Statistics Time Series https://www.123rf.com/photo_6622261_statistics-and-analysis-of-data-as-background.html

Time Series In business, a lot of things happen over time

Time Series Another variable we are interested in happens over time… changes over time… DEPENDS on what time is is…

Time Series This variable that depends on time we call the “dependent” variable

Time Series Time is called the “independent” variable – we can’t control it!

Time Series Data that change over time are called a “time series”

Time Series Time is the “input” variable that we put on the horizontal ↔ x-axis The other “output” variable goes on the vertical ↕ y-axis

Time Series Time series or not? Federal debt 1950-2017

Time Series Time series or not? Taxes paid by income level

Time Series Time series or not? Global atmospheric temperature 1880-2017

Time Series Time series or not? Average salary by education level

Time Series Time series or not? Average annual salary of US workers 1950-2017

Questions?

Time Series Forecasting Go to the Portal Open the spreadsheet

Time Series Forecasting Go to the Portal Open the spreadsheet

Time Series Forecasting Is it a time series?

Time Series Forecasting Suppose the Australian Tourist Bureau (your boss) wants to forecast the number of tourists in 2020…

Time Series Forecasting If the data are too volatile, (especially at the end of the series) we won’t be able to make a good forecast…

Time Series Forecasting Assume it will work! Add labels for two more columns: Trend and Forecast

Time Series Forecasting Add years up to 2020 at the bottom of the data

Time Series Forecasting Graph the data! Include the variable labels (and the two new columns)

Time Series Forecasting Include the forecast years

Time Series Forecasting Poof! A graph!

Time Series Forecasting Make it “purty”

Time Series Forecasting Redo the x-axis limits if necessary

Time Series Forecasting Poof! T-O-B!

Time Series Forecasting Does it look too volatile to make a forecast?

Time Series Forecasting Does it look too volatile to make a forecast? I’m willing to take the risk…

Time Series Forecasting Since it kinda looks like an increasing line will fit the data…

Time Series Forecasting To make a forecast, we need to come up with a line of best fit

Time Series Forecasting To make a forecast, we need to come up with a formula for a line of best fit

Time Series Forecasting To make a forecast, we need to come up with a formula for a line of best fit – a regression line

Time Series Forecasting Excel will do that for you! (yay)

Time Series Forecasting Click the “Data” tab Click “Data Analysis” Scroll to “Regression” Click “OK”

Time Series Forecasting Excel does this backward The “input” (x) should go first then the “output” (y)

Time Series Forecasting They didn’t consult me first… http://scottsauls.com/wp-content/uploads/2015/06/Shame.jpg

Time Series Forecasting Go to “Input X” Enter your “Year” data Include the label Only go down to the end of your observed data

Time Series Forecasting Now you can “Input Y” Enter your “Arrivals” Include the label Mark “Labels” Click “OK”

Time Series Forecasting Eek! dreamstime.com

Time Series Forecasting I’s OK, we’re not using most of it… http://www.shutterstock.com/s/whew/search.html

Time Series Forecasting The R Square will tell you in % how well the line is fitting the data – highlight it and click “%”

Time Series Forecasting Over 98% Is it a good fit?

Time Series Forecasting 98% is a SUPER fit (Usually it lurks around 25-35%)

Time Series Forecasting So, if it’s a good fit, lets make a forecast! http://blog.psychics.com/wp-content/uploads/2015/08/Crystal-ball.jpg

Time Series Forecasting Copy the “Coefficients” for “Intercept” and “Year” (include the labels)

Time Series Forecasting Paste them on your Tourism page (I put them in F3-G5)

Time Series Forecasting Believe it or not, this is the formula for our line of best fit!

Time Series Forecasting Arrivals = InterceptCoefficient + YearCoefficient × Year

Time Series Forecasting Arrivals = -332.474041 + 0.1682033 × Year

Time Series Forecasting Use that for our trend formula!

Time Series Forecasting Don’t forget the “$”s!

Time Series Forecasting Copy it down ALL the way to the bottom…

Time Series Forecasting Poof! Now you have a trend line! (And you didn’t have to draw it!)

Time Series Forecasting But, where is our forecast?

Time Series Forecasting It’s actually here

Time Series Forecasting The trend line after our observed data ends is the forecast

Time Series Forecasting Extending a regression line beyond the observed data produces forecast values

Time Series Forecasting To make it look obvious, go to the bottom of your data and highlight the forecast values

Time Series Forecasting Drag and drop them to the forecast column “D”

Time Series Forecasting Poof! You have a forecast!

Time Series Forecasting But… it’s detached from the trendline…

Time Series Forecasting Go back to the bottom of your data and type the last trend value in the forecast column

Time Series Forecasting Poof! It’s attached!

Time Series Forecasting Make it “purty”

Time Series Forecasting But, now your boss wants a forecast for 2025 https://henrytrocino.files.wordpress.com/2013/08/weeping-and-gnashing-of-teeth-300x236.jpg

Time Series Forecasting Don’t panic…

Time Series Forecasting Don’t panic… use your formula!

Time Series Forecasting Don’t panic… use your formula: Arrivals = -332.474041 + 0.1682033 × Year

Time Series Forecasting Arrivals = -332.474041 + 0.1682033 × 2025

Time Series Forecasting Add the new years at the bottom of your spreadsheet and copy your forecast formula

Time Series Forecasting There’s your forecast for 2025

Time Series Forecasting Adjust your x-axis limits

Time Series Forecasting Right click on any data line in your graph and click “Select Data”

Time Series Forecasting Click Forecast under “Legend Entries” then the “Edit” button

Time Series Forecasting Adjust the ending values for the series X and series Y data

Time Series Forecasting Click “OK” then Click “OK” Poof! A graph of your new forecast!

Time Series Forecasting The boss can’t beat you! https://previews.123rf.com/images/thirteenfifty/thirteenfifty1201/thirteenfifty120100085/12091333-devil-boss-cartoon-Stock-Vector.jpg

Questions?

Time Series Forecasting Go to the Annual CO2 sheet Create a graph of the time series data

Time Series Forecasting Because the data are now annual averages, the cyclical volatility is gone!

Time Series Forecasting Scientists use annual averages to smooth out the cyclical nature of the data

Time Series Forecasting Why would using moving averages be better than calculating annual averages?

Time Series Forecasting Annual averages have only one value per year Moving averages of monthly data will have 12 per year (after the initial “start-up period”)

Time Series Forecasting Statistical rule: More Data Is Better Than Less Data

Time Series Forecasting So, if you have monthly data, a moving average will preserve more data after smoothing than annual averages Moving averages are better!

Time Series Forecasting Why don’t scientists use them?

Time Series Forecasting Good question! They just don’t!

Time Series Forecasting Business people use Moving Averages!

Time Series Forecasting Back to our annual data… Looks like there is an upward trend!

Time Series Forecasting Click “Data” “Data Analysis” “Regression” “OK”

Time Series Forecasting The “Y Range” is the ppm CO2 data in column B The “X Range” is the Year data in column A Include the labels!

Time Series Forecasting Click “Labels” Click “OK”

Time Series Forecasting Highlight the “Coefficients” for “Intercept” and “Year” and copy them to the clipboard

Time Series Forecasting Paste them on your “Annual” sheet

Time Series Forecasting In the column labeled “Trend” fill in the formula for the line Copy it down

Time Series Forecasting Poof! Forecasts of ppm CO2 values!

Time Series Forecasting Drag the forecasts to the adjacent column labeled “forecasts”

Time Series Forecasting You can see the original data, the trend line and the forecast

Time Series Forecasting Does it look like a GOOD forecast?

Time Series Forecasting It would be considered a CONSERVATIVE forecast

Time Series Forecasting A better forecast would begin where the observed data left off

Time Series Forecasting Scroll down to where the forecast numbers begin

Time Series Forecasting Copy up to the last observed data line

Time Series Forecasting What would the forecast have to be to line up with the last observed data value?

Time Series Forecasting 393.81-388.33 = 5.48 The forecast would need to be 5.48 higher to start where the observed data ended

Time Series Forecasting Start a new forecast column: =d60+5.48

Time Series Forecasting Copy it down

Time Series Forecasting Adjusted forecast values

Time Series Forecasting A better forecast!

Questions?