chapter 10 – basic regression analysis with time series data
DESCRIPTION
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). - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 10 – Basic Regression Analysis with Time Series Data
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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)
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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
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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
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Examples of Time Series Data: Uncorrelated data, constant process model
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Examples of Time Series Data: Autocorrelated data
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Examples of Time Series Data: Trend
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Examples of Time Series Data: Cyclic or seasonal data
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Examples of Time Series Data: Nonstationary data
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Examples of Time Series Data: A mixture of patterns
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Cyclic patterns of different magnitudes
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Atypical events
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Atypical events
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Famous Time Series Expert –Yogi Berra
The future ain’t what it used to be.
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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.
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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
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Time Series Plot Example
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Time series plots
Notice that the histograms look very similar even though the time series behavior is very different
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Histogram of totacc
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When there are two or more variables of interest, scatter plots can be useful
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Forecasting
It is difficult to make predictions, especially about the future. – Neils Bohr
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Forecasting
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Forecasting is useful in many fields:
Business and industryEconomicsFinanceEnvironmental sciencesSocial sciencesPolitical sciences
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Data Analysis Process:
1. Problem definition2. Data collection3. Data analysis4. Model selection and fitting5. Model validation6. Model deployment7. Monitoring forecasting model
performance
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Time Series Example – Data Set FERTIL3
gfr – number of children born to every 1,000 women of childbearing age from 1913 to 1984.
Make a time series plot of gfr
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Time Series Example – Data Set FERTIL3
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Time Series Example – Data Set FERTIL3
pe – average real dollar value of the personal tax exemption from 1913 to 1984.
Make a time series plot of pe
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Time Series Example – Data Set FERTIL3
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Time Series Example – Data Set FERTIL3
We want to predict gfr.
Lets try this model:
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Time Series Example – Data Set FERTIL3
We want to predict gfr.
Notation for time series model slightly different:
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Time Series Example – Data Set FERTIL3
The regression equation isgfr = 96.3 - 0.0071 pe
Predictor Coef SE Coef T PConstant 96.344 4.305 22.38 0.000pe -0.00710 0.03592 -0.20 0.844
S = 19.9400 R-Sq = 0.1% R-Sq(adj) = 0.0%
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Time Series Example – Data Set FERTIL3
residual plots
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Time Series Example – Data Set FERTIL3
residual plots
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Time Series Example – Data Set FERTIL3
residual plots
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Time Series Example – Data Set FERTIL3
residual plots
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Time Series Example – Data Set FERTIL3
This model suffers from misspecification.
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Time Series Example – Data Set FERTIL3Scatter plot of gfr vs. pe
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Time Series Example – Data Set FERTIL3What could affect general fertility rate in the U.S.? Many things!How about these two:• World War II• Availability of the birth control pill
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Time Series Example – Data Set FERTIL3ww2 is a dummy variable• 1 if year is 1941 through 1945• 0 otherwisepill is a dummy variable • 1 if year is 1963 or greater• 0 otherwise
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Time Series Example – Data Set FERTIL3
Fit this model with two dummy variables.
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Time Series Example – Data Set FERTIL3
gfr = 98.7 + 0.0825 pe - 24.2 ww2 - 31.6 pill
Predictor Coef SE Coef T PConstant 98.682 3.208 30.76 0.000pe 0.08254 0.02965 2.78 0.007ww2 -24.238 7.458 -3.25 0.002pill -31.594 4.081 -7.74 0.000
S = 14.6851 R-Sq = 47.3% R-Sq(adj) = 45.0%
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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gfr = 98.7 + 0.0825 pe - 24.2 ww2 - 31.6 pillww2 is a dummy variable• 1 if year is 1941 through 1945• 0 otherwise
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gfr = 98.7 + 0.0825 pe - 24.2 ww2 - 31.6 pillpill is a dummy variable • 1 if year is 1963 or greater• 0 otherwise
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Time Series Example – Data Set FERTIL3
gfr = 98.7 + 0.0825 pe - 24.2 ww2 - 31.6 pill
Summary:• Adding pe and ww2 improves model significantly• Model gives insight into historical variables that
affect gfr• Model may not be very useful for future predictions
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Time Series Example – Data Set FERTIL3
Modeling with lags
Economic theory implies that there might be a lag effect on gfr (general fertility rate) from pe (tax value of having a child)
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Time Series Example – Data Set FERTIL3
Modeling with lags
Examine variables pe_1, pe_2, pe_3, and pe_4
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Time Series Example – Data Set FERTIL3
Making lags in Minitab is easy. Go to Stat > Time Series > Lag.
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
Residual plots:
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Time Series Example – Data Set FERTIL3
gfr = 95.9 + 0.073 pe - 0.006 pe_1 + 0.034 pe_2 - 22.1 ww2 - 31.3 pill
Predictor Coef SE Coef T PConstant 95.870 3.282 29.21 0.000pe 0.0727 0.1255 0.58 0.565pe_1 -0.0058 0.1557 -0.04 0.970pe_2 0.0338 0.1263 0.27 0.790ww2 -22.13 10.73 -2.06 0.043pill -31.305 3.982 -7.86 0.000
S = 14.2701 R-Sq = 49.9% R-Sq(adj) = 45.9%
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Time Series Example – Data Set FERTIL3
Personally, I think adding the two lags to this model over complicates the model for little gain. I recommend against inclusion of the two lags.