Accounting论文模板 – Time Series Analysis

Time series analysis deals with ways of breaking down data and is aimed at giving the data a more advance statistical meaning. It involves forecasting, trend and variation analysis among other things. Time series increases the usefulness of both the grouped and ungrouped data (Hamilton, 1994).

A table showing trend and variation for units of production of laptops

Table 1    
Year  QuarterInitial values (Y)Four figures moving totalsFour figures moving averages Two figures moving totalTrend values (T)Variation  [Y-T]
201110     
 2132     
   31278   
 3102  185.592.759.25
   430107.5   
 478  223.5111.75-33.75
   464116   
20121118  239.75119.88-1.88
   495123.75   
 2166  25212640
   513128.25   
 3133  267.5133.75-0.75
   557139.25   
 496  287.5143.75-47.75
   593148.25   
20131162  301.5150.7511.25
   631153.25   
 2202  317.25158.6343.37
   656164   
 3171  335.5167.753.25
   686171.5   
 4121  358179-58
   746186.5   
20141192  373.5186.755.25
   788187   
 2262  391.25195.6366.37
   817204.25   
 3213  4222112
   871217.75   
 4150  452226-76
   937234.25   
20151246  479.75239.896.11
   982245.5   
 2328  453.5226.75101.25
   832208   
 3258     
 4      

Seasonal variations for each quarter for units of production

Quarter one

       [-1.88 + 11.25 + 5.25 + 6.11] / 4 = 5.1825

Quarter two

       [40 + 43.37 + 66.37 + 101.25] / 4 =62.7475

Quarter three

       [9.25 + -0.75 + 3.25 + 2] / 4 = 3.4375

Quarter four

       [-33.75 + -47.75 + -58 +-76] / 4 = -53.875

A table showing trend and variation for manufacturing costs of laptops

TABLE 2 
YearquarterInitial values (Y)Four figures moving totalsFour figures moving averagesTwo figures moving totalsTrend values (T)Variation {Y-T}
201110     
 22014     
   53051326.25   
 31795  3091.51545.75249.25
   70611765.25   
 41496  36281814-318
   74511862.75   
201211756  37661883-127
   76131903.25   
 22404  38321916488
   77151928.75   
 31957  3923.251961.63-4.63
   79781994.5   
 41598  4043.52021.75-423.75
   81962049   
201312019  4161.52080.75-61.75
   84502112.5   
 22622  4278.52139.25482.75
   86642166   
 32211  4363.252181.6329.37
   87892197.25   
 41812  4448.252224.13-412.13
   90042251   
201412144  4525.752262.88-118.88
   90992274.75   
 22837  4572.752286.38550.62
   91922298   
 32306  4638.252319.13-13.13
   93612340.25   
 41905  4746.752373.38-468.38
   96262406.5   
201512313  4879.52439.75-126.75
   98922473   
 23102  4469.752234.88867.88
   79871996.75   
 32572       
 40     

Seasonal variations for each quarter for manufacturing costs of laptops

Quarter one

       [-127 + -61.75 + -118.88 + -126.75] / 4 = -108.595

Quarter two

[488 + 482.75 +550.62 + 867.88] / 4 = 597.3125

Quarter three

       [249.25 + -4.63 + 29.37 + -13.13] / 4 =65.215

Quarter four

[-318 + -423.75 + -412.13 +-468.38] / 4 = -405.565

A Forecast for units of production for each quarter 2016

A graph showing trend in units of production for the last 18 quarters

Key

Horizontal axis= quarters

Vertical axis=units of production

To be able to forecast the units to be produced in 2016, we use 2014 and 2015 values

Quarter one forecast

       = 15000

Quarter two forecast

       = {15000 + 24600} / 2

       = 19800

Quarter three

       = {15000 + 24600 + 32800} / 3

       =24134

Quarter four

       = {15000 + 24600 + 32800 + 25800} / 4

       = 24550

A Forecast for manufacturing costs for each quarter 2016

A graph showing trend in manufacturing costs for the last 18 quarters

KEY

Horizontal axis = quarters

Vertical axis = manufacturing costs

Manufacturing costs forecast for 2016

In order to forecast manufacturing costs for 2016, we shall use value from 2014 and 2015

 Quarter one forecast

       = 1,905,000

Quarter two forecast

       = {1,905,000 + 2,313,000} / 2

       = 2,109,000

Quarter three forecast

       = {1,905,000 + 2,313,000 + 3,102,000} / 3

       = 2,440,000

Quarter four forecast

       = {1,905,000 + 2,313,000 + 3,102,000 + 2,572,000} / 4

       = 2,473,000

Correlation coefficient and regression equation for the past 18 quarters between manufacturing costs of laptops and units of laptops produced.

QuartersXYX2Y2XY
 11322014174244056196265848
21021795104043222025183090
378149660842238016116688
41181756139243083536207208
51662404275565779216399064
61331957176893829849260281
796159892162553604258876
81622019262444076361327078
92022622408046874884529644
101712211292414888521378081
111211812146413283344219252
121922144368644596736411648
132622837686448048569743294
142132306453695317636491178
151501905225003629025285750
162462313605165349969568998
17328310210758496224041017456
182582572665646615184663576
∑ =∑x=3130∑y=38863∑x2=621268∑y2=87065075∑xy=9064957

N =18

Correlation coefficient (r)

r = 18(9064957) – [(3130) (38863)]/√[18(621268) – (3130)2] * √[18(87065075) –(38863)2]

       =41528036/88875448.588

               = 0.47

Regression equation

Y = a + bx

Where b is the slope and a is the intercept

       b = (n∑XY – (∑x)(∑y)) / (n∑x2 – (∑x)2)

          = (18*9064957 – (3130*38863) / (18*621268 – (3130)2)

        = 30.1

a = (∑y – b (∑x)) / n

      = (38863 – 30.1(3130) / 18

          = – 3075

References

Draper, N. R., & Smith, H., 2014. Applied regression analysis. John Wiley & Sons.

Fleischmann, B., Meyr, H., & Wagner, M., 2015. Advanced planning. In Supply chain management and advanced planning (pp. 71-95). Springer Berlin Heidelberg.

Granger, C. W. J., & Newbold, P., (2014). Forecasting economic time series. Academic Press.

Hamilton, J. D., 1994. Time series analysis (Vol. 2). Princeton: Princeton                                      university press

Kleinbaum, D., Kupper, L., Nizam, A., & Rosenberg, E., 2013. Applied regression analysis and other multivariable methods. Cengage Learning.

Montgomery, D. C., Jennings, C. L., & Kulahci, M. 2015. Introduction to time series analysis and forecasting. John Wiley & Sons.

Pardo, J., Zamora-Martínez, F., & Botella-Rocamora, P., 2015. Online Learning Algorithm for Time Series Forecasting Suitable for Low Cost Wireless Sensor Networks Nodes. Sensors, 15(4), 9277-9304.

Reuter, B., 2015. Demand planning of styrene plastics. In Supply Chain Management and Advanced Planning (pp. 377-390). Springer Berlin Heidelberg.

Scott, S. L., & Varian, H., 2014. Bayesian variable selection for nowcasting economic time series. In Economic Analysis of the Digital Economy. University of Chicago Press

Seber, G. A., & Lee, A. J., 2012. Linear regression analysis (Vol. 936). John Wiley & Sons.

Singh, P., 2015. Big Data Time Series Forecasting Model: A Fuzzy-Neuro Hybridize Approach. In Computational Intelligence for Big Data Analysis (pp. 55-72). Springer International Publishing.

Zhang, G. P., & Qi, M., 2005. Neural network forecasting for seasonal and trend time series. European journal of operational research, 160(2), 501-514.

Scroll to Top