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

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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

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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

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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.

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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 : 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 andNew Zealand Science, Mathematics and Technology Teacher Fellowship Scheme.