2. QM 2113 - Spring 2002 Business Statistics Analysis of Time Series Data: an Introduction

3. Agenda  Homework – Return first SPSS exercise set; comments – Collect second SPSS exercise set; questions?  SPSS – Demonstrate statistical estimation – Hypothesis tests One-tail Use of p-value (i.e., significance) – Copy/paste into Word or other applications – What about inferences about proportions?  Time series analysis

4. Conclusions About a Population or Process Population or Process Sample Parameter Statistic Inferences

5. Using SPSS Univariate Inferences  Parameter of concern – Averages – Not proportions  Hypothesis testing: – First, setup test (H 0 & H A, , sketch, decision rule) – Then: Analyze | Compare Means | One-Sample t Test  Estimation: Analyze | Descriptive Statistics | Explore

6. Recall Data Classifications  Three dimensions: data type, source, frame of reference  Type of data – Quantitative: ratio, interval, (ordinal?) – Qualitative: nominal, (ordinal?)  Source – Primary (e.g., WNB, KIVZ,... ) – Secondary  Frame of reference – Cross-sectional (e.g., WNB, KIVZ,... ) – Time series (e.g., ???)

7. What About the Gaming Company?  Data were “different”; a time series – Single variable – Observed regularly over 100 weeks time  Do basic descriptive statistics provide good summary measures? – Average and median? – Standard deviation? – Histogram?  Yes, and no!  Depends upon how “stable” the process is

8. We’re Still Sampling Demand Process Sample Over Time Parameter Statistic Inferences

9. Time Series Inferences: Forecasting  Forecasting – Judgmental methods – Quantitative methods Associative techniques (leading indicators) Time series techniques (treat time as factor)  Begins with analysis

10. Basic Time Series Techniques  Pattern-based – Trend (T) – Seasonal index (SI) – Combined trend and seasonal index (Comb)  Patternless – Averages Simple Moving (MA) – Exponential smoothing (ES) – Naive

11. Forecasting Overview  Stages – Analysis Determines forecasting model (i.e., method) Determines model parameters – Forecasting (application of model) – Monitoring  Forecast error – Basis for measuring forecast effectiveness\ – Error = Actual - Forecast – Primary summary measure is MAD

12. Time Series Analysis  Starts with scatterplot – Demand (y) versus Time (x) – Connect points with straight line segments  Generally treats time as if “factor”  Use scatterplot to identify patterns  Choose model based upon MAD – Use model to forecast past demand – Compare forecasts to actual past demand – Calculate MAD

13. Time Series Components  Patterns indicate components – Trend – Seasonality – Cyclicality – Randomness  Components dictate type of model

14. Time Series Model Summary  Trend y = b 0 + b 1 x  Seasonal index y = SI * y avg  Combined y = SI * (b 0 + b 1 x)  Exponential smoothing F t = F t-1 +  * (A t-1 - F t-1 )  Also: average, moving average, naive

15. Trend Analysis & Forecasting  Uses two familiar tools – Regression – Computer (Excel, SPSS, etc.)  Calculate regression model for demand (y) versus time period (x) –b0–b0 – b 1 (the trend, or “average change per quarter”) –R2–R2 – s yx (similar to MAD)

16. Example  Product #4 demand from SPC case  Plot the time series  What components appear to be present?  Trend analysis: y = ?? + ?? x R 2 = ??% S yx = ?? MAD = ?? For period 13, y = ??

17. Homework  Short report incorporating SPSS output  Time series analyses – Reading from Chapter 16 – Exercises