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September 2005Created by Polly Stuart1 Analysis of Time Series For AS90641 Part 3 Reporting

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2 Beginnings You have already done most of the analysis for the retail clothing sales data Now you need to write the report. Open a Word document and head it up. Copy across the spreadsheet that you produced using the previous presentation.

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3 Report The report needs to focus on the validity of the analysis you have done Every comment you make needs to be justified by referring to your analysis

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4 Step 1: Constant dollars You need to justify why you used constant dollars. The discussion in the last presentation will help you. Make sure you relate to the context. Drawing a graph to compare the original data and constant dollar data may be useful.

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5 Step 2: Discuss each component of the data Identify the trend in context. Identify and describe the seasonal pattern. Describe the pattern of the irregular and identify possible outliers. See if there are any long term cycles in your data Display your graphs as evidence for your comments. Be specific, think about the context.

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6 Part 3: Forecasting Justify the model you are using for the forecast by looking at the graphs of each model. Choose the best and use it to make your forecast. How good an estimate of the seasonal variation did you have? Think about how far ahead you are forecasting Evaluate how valid your forecast is in context. Does the forecast make sense? What are the things that could make it completely wrong?

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7 0 How well does your model follow the moving average trend line? What is happening to the seasonal variation as the trend changes? For how long do you think this model will be justified? Who might find this forecast useful?

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8 Step 4: Seasonally adjusted data Graph the actual (constant dollars), trend and seasonally adjusted data on the same graph. The seasonally adjusted data helps you compare values from different seasons. Calculate the % change between the quarters and comment

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9 0 Calculate the % change between some of the more recent quarters.

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10 Step 5: Improvements Should you have used an additive or multiplicative method? Justify your choice of model for the trend. Were your results affected by outliers?

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11 Outliers The purpose of time series analysis is to try to smooth the data. Extreme outliers can distort the estimation of trend and seasonal components. Identifying any outliers and discussing the effects on other components is important in your report.

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12 There are now optional slides showing: A process for identifying outliers. The use of a multiplicative model.

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13 Now finish off your analysis and report on retail clothing sales.

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14 The End A worked example answer based on this PowerPoint is available for you to check your answers

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15 More on outliers Definitions: –An outlier can be defined as an element in the irregular which is 1.8 standard deviations or more from the mean. –An extreme outlier can be defined as one which is more than 2.8 standard deviations from the mean.

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16 Calculate the mean and standard deviation of the outliers. (Notice that the values are scattered around zero.) Then identify the values which are outliers by the definitions on the previous slide.

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17 Three outliers have been found. None of them are extreme. Look at the effect on the graphs of the trend and the seasonal factor. Can you see how these outliers have affected the graphs? How many moving average values would be affected by the largest outlier? If you were forecasting for the next December, what would be the effect of this outlier?

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18 Multiplicative analysis Some series follow a multiplicative model where data values are found by: actual = trend x seasonal x irregular This means that where you would subtract in the analysis of an additive series you divide instead. Open the worksheet marriage from examples.xls

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19 Marriage data Always begin by drawing the series. Does this qualify as multiplicative?

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20 Notice this step!

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21 And this one.

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22 And this one!

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24 Notice: The seasonal component is greater than 1 for December and March and June. For September it is a lot less. Look at the seasonal pattern on the graph on the previous slide.

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25 The irregular component has values scattered around 1. In an additive series values would be scattered around zero. Find any outliers. Check them out on the graph.

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26 This is the actual end! Haere rā ngā tauira mā!

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