Time Series Analysis PDF

Time Series Predicting the future is hard, especially if it hasn't happened yet... (Yogi Berra)  What is a Time Series? - Measurements of observations are taken at regular intervals (days, months, quarterly, years). Common examples of time series are: Number of student absences...

Time Series Predicting the future is hard, especially if it hasn't happened yet... (Yogi Berra)  What is a Time Series? - Measurements of observations are taken at regular intervals (days, months, quarterly, years). Common examples of time series are: Number of student absences Carbon-dioxide levels Supermarket sales Number of hits to a website Write down another example of time series.  Why do we use time series? To model the past, so we can make predictions about the future Some examples: - How much of a budget to allow for photocopying in the math department? - How much you could sell your house for?  Analysis to Predictions to Decisions A time series analysis consists of two steps: 1. Analysing the trend and features of the data; modelling the trend and features. 2. Using the model to predict (forecast) future values, which can be used to make decisions.  Why are we interested in them? Collect data on the number of customers at Analysis KFC per hour and model this. Predictions How many customers will KFC have in the next weekend? Decisions Ensure enough staff are working to cope with the demand.  What are the key areas for analysis? THE OVERALL TREND - where are we headed? There could also be short term trends or sometimes the most recent trend is what's important...... PEAKS, TROUGHS, SPIKES, OTHER ANOMALIES - key events in the data PATTERNS / SEASONALITY - not autumn etc higher/lower MODELLING / FORECASTING / PREDICTING Things to think about when writing about time series Use words like around, Use numbers with units approximately, on average, including estimating trends because statistical analysis is and seasonality never exact Make links to the context by Make any claims with justifying talking about what the data is evidence and consider other actually measuring possible explanations Make statistical statements Present relevant information with explanations about what ensuring that it makes sense to you are doing you Overall trend  Raw data What is the red line showing? Like the overall trend How do you think they calculated the red line? Taken an average of values for each month. ber ptem Se Area of sea ice (millions of square kilometers) Why is it not a straight line? Fe This line is a bit sensitive bruto the peaks on our graph - which is why we ary get this little up bit in the middle Months and years  Example – overall trend Weed Killer sales. By around how much per $3000 more over 16 What's the Increasing quarter? quarters, around $188 overall direction Positive per quarter (trend)? How fast are the average Slowly sales are increasing? Steadily What's the time What's the time measurement? period? 2008 2009 2010 2011 2012 What are we Summer 2008 - measuring? Weed killer sales ($) Quarters (three months) Spring 2012 Raw data - what do you see? April 2006 until March 2011 What's the time period? How fast is the average Months What's the time area of sea ice increasing? measurement? It's not!! It is staying at Area of sea ice (millions of about 8.5 millions of square What are we kilometers of ice ber square kilometers) measuring? m epte Area of sea S Pretty stationery What's the ice (millions overall direction (trend)? of square kilometers) So not increasing per month By around how really - staying the same much per month? Fe bru ary Months and years Example for estimating the increase for each quarter Graph showing wine consumption over time A city’s temperature in °C for 2 years Seasonal effect What is the overall trend?  iNZight doesn't give you labels, so you Raw data would have to add these yourself. Which month is that highest peak and which month is the lowest? We would have to look at our raw data to tell us this m ber epte S Area of sea ice (millions of square kilometers) Fe bru ary Months and years  Raw data - what do you see? When is the area of sea ice typically highest and Are there any Every 12 months the pattern repeats. by about how much? seasonal patterns in Highest in September (after winter) In September, with around 6 the area of sea ice? and lowest in February (after summer) million square kilometers of ice higher than the average ber ptem When is it the Se lowest? Area of sea In February, with around 7 million square kilometers of ice (millions ice lower than the average of square kilometers) Fe bru ary Months and years  Example Weed Killer sales. Every four Are there any seasonal quarters patterns in the sales? When are sales typically lowest and In winter, with sales by about how much? about $10000 less than the average. 2008 When are sales 2009 typically 2010 In spring, 2011 with sales 2012 highest and by about how about $15000 more much? than the average. Predictions Predictions  Example How much would you expect the Seasonal Weed Killer sales to be next Winter? quarte r e in crea sin g by an average of $188 per Weed Killer sales ar Somewhere around $9000 In winter, sales are about $10000 less than the average. 2008 2009 2010 2011 2012