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Here is a step-by-step guide to the processes you need to take to learn this topic
Here is a step-by-step guide to the processes you need to take to learn this topic
- Introduction of Time Series
- Data to explore and experiment with
- Writing a question, including the purpose & where the data came from
- Creating the graphs in iNZight
- Analysis
- Forecasting
- Conclusion
- Reflection / Improvements
- Exemplars
1: Introduction to Time Series
1: Introduction to Time Series
You will understand how Time Series analysis provides insights real life situation that change of time.
You will understand how Time Series analysis provides insights real life situation that change of time.
OVERVIEW OF TIME SERIES ANALYSIS
Introduction including Purpose and Research about the context
Long Term Trend
Seasonal Variation
Decomposition and Residuals
Predictions/Forecasts
Refining and improving model
Conclusions
Time series analysis provides insights into measured real life situations that change over time. It can also be used to make informed predictions of future behaviour to allow crucial decision making for businesses, economists, scientists and politicians. For example, a time series analysis of retail sales might show a peak in sales in December and a general trend of growing sales from year to year.
A time series is a set of numerical measurements of the same variable, taken at evenly spaced intervals over time. Time series data can be collected yearly, quarterly, monthly, weekly, daily, or even hourly. You can tell a graph of a time series because it always has a time scale along the horizontal axis and the measurement on the vertical axis.
Click through from this image to a nice (topical, illustrated) time series. How many "parts" can we logically divide this series up into? What happens in each part? (Much of the climate science modelling we see reported is fancy time series analysis)
2: Datasets to explore
2: Datasets to explore
Use the datasets below to create different Timeseries graphs
Use the datasets below to create different Timeseries graphs
These links will take you directly to iNZight Time Series where you can start to look at what the graphs look like.
Scroll down in this folder to see some of the datasets we have available. To open them in inzight or inzight lite (online), DOWNLOAD as csv files (this is important) and save to your computer somewhere obvious. Then click "import dataset" and open the file. Then go to "advanced module" to find the "time series module".
3: Question/Hypothesis
3: Question/Hypothesis
Be able to write a question, state a hypothesis and back your ideas up with research
Be able to write a question, state a hypothesis and back your ideas up with research
This can be completed after your have played with the graphs to see what look like before you write your question.
Look at graphs for all variables before deciding on an investigative question - do some “googling” first! Choose one that is interesting, but also that shows reasonably regular seasonal variation.
Description and Investigative Question
Description of topic (one sentence)
Investigative Question
Aim / Interest (Why worth investigating? Questions? Hypothesis?)
Data
Source
Definition and description of variables
Important aspects of survey details / validity
Research
The most important factors that might affect xxx
Research such as … suggests that xxx will be increasing / decreasing over time because…
Useful words:
XXX data is a useful measure of…
In this report xxx is investigated and predicted for …
An understanding of xxx over time might be useful in order to…
This data was collected by… This might affect the findings of this study because…
This survey data is likely to be valid for predicting xxx because…
Factors that research suggests may influence xxx include…
4: Creating Graphs in iNZight
4: Creating Graphs in iNZight
Using iNZight for Time Series Analysis.webm5: Analysis
5: Analysis
5.1 - Trend
5.1 - Trend
Example Answers to Trend examples - beer consumption and road toll
Time series graph
Tell the story:
Describe overall trend from left to right
Average rate of change (in context – what does this mean?)
Piecewise description (are there sections you can talk about? One paragraph per section (increasing, stable, decreasing))
Don't forget dates, specific values/quantities, units
Link to research – why might we see this trend? What assumptions are we making? Why is this a ‘sensible’ trend?
Useful words:
As seen in the graph/ According to the graph...
Rapid/steady/gradual/plateau/sudden/generally/ relatively steep
Overall Increase/decrease/stable trend
Gradient of ... shows an average weekly/monthly/quarterly/annual
This means xxx is increasing / decreasing xxx per xxx
This trend assumes that … makes sense because...
5.2 - Seasonal Analysis
5.2 - Seasonal Analysis
Lesson 3 Time series - seasonal effects - lesson 3 updated.pdfSeasonal graph
Tell the story:
There is clear / limited evidence / no evidence of seasonality in this series as seen in the following graphs.
Peaks and Troughs - identify high and low seasons and any unusual seasons (outliers)
Don't forget specific values and units – quantify amount above or below trend
Context – what does this mean? Link back to investigative question.
Statistics – what assumptions are we making?
Research – why might we see this seasonal pattern?
Useful words/phrases:
Overall there is clear seasonality shown in the data
As seen in the estimated seasonal effects plot…
The estimated seasonal effect shows that...
Considerably, significantly, slightly, normally
Higher / Lower / Peak / Low / Trough
Above / below the trend
This is possibly due to… This may be because… This may be caused by… This supports… This is justified by…
One would expect this because…
5.3 - Decomposition Analysis
5.3 - Decomposition Analysis
Lesson 4 - Time Series - Outliers and the appropriateness of the model updated.pdfDecomposition graph
Discuss Variation
Summary Of Variation Table
Trend – what % of the variation in the data is from the trend?
Seasonal – what % of the variation in the data is from the seasonality?
Residual– what % of the variation in the data is from the residuals?
Discuss usefulness of model
Discussion of main source of variation in the model and link to its usefulness for predictions / forecasting / extrapolating beyond the data.
Highlighting and explaining outliers (using residuals)
Recomposition graph - how well does the model (green) fit the data (black) - are there some areas where it doesn't fit so well? (discuss residuals of unusually high or low values with reasons). This is basically seeing if we can trust our model to make predictions. Do the residuals follow a pattern, are there areas where the residuals are larger (where model doesn't fit well)?
If the seasonality is growing (and residuals are getting worse), you may consider fitting a multiplicative model instead (be careful and only do if you understand it). Compare the residuals from both models to decide which is better.
Useful words/phrases:
The residual is relatively small (percentage)
There is an unusual residual … This may have been caused by…
Xx% of the variation in the data is explained by the trend
Xx% of the variation in the data is attributed to seasonality
The residual component accounts for Xx% of the variation in the data
This model is likely to be useful for forecasting because…
The large proportion of variation in the residuals means this is not a particularly useful model for…
Percentage of each Time Series Component
Residual component = single biggest residual / raw data range x100
(NOT max-min)
6: Forecast & Predictions
6: Forecast & Predictions
Lesson 5 - Time Series - Predictions updated.pdfForecasts in iNZight lite.webmForecast graph
Point predictions (within an interval of lower and upper limits)
Robustness of predictions
Don't forget units!
Useful words:
This model predicts xxx to be xxx in
In the near future it is predicted that xxx
Prediction Interval (95% Confidence Interval)
The actual values are close to those predicted which suggests…
Actual value / Predicted Value
Factors that might affect the accuracy of this prediction include…
Robustness Check - how to remove the last few rows using inzight to see how good your model is at predicting.
Robustness using iNZight lite.webm7: Conclusion
7: Conclusion
Time Series - Lesson 6b - Conclusion.pdfUseful phrases:
This report investigated… and used this analysis to predict…
From my research I found that...
Analysis of the data showed a trend of… and seasonal effect…
This model was used to forecast…
These forecasts are likely to be robust because…
Possible uses of this data are…
A further variable that was considered was…
Possible limitations of this model include…
To improve my investigation I could have...
These findings are useful because…
Concise summary linked to original purpose of the investigation
Purpose of report
Brief description of model
What the model predicted
Summary of usefulness or limitations of model / how the model might be improved
Summary of investigation into other relevant variable
Summary of what this means in context / research / future investigations
8: Reflection / Improvements
8: Reflection / Improvements
This can be incorporated into any section above as relevant
This can be incorporated into any section above as relevant
Time Series - lesson 6a - excellence updated.pdfComparing different time series can be very interesting and meaningful to your context.
inzight demo: Comparing and combining different time series to make a more meaningful report.
More info about Index Series (comparing two variables by looking at percentage changes eg instead of raw data) or Adjusting for inflation by CPI (deflated values) can be found online. eg. Otago maths website
Evaluate the adequacy of the model
Limitations of forecasting
What might change in the future that would make your forecast invalid?
Limitations of data to answer investigative
What does the data not tell you in relation to the investigative question?
Consider other relevant variables
Repeat investigation for a related variable
Compare and contrast different components
Consider if an additive or multiplicative model is more appropriate
Create a new variable from your original variables (eg. amount $ per capita by dividing by population)
Useful words/phrases:
This forecast is dependent on…
If xxx changed then…
The data covers…
One variable that is likely to be related to xxx is xxx
It is likely that as xxx increases xxx increases / decreases
See also the MathsNZ notes on how to get Excellence
Additive vs Multiplicative Models
Mostly for this standard you should be focusing on additive models. If the data shows an increasing or decreasing seasonality then a multiplicative model might be more appropriate. Compare the seasonal effects, the recomposed model, the residuals and the predictions to decide which is best for your data. https://www.youtube.com/watch?v=CfB9ROwF2ew
9: Exemplars and Assessment info
9: Exemplars and Assessment info
Your assessment can be submitted in a number of different formats.
An infographic with graphs and some detail, accompanied by an interview or screencast explaining in more detail, plus an annotated bibliography of the relevant research.
A series of podcasts or videos explaining each section with graphs/ brief notes on slides or doc, plus an annotated bibliography of the relevant research.
A report on slides or google doc or using a more professional program like CANVA
Modes of Assessment - below are some exemplars to demonstrate how you could choose to present your internal.
You may write a traditional report, create a slideshow, create an infographic poster along with extra info in the slides assigned to you, create a series of podcasts or videos (embedded in the slides is easiest),
Example of a professional report (started) on canva
TIME SERIES eg in canva.pdfStudent Exemplar completed in canva:
Time Series analysis Air Polution exemplar.pdfExample of an infographic that shows the basic (ach) detail, which could be accompanied by an interview or screencast explaining more detail, plus an annotated bibliography of the research undertaken and what that showed.
Supermarket Sales.pdfExemplar of a video report with a powerpoint of slides to hold all research and graphs for the milestones before final video produced. (video is embedded and can be watched by clicking on the 2nd-4th slides)
Ben Bonne - 91580 Time series ASSESSMENT (slides format).pdfThese exemplars are in a traditional report style: NZQA exemplars
Other exemplars: Mixed achievement levels produced by Chris Wild (Ak uni)
Merit - rainfall Excellence - food for thought polar ice
NZQA Bits & Pieces
NZQA Bits & Pieces
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