical-Irregular variation

Forecasting

Show all detailed calculations.

Plot the actual and predicted values against time on the same graph.

Copy of the data.

Calculation of seasonal indices.

Calculation of Trend Line

Graph of original data and the trend line

Graph of Seasonal indices

Graph of Predicted and actual values vs. time."

Calculation of seasonal index

Seasonal index are computed using ratio of moving average method.

Details

Centered Moving Average and De-seasonalization

Centered

Moving Ratio to

t Year Quarter Total Sales Average CMA

1 2002 1 2,102

2 2002 2 3,144

3 2002 3 3,235 3162.625 1.023

4 2002 4 4,011 3136.500 1.279

5 2003 1 2,419 3166.625 0.764

6 2003 2 2,618 3324.750 0.787

7 2003 3 4,002 3363.250 1.190

8 2003 4 4,509 3482.875 1.295

9 2004 1 2,229 3566.000 0.625

10 2004 2 3,765 3412.750 1.103

11 2004 3 3,520 3319.750 1.060

12 2004 4 3,765 3249.000 1.159

13 2005 1 2,229 3235.125 0.689

14 2005 2 3,199 3330.250 0.961

15 2005 3 3,975 3382.875 1.175

16 2005 4 4,071 3464.750 1.175

17 2006 1 2,344 3581.375 0.654

18 2006 2 3,739 3636.750 1.028

19 2006 3 4,368 3822.625 1.143

20 2006 4 4,121 4059.250 1.015

21 2007 1 3,781 4235.875 0.893

22 2007 2 4,195 4612.500 0.909

23 2007 3 5,325 5427.500 0.981

24 2007 4 6,177 6559.625 0.942

25 2008 1 8,245 7609.750 1.083

26 2008 2 8,788 8729.250 1.007

27 2008 3 9,133 9230.875 0.989

28 2008 4 11,325 9319.500 1.215

29 2009 1 7,110 9847.375 0.722

30 2009 2 10,632 10435.500 1.019

31 2009 3 11,512 11480.125 1.003

32 2009 4 13,651 12711.375 1.074

33 2010 1 13,141 13997.000 0.939

34 2010 2 14,451 15555.750 0.929

35 2010 3 17,978

36 2010 4 19,655

The computed ratio to moving average values are averaged and adjusted to computed the final value of seasonal index.

Calculation of Seasonal Indexes

1 2 3 4

2002 1.023 1.279

2003 0.764 0.787 1.190 1.295

2004 0.625 1.103 1.060 1.159

2005 0.689 0.961 1.175 1.175

2006 0.654 1.028 1.143 1.015

2007 0.893 0.909 0.981 0.942

2008 1.083 1.007 0.989 1.215

2009 0.722 1.019 1.003 1.074

2010 0.939 0.929

mean: 0.796 0.968 1.071 1.144 3.979

Adjusted: 0.800 0.973 1.076 1.150 4.000

The original values of the time series is divided by the seasonal index to obtain the de-seasonalized values.

Centered Moving Average and Deseasonalization

Seasonal Total Sales

t Year Quarter Total Sales Indexes Deseasonalized

1 2002 1 2,102 0.800 2,626.1

2 2002 2 3,144 0.973 3,231.0

3 2002 3 3,235 1.076 3,005.9

4 2002 4 4,011 1.150 3,487.0

5 2003 1 2,419 0.800 3,022.1

6 2003 2 2,618 0.973 2,690.4

7 2003 3 4,002 1.076 3,718.5

8 2003 4 4,509 1.150 3,920.0

9 2004 1 2,229 0.800 2,784.8

10 2004 2 3,765 0.973 3,869.1

11 2004 3 3,520 1.076 3,270.7

12 2004 4 3,765 1.150 3,273.2

13 2005 1 2,229 0.800 2,784.8

14 2005 2 3,199 0.973 3,287.5

15 2005 3 3,975 1.076 3,693.5

16 2005 4 4,071 1.150 3,539.2

17 2006 1 2,344 0.800 2,928.4

18 2006 2 3,739 0.973 3,842.4

19 2006 3 4,368 1.076 4,058.6

20 2006 4 4,121 1.150 3,582.7

21 2007 1 3,781 0.800 4,723.7

22 2007 2 4,195 0.973 4,311.0

23 2007 3 5,325 1.076 4,947.8

24 2007 4 6,177 1.150 5,370.1

25 2008 1 8,245 0.800 10,300.8

26 2008 2 8,788 0.973 9,031.1

27 2008 3 9,133 1.076 8,486.1

28 2008 4 11,325 1.150 9,845.6

29 2009 1 7,110 0.800 8,882.8

30 2009 2 10,632 0.973 10,926.1

31 2009 3 11,512 1.076 10,696.6

32 2009 4 13,651 1.150 11,867.8

33 2010 1 13,141 0.800 16,417.5

34 2010 2 14,451 0.973 14,850.7

35 2010 3 17,978 1.076 16,704.6

36 2010 4 19,655 1.150 17,087.5

Trend Analysis

The plot of the De-seasonalized values suggest that quadratic trend is appropriate for the data.

Coefficients Standard Error t Stat P-value

Intercept 4563.903 568.4031 8.029341 2.9E-09

Time -411.346 70.83851 -5.80681 1.7E-06

Time2 21.02438 1.857026 11.32153 6.62E-13

The estimated quadratic trend equation is

De seasonalized sales = 4563.903 -411.346 *Time +21.0243*Time2

The predicted values are multiplied with the seasonal indies to obtain the re -seasonalized predicted sales

The model adequacy measure R2 suggest that the model is able to explain 94.62% variability in the data.

Regression Statistics

Multiple R 0.972734637

R Square 0.946212673

Adjusted R Square 0.942952835

Standard Error 1074.234694

Observations 36

Time Deseasonalized Sales (Predicted) Seasonal Indexes Total Sales Reseasonalized

1 4173.581693 0.800 3340.648

2 3825.309338 0.973 3722.358

3 3519.085749 1.076 3787.337

4 3254.910925 1.150 3743.989

5 3032.784867 0.800 2427.523

6 2852.707575 0.973 2775.932

7 2714.679048 1.076 2921.612

8 2618.699287 1.150 3012.181

9 2564.768291 0.800 2052.91

10 2552.886061 0.973 2484.18

11 2583.052597 1.076 2779.952

12 2655.267898 1.150 3054.245

13 2769.531965 0.800 2216.808

14 2925.844797 0.973 2847.101

15 3124.206395 1.076 3362.357

16 3364.616759 1.150 3870.179

17 3647.075888 0.800 2919.218

18 3971.583782 0.973 3864.696

19 4338.140442 1.076 4668.826

20 4746.745868 1.150 5459.985

21 5197.40006 0.800 4160.14

22 5690.103017 0.973 5536.964

23 6224.854739 1.076 6699.36

24 6801.655227 1.150 7823.662

25 7420.504481 0.800 5939.573

26 8081.4025 0.973 7863.907

27 8784.349285 1.076 9453.959

28 9529.344836 1.150 10961.21

29 10316.38915 0.800 8257.517

30 11145.48223 0.973 10845.52

31 12016.62408 1.076 12932.62

32 12929.81469 1.150 14872.63

33 13885.05407 0.800 11113.97

34 14882.34222 0.973 14481.81

35 15921.67913 1.076 17135.35

36 17003.0648 1.150 19557.92

https://brainmass.com/statistics/regression-analysis/time-series-apple-inc-446371