STA 317, Fall 2017, Daily
Recaps
(MWF: 10:00 – 10:50, MP
312)
Final Exam: Wednesday, December 13, 10:10am.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Minitab Examples: Ex01 Ex02 Ex03 Ex04a Ex04b Ex05
Ex06 Ex07 Ex08 Ex09 Ex10 Ex11 Ex12 Ex13 Ex14
Assignment #7: [TS1 TS2 TS3]: Due Wednesday, December 13
F, December 8
Finished
the discussion on Prediction Intervals for future forecasts; verified several
prediction intervals on Minitab results for the the MA(q), AR(1), and ARMA(1,1); reviewed for the Final
Exam.
W, December 6
Continued
in chapter 5 on forecasting future values in a time series; looked at the
structure of forecasts for the MA(q), AR(1), AR(2), and ARMA(1,1) processes; distributed
results for examples of the MA(q), AR(1), and ARMA(1,1) processes; developed the prediction interval for a future
forecast value based on the time series expressed as an infinite moving average
process; looked at the structure for the prediction intervals in AR(1), MA, and
ARMA(1,1) processes; began calculating/verifying prediction intervals from some
example time series.
M, December 4
Returned
Test #3; continued in chapter 5 on forecasting; finished the optimal
exponential smoothing as an ARIMA(0,1,1) model; developed the approach to
finding predictions of future values in a time series; examined the particulars
for the MA(q), AR(1), AR(2), and ARMA(1,1) processes; began an example on the
AR(1) process (Results).
F, December 1
Finished
chapter 4 on estimating an ARIMA models; mentioned seasonal ARIMA models and
their features; examined the auto correlation function and p. acf to see appropriate levels of differencing and
regressive parameters; used the CO2 time series data to fit an appropriate
seasonal ARIMA model; compared the ARIMA model results to the seasonal
decomposition results. [Results];
began chapter 5 on forecasting; reminded of the approaches when using
trend/seasonal models; introduced the general notation for a forecast value;
began developing the optimal approach for the exponential smoothing as an ARIMA
(0,1,1) [Results]
W, November 29
Test
#3
M, November27
Reviewed
for Test #3
M, November 20
Went
over some final points on the ARMA(1,1) and the
Results demonstrated on model from
Friday; went over a few more Time Series Examples to determine the appropriate
model, and check on the auto-correlations (Results).
F, November 17
Continued
in chapter 4 on determining an appropriate model from an observed time series;
discussed the case of a MA(q) process and its signature of the a.c.f “cutting off”
after lag q; also discussed the iterative approach to minimizing SSE;
distributed the Results of an MA(2)
process and developed the fitted model; discussed the ARMA(p,q)
model and the use of the acf and the p.acf to the identify an appropriate model; looked at the Results of an ARMA(1,1) Model, and the
subjectivity involved in deciding on an appropriate model; looked at another
time series (Results) to determine an
appropriate model.
W, November 15
Continued
in chapter 4; discussed the fitting of an AR(2) model and interpretation of the
coefficient 
in the model,
and formulas for the coefficients in the estimated model; introduced the partial auto-correlation function and
its use in determining the general order of an AR(p) process; looked at all
these aspects with the Results of an AR(2)
process.
M, November 13
Continued
in chapter 4 on estimating and fitting an ARIMA model; discussed differencing
to achieve approximate stationarity; discussed the problem and detection of
over-differencing; started on the fitting of an AR processes as essentially
multiple linear regression models using past values as independent variables;
mentioned the particulars of the estimation of an AR(1) process; distributed Results for an AR(1) process;
mentioned that Test #3 would be Wednesday, November 29.
Assignment #6: Due Friday,
November 17
F, November 10
Wrapped
up the discussion of the ARMA(p,q) models; restated
the properties of the auto-correlation function, and reviewed the general
situation in determining whether a series is stationary and/or invertible;
looked at the special case of the ARMA(1,1); developed the autocorrelation
function and its features; looked at the Simulated
Results of an ARMA(1,1) process to verify the correlation function; began
discussing initial differencing and the formal structure of the ARIMA(p,d,q) model; looked at a quick example to see the
differencing to see a process become stationary; Began chapter 4 on estimating
and fitting an ARIMA model; discussed differencing to achieve approximate;
stationarity; mentioned other reminders
on choosing a model from the observed time series.
W, November 8
Continued
discussing ARMA(p,q) models; discussed the general situation in determining
whether a series is stationary and/or invertible; examined the infinite moving
average form of the process to see when it is stationary; looked at the special
case of the ARMA(1,1); developed the autocorrelation function and its features.
M, November 6
Finished
the discussion of Auto-Regressive Processes; Looked at several Examples of autocorrelation
functions to recognize the signature of the processes, and verified the
values of some of the lag correlations; Also viewed the correlograms of several
time series to decipher what was the underlying process; briefly began
discussing ARMA(p,q) models and their structure; discussed the properties of
stationary and invertible, and in particular those properties in the ARMA(1,1)
process.
F, November 3
No
class meeting: Lecture Notes
Results: First Example AR1; Second Example AR1;
First Example
AR2; Second Example
AR2
W, November 1
Finished
discussing the MA(q) discussed invertibility and how
to determine if the process is invertible; revisited the Backward operator B
notation and its form of the MA(q) process; began the formal introduction of an
AR(p) process; considered the AR(1) process; demonstrated how to write the
AR(1) as an infinite MA process to develop the auto correlation function and
variance of X(t).
M, October 30
Nearly
finished the discussion on the MA(q) process; restated
the properties of the process, in particular, the autocorrelation function;
used a Minitab simulation (Results)
to demonstrate the autocorrelation function and its “signature”; discussed
“invertibility” and how to determine if the process is invertible; introduced
the Backward operator B notation and its form of the MA(q) process, and the
necessary condition to be “invertible”.
F, October 27
Test
#2
W, October 25
Reviewed
for Test #2
M, October 23
Finished
the discussion on the random walk time series; restated the theoretical
properties; used a Minitab simulation to see the non-stationary series and the
(acf); looked at the differenced series to see it is
stationary (Results); began
discussing a moving average process of order q, MA(q); stated the general model
for a moving average process; started developing the properties including the
covariance and auto correlation function for the MA process.
Assignment #5: Due Friday,
October 27, [Data: TS#1 TS#2]
F, October 20
Continued
with the early part of chapter 3; restated the general properties of a time
series process (mean, variance, covariance, and autocorrelation function;
mentioned some additional properties on the theoretical (acf)used
a Minitab Simulation to show these properties for the purely random stationary
process (Results);
examined the time series plot and sample (acf) plot;
introduced the Random Walk Process; looked at the properties to show this process
is not stationary; used the difference operator to show the differenced series
is stationary.
W, October 18
Finished
up the ideas of autocorrelation; completed Minitab Example #13; mentioned the
significance limits for the test of a correlation at lag k; reintroduced
differencing to remove a linear trend to produce a stationary series; examined
the autocorrelation plots of seasonal data with a linear trend and additive
seasonal effects; introduced seasonal differencing to remove seasonal effects;
made some final comments on differencing; looked at several plots of the
autocorrelation for seasonal data in Minitab Example #14; began chapter 3 with
some ideas on a stochastic process; covered the properties (Mean, Variance,
Covariance) of a time Series Process; discussed the purely stationary time
series and its autocorrelation function.
F, October 13
Continued
with the ideas involving autocorrelation; nearly finished Minitab Example #13;
looked at the output to see the plot of x(t) v. x(t-1)
the lagged time series; discussed the T test for a particular lag auto
correlation and the BL-Q statistic for the test of all autocorrelations through
some lag k; mentioned the inclusion of seasonal effects and their impact on the
autocorrelation function; announced that Test
#2 would be Friday October 27.
Assignment #4: Due Wednesday,
October 18 [Data: TS#1 TS#2]
W, October 11
Began
discussing autocorrelation; reviewed the formula and properties of the sample
correlation between two variables; introduced the notion of the correlation
between “nearby” values in a time series; introduced the “Correlogram” (plot of the
autocorrelation versus the lag k); mentioned the significance limits in the
plot as a test of a significant auto correlation; mentioned the formula for the
significance limit at lag k; examined the correlation plot for a time series
with linear trend to see the auto correlations diminishing slowly; looked at
some of these notions with Minitab Example #13;
M, October 9
Finished
discussing decomposition for the quadratic model with multiplicative seasonal
effects; covered the exponential model with multiplicative seasonal effects; covered
the natural logarithm transformation to create an additive model and its
subsequent decomposition; used Minitab Example #12 to see the results.
F, October 6
Continued
discussing seasonal effects: discussed the seasonal decomposition (both
additive and multiplicative seasonal effects) for a quadratic trend model
beginning with the “Detrended” data and finding
seasonal effects with “seasonal only” decomposition; covered the first part of
Minitab Example #12 to produce the quadratic Trend with multiplicative seasonal
effects; mentioned the interpretation of a multiplicative seasonal index;
briefly started the exponential model with multiplicative seasonal effects;
mentioned the natural log transformation to create a linear trend model with
additive seasonal effects.
W, October 4
Continued
discussing seasonal effects: began discussing the seasonal decomposition as an
approach to isolate seasonal effects and the trend effects; carefully developed
the approach to seasonal decomposition with a linear trend and additive
seasonal effects; followed each step of the process with results from Minitab
Example #11, and made forecasts to compare to the regression approach;
mentioned the interpretation of the seasonal index in the decomposition
approach.
M, October 2
Finished
discovering some ideas in differencing a time series; restated the notation;
also mentioned seasonal differencing if desired; went over some ideas with
Minitab Example #9 on the annual sales data to compare differencing with the
linear trend analysis; began discussing seasonal effects; mentioned three basic
forms of a time series model incorporating seasonal effects; revisited multiple
linear regression using indicator variables to incorporate the “seasons”;
discussed the interpretation of the coefficients of the indicator variables;
looked at Minitab Example #10 to see the Regression view of using indicator
variables in the model.
F, September 29
Continued
covering double exponential smoothing; revisited the two smoothing parameters
α and γ and the philosophy in choosing their values; discussed using
Simple Linear Regression to get starting values for level and trend components;
examined these ideas with Minitab Example #8; mentioned differencing as a
technique to achieve stationarity in a time series; introduced the notation and
definition of the difference operator, ▽Xt and the
second order differencing.
Assignment #3: Due Friday,
October 6 [Data: Q1 Q2]
W, September 27
Made
some final remarks regarding single exponential smoothing; finished discussing
Minitab Example #7; compared the MA results and the Exponential smoothing
results on their forecast accuracy; briefly began covering double exponential
smoothing; discussed the two smoothing parameters α and γ and the
structural development of a smoothed value incorporating trend and “mean”
components; mentioned the approach to the initial smoothed value and trend
component.
M, September 25
Test
#1
F, September 22
Reviewed
the major topics for Test #1; returned to the topic of Single Exponential
Smoothing; discussed the forecasting with exponential smoothing, and went over
the forecasts on Minitab Example #7; made a cautionary comment about the smoothing
constant being greater than 1.
W, September 20
Made
some reminder remarks regarding the Moving Average smoothing technique;
mentioned the choice of centered versus uncentered
when forecasting and the general approach to forecasting and the prediction
interval; introduced Single Exponential Smoothing; developed the structure of
the smoothed series, and the properties of the smoothing constant 
, and the reasoning behind choosing α looked at
the creation of the smoothed time series in a simple example.
M, September 18
Began
covering “filtering” or smoothing of a time series; stated when these are
appropriate, their objective, and general structure; discussed the moving
average and it construction; also discussed the length of the MA and the end-point
problem with using a centered MA, and the “lag” problem with the “un-centered”
MA; calculated the MA in some simple examples; began looking at the MA results
in Minitab Example #6 for the Average Monthly Price for Gas Time Series.
F, September 15
Finished
the basic trend models; looked at each of the Trend models in Minitab Example
#5 with data representing yearly sales; saw the development of the exponential
model through the transformation of the original series and the
“untransforming” to the exponential model; verified the asymptote and intercept
on the S-Curve trend model; mentioned the measures of accuracy: (MAPE, MAD,
MSD), and made a couple comments regarding them in traditional regression.
Assignment #2: Due Wednesday, September
20 [Data: TS#1
TS#2
TS#3]
W, September 13
Began
discussing trend analysis; covered the linear and quadratic trend analysis;
reminded that these are the linear model and quadratic model in regression of Xt versus the time periods t; covered the development of
the exponential (growth/decay) model through linear regression on the log
transformation, then the “un-transforming” to the exponential model; discussed
the S-Curve trend analysis and its features of the intercept, asymptote, and
model; began looking at these trend analyses with Minitab Example #5.
M, September 11
Continued
in the early part of chapter 2; restated the idea of a “stationary” time series;
displayed a quick Plot of a
“Stationary time Series; began a more formal discussion of time series
plots and identifying features; displayed Minitab Example #4a of the time Series
Plot of Dr. Agard’s weight recorded annually; looked at the plots on Minitab
Example #4b and discussed the features and made some criticisms; made a few
final points regarding transformations of a time series; announced
that Test #1 would be Monday, September 25.
F, September 8
Started
Chapter 1 on Time Series; discussed some very general ideas about time series
data; mentioned a few fundamental departures from the usual statistical
environment; mentioned our basic objectives in time series analysis; started
Chapter 2 on descriptive statistics as related to time series data; discussed
sources of variation; mentioned the ideal notion of a “stationary” time series:
W, September 6
Wrapped
up the review of multiple regression ideas; restated the approach to the
analysis for a model including indicator variables; went over the questions on Minitab Example #3.
F, September 1
Continued
with a review of multiple linear regression ideas; discussed the multiple
linear regression situation involving a quadratic relationship between a
dependent variable Y and on independent variable X; discussed the structure of
the analysis and carefully went over Minitab Example #2; discussed
the role of indicator variables to incorporate a qualitative variable into a
regression model; covered the general approach to the analysis; very briefly
began covering Minitab Example
#3.
W, August 30
Began
reviewing Multiple Linear Regression; mentioned the overall objective and
introduced the “full” model in multiple linear regression; discussed the
testing for usefulness of the full model and the follow-up tests for the significance
of the individual variables; discussed the interpretation of the coefficients
in the regression model; discussed the strength of the model, and
estimation/prediction when appropriate; discussed the multiple linear
regression situation involving a quadratic relationship between a dependent
variable Y and one independent variable X; discussed the structure of the
analysis; discussed the role of indicator (or dummy) variables to incorporate a
qualitative variable into a regression model; covered the interpretation of the
coefficient for an indicator variable.
Assignment #1: Due Wednesday,
September 6 [Data]
M, August 28
Covered the remaining parts to Minitab Example #1.
F, August 25
Nearly
finished the review of Simple Linear Regression; covered formal estimation and
prediction with the regression model; discussed the objective, their
interpretations, how the intervals compare, and when it is not appropriate to
make predictions; discussed the use of various graphs of the residuals to check
the model assumptions and potential model inadequacy; briefly started on
Minitab Example #1.
W, August 23
Continued
with the review of Simple Linear Regression; discussed the interpretation of
the sample intercept and slope; mentioned the standard deviation of the model,
S; discussed the hypothesis test for a significant linear relationship; began
discussing the correlation and its properties; discussed the coefficient of
determination, R2, and its properties, and provided some
“subjective” guidelines.
M, August 21
Distributed
and discussed the Course Syllabus and Objectives; introduced the class website where
all course documents will be housed; mentioned where to find the Mathematics
and Statistics Department Syllabus; briefly began a review of Simple Linear
Regression Analysis; covered the simple linear model for a population; stated
the model, discussed the interpretation of the intercept and slope, and stated
the assumptions about the random errors; discussed the scatter plot and its
interpretation; discussed the estimation of the model with the fitted line or
regression line; discussed the interpretation of the sample intercept and
slope.