Chapter 10 – Basic Regression Analysis with Time Series Data
What is Time Series Data and why is it Different? There is a time ordering of the data The past can affect the future, but the future cannot affect the past. Example: National population from 1900 to 2006 (data set NATPOP)
What is Time Series Data and why is it Different? Random nature of times series data Formally, the process that generates time series data is called a stochastic or time series process
What is Time Series Data and why is it Different? Random nature of times series data Random sample from a population vs. random sample of time series data
Examples of Time Series Data: Uncorrelated data, constant process model
Examples of Time Series Data: Autocorrelated data
Examples of Time Series Data: Trend
Examples of Time Series Data: Cyclic or seasonal data
Examples of Time Series Data: Nonstationary data
Examples of Time Series Data: A mixture of patterns
Cyclic patterns of different magnitudes
Atypical events
13 Atypical events
Famous Time Series Expert – Yogi Berra The future ain’t what it used to be.
Famous Time Series Expert – Yogi Berra You can observe a lot just by watching. The basic graphical display for time series data is the time series plot which is just a graph of the observations vs. time periods.
Time Series Plot Example Open TRAFFIC2 data set and make time series plot of year vs. statewide total accidents (totacc) In Minitab need to choose series and time stamp
Time Series Plot Example
Time series plots Notice that the histograms look very similar even though the time series behavior is very different
Histogram of totacc
When there are two or more variables of interest, scatter plots can be useful
Forecasting It is difficult to make predictions, especially about the future. – Neils Bohr
Forecasting
Forecasting is useful in many fields: Business and industry Economics Finance Environmental sciences Social sciences Political sciences
Data Analysis Process: 1.Problem definition 2.Data collection 3.Data analysis 4.Model selection and fitting 5.Model validation 6.Model deployment 7.Monitoring forecasting model performance
Time Series Example – Data Set FERTIL3 gfr – number of children born to every 1,000 women of childbearing age from 1913 to Make a time series plot of gfr
Time Series Example – Data Set FERTIL3
pe – average real dollar value of the personal tax exemption from 1913 to Make a time series plot of pe
Time Series Example – Data Set FERTIL3
Scatter plot of gfr vs. pe
Time Series Example – Data Set FERTIL3 What could affect general fertility rate in the U.S.? Many things! How about these two: World War II Availability of the birth control pill
Time Series Example – Data Set FERTIL3 ww2 is a dummy variable 1 if year is 1941 through otherwise pill is a dummy variable 1 if year is 1963 or greater 0 otherwise
Time Series Example – Data Set FERTIL3
gfr = pe ww pill ww2 is a dummy variable 1 if year is 1941 through otherwise
gfr = pe ww pill pill is a dummy variable 1 if year is 1963 or greater 0 otherwise
Time Series Example – Data Set FERTIL3
Making lags in Minitab is easy. Go to Stat > Time Series > Lag.
Time Series Example – Data Set FERTIL3