Time Series Analysis ( AS 3.8)
Rachel Passmore
Endeavour Teacher Fellow
Using iNZight
Rachel Passmore
OverviewStatistics : What has changedChanges from AS 3.1 to draft AS 3.8iNZight – what is it ? How do I get it?
How do I use it?Data for iNZightTime Series Analysis using iNZightSeasonal Lowess & Holt-Winters modelsSummary of ResourcesFeedback on AS 3.8 changes
Old AS 3.1 vs Draft AS 3.8AS 3.1 DRAFT AS 3.8
Achieved Level Using EXCEL Using EXCEL
1. Calculate smoothed, ISE,ASE. Fit linear regression to smoothed series
2. Time series plot 3. Describe trend in
context.
1. NO CHANGE2. NO CHANGE3. NO CHANGE4. Describe trend
AND seasonal pattern – not necessarily in context
5. Calculate one prediction.
Merit Level 1. Calculate one prediction in context .
1. Comment on accuracy of prediction.
Excellence Level 1. Comment on 2 further features.
2. Comment on 3 items from list of 5.
1. Comment on further features as before – NEW other relevant variables, or deeper understanding
Rachel Passmore
Draft AS 3.8 Time SeriesDraft AS 3.8 DRAFT AS 3.8
Achieved Level Using EXCEL Using iNZight
1. Calculate CMM,ISE,ASE for one series
2. Plot raw, smoothed + linear regression equation.
3. Calculate >= 1 forecast4. Describe trend and seasonal
pattern, not necessarily in context. Use gradient to quantify trend
1. Calculations performed by iNZight.2. Produced automatically as well as seasonal effects, average seasonal effects, predictions and residuals.3. Produced automatically4. Describe trend and seasonal pattern not necessarily in context. (Use first and last trend values to quantify trend).
Merit Level 1. to 4. As above but no labelling errors on plots and details of calculations required. Context of forecast required.5. Comment on accuracy of predictions
1. Not required2. Produced automatically3. Produced automatically. Context
required.4. As above but in context5. Prediction Intervals provided. Visual
inspection of fit of model & consistency of seasonal pattern.
Excellence Level 1. Comment on accuracy of predictions, unusual features, improvements, other relevant variables or demonstrate deeper understanding of series/model. No indication provided on how many required for Excellence
1. iNZight provides much greater potential at Excellence level. Residual analysis, comparison with other series, comparison with computed series ( differences, sums or ratios of series)Rachel Passmore
Rachel Passmore
What is iNZight ?Data analysis and inference tool developed by
University of Auckland Statistics DepartmentFREE – download from Census@School OR
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 & 2NEW module – Time Series
Rachel Passmore
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
Examples of analysis
Rachel Passmore
Summary of iNZight features for time series analysisShift from emphasis on calculations to
visual interpretationPotential to compare differences &
similarities between seriesPotential 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
Seasonal Lowess ModeliNZight 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 targetX value becomes theSmoothed value.Smaller weights at edge of window
window
xtarget
Rachel Passmore
Holt Winters prediction modelFirst developed in early 1960sUses a technique called
EXPONENTIAL SMOOTHINGAssumes next value is weighted sum of previous valuesWeights 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
Comparison of Prediction ModelsSeries Series
descriptionTrend + ASE Comparison
with Holt-Winters
Constant linear trend + consistent seasonal pattern
Trend extrapolation, ASEs calculated, reasonable predictions
Little difference if any in either fitted values or predictions
Non-linear trend + consistent seasonal pattern
Achieved /Merit – linear trend fitted, predictions poor.Excellence – consider piece-wise or non-linear models. Predictions could still be poor.
Copes well with non-linear trend resulting in improved predictions
Non-linear trend and inconsistent seasonal pattern
Excellence – may consider multiplicative models but not expected to provide equations
Excellence – consider multiplicative model but option not available on iNZight.
Rachel Passmore
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
SUMMARY OF RESOURCESiNZight Time series module – AVAILABLE NOWDatasets in correct format – some available now, more on
the way ! - Census@School websiteiNZight data file tips – Census@School website Teacher’s guide to Seasonal Lowess & Holt-Winters model
– Census@SchoolDocument tracking changes from 3.1 through to 3.8 using
iNZight – to be uploaded on Census@School websiteWorked exemplars using iNZight – Polar Ice & Food for
Thought- Census@School websiteAudio demo on iNZight available – time series one soon (http://www.stat.auckland.ac.nz/~wild/iNZight/)
Rachel Passmore
Rachel PassmoreContact DetailsHome email : [email protected]
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 andNew Zealand Science, Mathematics and Technology Teacher Fellowship Scheme.