Time Series Analysis ( AS 3.8)

1. Time Series Analysis ( AS 3.8) Using iNZight Rachel Passmore Endeavour Teacher Fellow

2. Overview • Statistics : What has changed • Changes from AS 3.1 to draft AS 3.8 • iNZight – what is it ? How do I get it? How do I use it? • Data for iNZight • Time Series Analysis using iNZight • Seasonal Lowess & Holt-Winters models • Summary of Resources • Feedback on AS 3.8 changes Rachel Passmore

3. Old AS 3.1 vs Draft AS 3.8 Rachel Passmore

4. Draft AS 3.8 Time Series Rachel Passmore

5. What is iNZight ? • Data analysis and inference tool developed by University of Auckland Statistics Department • FREE – download from Census@SchoolOR http://www.stat.auckland.ac.nz/~wild/iNZight/dlw.html Versions available for Windows, Mac & Linux • Useful for AS – 3.8,3.9,3.10, • 3.11 & at Level 1 & 2 • NEW module – Time Series Rachel Passmore

6. Data files for iNZight • Software download includes some data sets • Polar ice & Food for thought – current NZQA exemplars • Statistics NZ – currently compiling 15 – 20 series for schools • Series from University of Auckland Time series course • Rob Hyndman’s Time Series Data Library • http://datamarket.com/data/list/?q=provider:tsdl • Infoshare – new data service from Statistics NZ Format of Data files • EXCEL files OK if saved with .csv (comma delimited) file extension • Time & variable notation protocol • NO COMMAS • Additional information about variables including units must be provided separately Rachel Passmore

7. Examples of analysis Rachel Passmore

8. Summary of iNZight features for time series analysis • Shift from emphasis on calculations to visual interpretation • Potential to compare differences & similarities between series • Potential to compute further series – sum, difference, ratio ……or other transformation • Use of Seasonal Lowess for smoothing & Holt-Winters for predictions • BUT draft new AS 3.8 does not currently accommodate all iNZight features. Rachel Passmore

9. Seasonal Lowess Model • iNZight uses Seasonal Lowess Model to produce smoothed values • A weighted least squares regression line is fitted to points inside the window • The point at the target • X value becomes the • Smoothed value. • Smaller weights at • edge of window Rachel Passmore

10. Holt Winters prediction model • First developed in early 1960s • Uses a technique called EXPONENTIAL SMOOTHING • Assumes next value is weighted sum of previous values • Weights decrease by a constant ratio and if plotted will lie on exponential curve. • Holt-Winters smooths level, trend and seasonal sub-series to produce prediction. • Additive Model Rachel Passmore

11. Comparison of Prediction Models Rachel Passmore

12. BUT…………………….. • Holt Winters additive model only valid for consistent seasonal pattern. If seasonal pattern varies a Holt-Winters multiplicative model should be used or series transformed. • Option for multiplicative model not available. • Default setting of two years predictions provided on plot. • Table of prediction values & intervals need to rounded appropriately Rachel Passmore

13. SUMMARY OF RESOURCES • iNZight Time series module – AVAILABLE NOW • Datasets in correct format – some available now, more on the way ! - Census@School website • iNZight data file tips – Census@School website • Teacher’s guide to Seasonal Lowess & Holt-Winters model – Census@School • Document tracking changes from 3.1 through to 3.8 using iNZight – to be uploaded on Census@School website • Worked exemplars using iNZight – Polar Ice & Food for Thought- Census@School website • Audio demo on iNZight available – time series one soon (http://www.stat.auckland.ac.nz/~wild/iNZight/) Rachel Passmore

14. Rachel Passmore • Contact Details • Home email : passm@vodafone.co.nz ANY QUESTIONS ? COMMENTS WELCOMED ! With thanks to University of Auckland Statistics Department ( Chris Wild, Mike Forster and Maxine Pfannkuch), Teachers Ruth Kaniuk,Dru Rose & Rebecca Fowler and New Zealand Science, Mathematics and Technology Teacher Fellowship Scheme. Rachel Passmore