Explore BrainMass

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.

    © BrainMass Inc. brainmass.com December 24, 2021, 10:08 pm ad1c9bdddf
    https://brainmass.com/statistics/regression-analysis/time-series-apple-inc-446371

    Attachments

    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

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

    © BrainMass Inc. brainmass.com December 24, 2021, 10:08 pm ad1c9bdddf>
    https://brainmass.com/statistics/regression-analysis/time-series-apple-inc-446371

    Attachments

    ADVERTISEMENT