Time Series Presentation at AMA

Report
Time Series Analysis ( AS 3.8)
Using iNZight
Rachel Passmore
Endeavour Teacher Fellow
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
Old AS 3.1 vs Draft AS 3.8
AS 3.1
DRAFT AS 3.8
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.
2.
3.
4.
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
Achieved Level
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NO CHANGE
NO CHANGE
NO CHANGE
Describe trend AND
seasonal pattern – not
necessarily in context
5. Calculate one
prediction.
Draft AS 3.8 Time Series
Achieved Level
Draft AS 3.8
DRAFT AS 3.8
Using EXCEL
Using iNZight
1.
2.
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).
3.
4.
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
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.
2.
3.
4.
5.
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)
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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.
What is iNZight ?
 Data analysis and inference tool developed by
University of Auckland Statistics Department
 FREE – download from [email protected] 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 & 2
 NEW module – Time Series
Rachel Passmore
Data files for iNZight
•
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•
•
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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
•
•
•
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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
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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.
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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
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window
xtarget
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
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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 nonlinear 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 HoltWinters 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 RESOURCES
 iNZight Time series module – AVAILABLE NOW
 Datasets in correct format – some available now, more on
the way !
- [email protected] website
 iNZight data file tips – [email protected] website
 Teacher’s guide to Seasonal Lowess & Holt-Winters model
– [email protected]
 Document tracking changes from 3.1 through to 3.8 using
iNZight – to be uploaded on [email protected] website
 Worked exemplars using iNZight – Polar Ice & Food for
Thought- [email protected] website
 Audio demo on iNZight available – time series one soon
(http://www.stat.auckland.ac.nz/~wild/iNZight/)
Rachel Passmore
Rachel Passmore
 Contact Details
 Home 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 and
New Zealand Science, Mathematics and Technology Teacher Fellowship
Scheme.
Rachel Passmore

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