Explore BrainMass

# Time Series for Apple, Inc

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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!

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
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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!