Statistics NonLinear Time Series Time Series Forecasts Not

Statistics Non-Linear Time Series

Time Series Forecasts Not all time series are straight lines

Time Series Forecasts Not all time series are straight lines… most are not!

Time Series Forecasts RSQ = 98. 7%

Time Series Forecasts Is it a good forecast?

Time Series Forecasts We need a curved trendline!

Time Series Information in a spreadsheet about the data is called… }

Time Series Information in a spreadsheet about the data is called… } metadata

Time Series Forecasts Go to the second sheet: Curv. Fcst

Time Series Forecasting We need to come up with a curvey formula!

Time Series Forecasting The quadratic formula makes a curve y = ax 2 + bx + c

Time Series Forecasting It has an “x 2” in it: y = ax 2 + bx + c

Time Series Forecasting If we use a squared “time” term, we’ll get a curve!

Time Series Forecasting Right click on the “B” Add a new column next to “Year”

Time Series Forecasting Call it “Yr^2” Fill in the formula to square the Year

Time Series Forecasting Copy it down clear to the bottom

Time Series Forecasting Go to “Regression”

Time Series Forecasting This time, TWO columns (A and B) will go into the x values! Only go down as far as the last y-value

Time Series Forecasting This is called a “multiple regression” when you have more than one x input Excel handles it just fine!

Time Series Forecasting There is also “multivariate regression” when you have more than one y output Excel can’t do these…

Time Series Forecasting See why it’s important to include the labels?

Time Series Forecasting You don’t have to figure out which coefficient is which!

Time Series Forecasting Create your trend formula and copy it down

Time Series Forecasting Do you think this is a good forecast? Why or why not?

Time Series Forecasting Observed values were: 2006: $268, 2007: $266, 000 2008: $242, 700 2009: $216, 900 2010: $220, 000 Were you close? What happened?

Questions?

Cyclical Forecasting Time series data often are annual summaries

Cyclical Forecasting Time series data for months or quarters often exhibit a cycle

Cyclical Forecasting Time series data for months or quarters often exhibit a cycle: candy sales are highest at what times during the year?

Cyclical Forecasting What if our time series data has a cyclical pattern as well as a trend?

Cyclical Forecasting If you include the cycle in the forecast, you will have a better forecast!

Cyclical Moving Average Suppose our data looks like:

Cyclical Moving Average Is it cyclical?

Cyclical Moving Average Count from the max of the pattern

Cyclical Moving Average Start over on the next max

Cyclical Moving Average Is the cycle “ 4” for the most part?

Cyclical Forecasting Open the spreadsheet in the Portal

Cyclical Forecasting We need a way to include the cycle in our equation

Cyclical Forecasting Add another column Label it “Cycle”

Cyclical Forecasting Check the data values for the first year to see which is the highest value

Cyclical Forecasting In the “Cycle” column, mark it with a number (use 4, since this is quarterly data)

Cyclical Forecasting Now check the data values to find the lowest value during the first year

Cyclical Forecasting Mark it with a different number (use 1 since it’s low)

Cyclical Forecasting Check to see if the max quarter for the following year is the same

Cyclical Forecasting Check to see if the min quarter for the following year is the same

Cyclical Forecasting If they are (or at least are close) you have a pattern!

Cyclical Forecasting A cycle is often symmetrical Our “ 1” has 1 space before the “ 4” followed by 1 space before the low value for the following year

Cyclical Forecasting Fill in the blank spaces with a value between 1 and 4 (2, 2. 5, or 3)

Cyclical Forecasting If your data are not symmetrical, that’s OK!

Cyclical Forecasting Asymmetrical patterns are very common in business data

Cyclical Forecasting Monthly data often have a couple of spikes Fill these in with numbers approximating how high the spikes go, how low the depressions go, and fill in the spaces with “smoothed” values

Cyclical Forecasting Now copy this pattern for the year down for the entire series!

Cyclical Forecasting Now we can create a regression equation that includes the linear increase over time (based on year), the curvilinear increase in trend over time (if you have one – we don’t) and the cyclical annual pattern for the months (using the cycle data)

Questions?

Cyclical Forecasting Forecast UK tourism

Questions?