QMT 3001 BUSINESS FORECASTING. Exploring Data Patterns & An Introduction to Forecasting Techniques. Aysun KAPUCUGİL-İKİZ, PhD.

Transcription

1 1 QMT 3001 BUSINESS FORECASTING Exploring Data Patterns & An Introduction to Forecasting Techniques Aysun KAPUCUGİL-İKİZ, PhD. Forecasting 2 1

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4 Time Series Data Patterns Horizontal (stationary) / Trend / Cyclical / Seasonal 7 The two steps in analyzing time series data are: (a) Graph the time series data The data should be graphed to visually see the type of pattern: is the series progressively increasing or is it decreasing through time? There are various graphing techniques available including scatter diagrams, line graphs, or bar graphs. You can choose the visual approach that is optimal for your data. (b) Generate an autocorrelation function The pattern of the autocorrelations will usually help explain the pattern of the data. The autocorrelation output will also provide you with statistical tests to determine if the autocorrelation is important (i.e., "significant" in statistical terms). 8 A stationary data series does not increase or decrease over time. 4

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6 11 12 Y t = observation in time period t = observation at time period t-k Yt k 6

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9 17 Stat > Time Series > Autocorrelation 18 9

10 19 randomness trend 20 seasonality Is AC significant? 10

11 21 22 The standard error is the The standard error is the difference between a predicted value and the actual value for a variable. If the autocorrelation coefficient is divided by the standard error, the outcome should be >2 for a significant outcome. 11

12 23 "Box-Ljung Statistic" (BLS) or modified Box-Pierce Q Statistic: Sa.05 or less of level of significance value of Box-Ljung, is desirable - this means the forecaster has a less than a 5% chance of being wrong in stating autocorrelation exists between two variables

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15 29 30 Differencing data is needed when forecasting two data patterns: 1. Data with a trend. 2. Data with a strong autocorrelation component at lag 1 (above 0.90), where the autocorrelation at subsequent lags diminishes slowly. Differencing simply generates a new time series by subtracting the current value from the previous value for the entire original series. 15

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19 37 Examples Example: "Anna-Marie's Pools and Spas" is a chain of stores in Manitoba selling pools and pool supplies. 38 Anna-Marie is considering opening a new store in Saxon, Manitoba and has approached you as an advisor. She has a number of markets she is considering for her new store and wants to carefully examine each of these markets before making her selection. She wants to know if this is a good year to open a new store in Saxon, or if she would be better advised to wait a few years. She has asked you to examine the pattern of pool sales in Saxon in past years, using data on pool permits as a proxy for sales. Table shows this data for the last 15 years. 19

20 The first step is to graph this data over time. 39 The next step in the analysis is to generate the autocorrelation function, to see if the data is indeed random

21 Correlogram Example: Table shows the number of houses under construction (housing starts) in July in Toronto for the period 1994 to

22 Scatter graph

23 45 Housing under Construction in Toronto, Monthly, from January 1972 to May 2005 (extended the housing data series back to 1972 and include all months, rather than just July.) To illustrate a cyclical pattern 46 For forecasting purposes this indicates that the future values will depend on the last available level. However, using this approach to forecast cyclical time-series is problematic When time series data changes by small margins from period to period, the best approach is to explore how the data moves (e.g., the rate of change). "differencing". 23

24 An example of differenced data for the first five rows of the Housing Under Construction database. 47 = Differenced Data 48 24

25 49 50 Example: When is the best time for the new home builder to hold open houses in order to time these with the wedding market? Table shows the number of marriages recorded in Canada from 1995 to 2004, on a quarterly basis (3 month intervals). 25

26 Side-by-side Bar Chart

27 53 The optimal forecasting technique for any given situation depends on the nature of available data and the decision to be made or problem to be solved

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30 59 60 Other Factors for Choosing a Forecasting Technique: Level of Details. Time horizon. Based on judgment or data manipulation. Management acceptance. Cost. 30

31 Types of Forecasts Forecasting Techniques No single method is superior Qualitative Models: attempt to include subjective factors Time-Series Methods: include historical data over a time interval Causal Methods: include a variety of factors Delphi Methods Moving Average Regression Analysis Jury of Executive Opinion Exponential Smoothing Multiple Regression Sales Force Composite Consumer Market Survey Trend Projections Decomposition General considerations for choosing the appropriate method 62 Method Uses Considerations Jd Judgment Can C be used in the absence of Subjective Sbj i estimates are subject to the historical data (e.g. new product). Most helpful in medium- and long-term forecasts biases and motives of estimators. Causal Time series Sophisticated method Very good for medium- and long-term forecasts Easy to implement Work well when the series is relatively stable Must have historical data. Relationships can be difficult to specify Rely exclusively on past data. Most useful for short-term estimates. 31

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36 72 Example: Check the quality of forecast of the data on July Housing Under Construction Compare two forecasts using: 1. the second naïve forecast (which includes a difference term) 2. moving average method The in-sample period will be 1994 to 2002, the out-of-sample check will use the years 2003 and First step: Check the errors of the forecast for autocorrelation. 36

37 Results for the naïve forecast 74 Results for the moving average forecast 75 37

38 Results for the moving average forecast 76 Second step: Check the errors for 2003 and 2004 and test which forecast produces a more accurate result

39 the "in-sample" test 78 the "out-of-sample" test 79 39

40 80 The out-of-sample test confirms the results of the in-sample test. The error measures are all much larger for the moving average forecast than they are for the naïve forecast. This confirms that the naïve forecast is superior for short-term forecasts for this data. REFERENCES 82 Business Forecasting. John E. Hanke and Dean W. Wichern, 9th Edition, Pearson Education,