Statistics Cyclical Time Series Cyclical Forecasting Time series

Statistics Cyclical Time Series

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 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

Time Series Make a graph

Time Series Make it “purty”

Time Series Why does it start in July 1998? ?

Time Series Right click on the x-axis dates to adjust the start and end dates

Time Series Click: “Format Axis”

Time Series What are 36000. 0 and 43000. 0? ?

Time Series Excel uses a “Julian Date” calendar (weird and hard to understand)

Time Series In Excel: January 1, 1900 is day 1 July 1, 1998 is day 35975 (because it is 35, 975 days after January 1, 1900)

Time Series The formula to convert a date to an Excel date is: =ROUNDDOWN(((YEAR(A 1)1900)*365. 24), 0)+A 1 DATE(YEAR(A 1), 1, 0)

Time Series 3/31/2000 (our first date) is day 36615. 0

Time Series 12/31/2014 (our last date) is day 42002. 0

Time Series So we know our data starts at 35615, but we also want to get the right Mo-Yr shown on the graph, and not have the first datapoint chopped off of our graph…

Time Series …and maybe start with Jan rather than March? I just mess around with (iterate) the values until I get what I want…

Time Series Change the minimum to 36527 and the maximum to 42065 with major unit 732

Time Series Better!

Time Series Note: for our class, I’ll give you the numbers…

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

Cyclical Forecasting Add another column Label it “Cycle”

Cyclical Forecasting Using the data values for the first year, see which has 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 Note: the Excel regression app will not handle dates in the form: 5/14/2017 Add a "Year" column using: =YEAR(A 11)+(MONTH(A 11)-1)/12

Cyclical Forecasting Forecast electricity consumption in Portugal

Questions?

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!

Questions?