Example of Decomposition
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You wish to predict trade employment for the next 12 months using data collected over 60 months. Because the data have a trend that is fit well by trend analysis' quadratic trend model and possess a seasonal component, you use the residuals from trend analysis example (see Example of a trend analysis) to combine both trend analysis and decomposition for forecasting.

1    Do the trend analysis example.

2    Choose Stat > Time Series > Decomposition.

3    In Variable, enter the name of the residual column you stored in the trend analysis.

4    In Seasonal length, enter 12.

5    Under Model Type, choose Additive. Under Model Components, choose Seasonal only.

6    Check Generate forecasts and enter 12 in Number of forecasts.

7    Click Storage. Check Forecasts and Fits.

8    Click OK in each dialog box.

Session window output

Trend Analysis for Trade

 

 

Data      Trade

Length    60

NMissing  0

 

 

Fitted Trend Equation

 

Yt = 320.76 + 0.509×t + 0.01075×t^2

 

 

Accuracy Measures

 

MAPE   1.7076

MAD    5.9566

MSD   59.1305

 

 

Forecasts

 

Period  Forecast

61       391.818

62       393.649

63       395.502

64       397.376

65       399.271

66       401.188

67       403.127

68       405.087

69       407.068

70       409.071

71       411.096

72       413.142

 

 

Time Series Decomposition for RESI1

 

 

Additive Model

 

 

Data      RESI1

Length    60

NMissing  0

 

 

Seasonal Indices

 

Period     Index

     1   -8.4826

     2  -13.3368

     3  -11.4410

     4   -5.8160

     5    0.5590

     6    3.5590

     7    1.7674

     8    3.4757

     9    3.2674

    10    5.3924

    11    8.4965

    12   12.5590

 

 

Accuracy Measures

 

MAPE  881.582

MAD     2.802

MSD    11.899

 

 

Forecasts

 

Period  Forecast

61       -8.4826

62      -13.3368

63      -11.4410

64       -5.8160

65        0.5590

66        3.5590

67        1.7674

68        3.4757

69        3.2674

70        5.3924

71        8.4965

72       12.5590

Graph window output

 

 

Interpreting the results

Decomposition generates three sets of plots:

·    A time series plot that shows the original series with the fitted trend line, predicted values, and forecasts.

·    A component analysis - in separate plots are the series, the detrended data, the seasonally adjusted data, the seasonally adjusted and detrended data (the residuals).

·    A seasonal analysis - charts of seasonal indices and percent variation within each season relative to the sum of variation by season and boxplots of the data and of the residuals by seasonal period.

In addition, Minitab displays the fitted trend line, the seasonal indices, the three accuracy measures- MAPE, MAD, and MSD (see Measures of accuracy) - and forecasts in the Session window.

In the example, the first graph shows that the detrended residuals from trend analysis are fit fairly well by decomposition, except that part of the first annual cycle is underpredicted and the last annual cycle is overpredicted. This is also evident in the lower right plot of the second graph; the residuals are highest in the beginning of the series and lowest at the end.