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 AS 3.1 DRAFT AS 3.8 Achieved Level
Using EXCEL
Calculate smoothed, ISE,ASE. Fit linear regression to smoothed series
Time series plot
Describe trend in context.
NO CHANGE
Describe trend AND seasonal pattern – not necessarily in context
Calculate one prediction.
Merit Level
1. Calculate one prediction in context .
1. Comment on accuracy of prediction.
Excellence Level
Comment on 2 further features.
Comment on 3 items from list of 5.
1. Comment on further features as before – NEW other relevant variables, or deeper understanding
Potential to exploit
Rachel Passmore

4. Draft AS 3.8 Time Series Draft AS 3.8 DRAFT AS 3.8 Achieved Level
Using EXCEL
Using iNZight
Calculate CMM,ISE,ASE for one series
Plot raw, smoothed + linear regression equation.
Calculate >= 1 forecast
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 automatically
4. 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
Not required
Produced automatically
Produced automatically. Context required.
As above but in context
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

5. What is iNZight ?
Data analysis and inference tool developed by University of Auckland Statistics Department
FREE – download from OR 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 Format of Data files
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
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
Switch to iNZight to show how these outputs are produced. Highlight two statistical techniques being used – Seasonal Lowess Model and Holt-Winters for predictions
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.
Describe Seasonal Lowess Model on board.
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
Describe on whiteboard
Rachel Passmore

11. Comparison of Prediction Models
Series
Series description
Trend + 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

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
OR DO we consider individual components’ contribution to overall variance of series.
Rachel Passmore

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

14. Rachel Passmore Contact Details
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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