be subject to ARMA models. Often, differencing a time series results in satisfying stationarity
requirements. This implies that if y t is not stationary, y t might end up being stationary, where y t
= y t y t 1 . The differenced time series, when modeled
two lags of housing starts and that housing completions do not affect housing starts.
The equation for housing completions suggests that only two coefficients, that is, the third
lag for starts and the third lag for completions, returned statistically sig
Akaike and Schwartz Information Criteria (AIC and SIC) are the tools used to select appropriate
models. These tools are more comprehensive than an ordinary measure of fit, such as R 2 .
When models are being compared, we select the model that returns the
Toronto CMA data return similar results for cross-correlations. Significant positive correlation
between housing starts and completions can be observed in Figure 11.16 , preceded by
the Stata code used to generate it. However, the cross-correlation betwee
methods, have revisited the study. In particular, they question Fairs findings about the effect of
duration of marriage on the likelihood of having an extramarital affair. Fair found that the likelihood
of an extramarital affair increases with the duratio
7. Hamel, M.B., Blumenthal, D., Collins, S.R. (2014). Health care coverage under the
Affordable Care Acta progress report. The New England Journal of Medicine ,
371 (3), 275281.
8. Blumenthal, D., Abrams, M., Nuzum, R. (2015). The Affordable Care Act at 5
I present a detailed commentary from tabulations performed on the data set. However, for the
sake of brevity, I reproduce results from a select few tabulations. The script provided on the
books website carries the entire code for all tabulations.
The surv
I test these assumptions using a data set on intercity travel in Australia. I estimate a conditional
logit model to capture the travel mode choices. The data set comprises 210 respondents.
The model consists of four choices: air, bus, car, and train. Vari
ytitle(unemployment rate in percent) /
ytitle(, alignment(default) /
ytitle(Median home prices for new housing ($), axis(2) ttitle(Months)
/
title(Unemployment rate and Median home prices in the US,
size(medium) /
note(Data obtained from Federal Reserve E
gg
exp
1 exp exp
2
12
Equation 9.22
()()()=
+
P walk
gg
1
1 exp exp 1 2
Equation 9.23
Interpreting Multinomial Logit Models
The interpretation of coefficients in a multinomial logit model is slightly complicated. It is possible
to have a decline in P ij w
the housing starts could be an ARIMA(1,0,1) process because the ACF does not depict a
geometrically
declining pattern. Because the autocorrelation and partial autocorrelation functions
of covariance stationary processes approach zero at large displacement
spatial analysis to understand the determinants of income polarization in Toronto. The slightly
modified version reproduced here illustrates the utility of GIS and spatial analysis. I conducted
a spatial analysis of the data to determine the deep-rooted p
in the first place. I used a data set from the 1980s to illustrate how the presence of young
children, education attainment of women and their husbands, and workers age explained the
likelihood of a woman working. A not-so-surprising finding was that wome
GIS. We see that Central Park in Manhattan has also been included in trade areas of neighboring
restaurants. Restaurant owners can also generate revised trade areas that exclude Central Park
if so desired. The resulting trade areas are presented in Figure
between 20 and 40 km
between 40 and 60 km
greater than 60 km
69.72686
63.44869
43.35377
24.64542
24.22836
24.37141
Total 38.88224
Figure 10.26 The share of rental housing units declines with distance from downtown
Table 10.1 lists the variables and their
the issues with autocorrelation and heteroskedasticity. I am reporting the OLS results here and
encourage the readers to re-estimate the same model with the NeweyWest robust standard
errors.
Table 11.4 presents the results.
The first model labeled reg1 in
The shock ( t ) is uncorrelated over time and is also expressed as t ~ WN (0, 2 ). Hence,
y t ~ iid WN (0, 2 ), which implies that y t is independently and identically distributed with 0 mean
and
constant variance. You should know that when someone refers
differenced time series
ARIMA versus OLS Model
Once again, I compare the ARIMA forecasts with the ones obtained from the OLS model. The
results are plotted in Figure 11.27 . The OLS forecasts are listed as Fitted values in the figure.
Note that compared t
adds only one lag of the house price index to the ARIMA(1,1,1) model. The results are presented
in Table 11.9 .
The ARIMA(1,1,1) model with six lags of the housing price index returned statistically
significant coefficients for the autoregressive and movi
Lets begin with the discussion of what is meant by data mining . There are two divergent
approaches to data mining. One is the traditionalist approach of considering data mining
synonymous
to statistical analysis. The other group insists that it differs f
Jx
1
ki
' Equation 9.17
Multinomial Logit Models 379
Remember that we arbitrarily set the coefficients of alternative 1 as 0.
For the multinomial case, assume we have three modes: 1) automobile, 2) transit, and 3)
walk. We will have two logits; that is, t
yy
T
y
T
s
tT
tyty
t
T
ty
1
1
2
Equation 11.16
Time Series Econometrics 481
Bartlett (1946), quoted in Gujarati (1995, p. 717), has established that for purely random
processes, is approximately normally distributed with zero mean and a variance equaling
2025: 308 tracts, 59% of city. 2005 actual: 206 tracts, 40% of city
City #1:
City #2:
City #3:
Figure 10.15 Income polarization in Toronto
Source: http:/www.urbancentre.utoronto.ca/pdfs/curp/tnrn/Three-Cities-Within-Toronto-2010Final.pdf
Spatial Analysis
Data Source: Statistics Canada, Census 2006. Calculations by the author
444 Chapter 10 Spatial Data Analytics
Also, note that the very low-income category is non-existent in local suburban municipalities,
such as Markham, Milton, Oakville, Richmond Hill,
Husbands education (%)
College educated 45 55
Did not attend college 40 60
Wifes income
Log of wifes wages 0.97 1.19
Family income (000s)
Family income excluding wifes 21.7 18.94
360 Chapter 9 Categorically Speaking About Categorical Data
Table 9.8 lists
+
P auto exp
exp exp exp
V
VVV
a
atw
( )=
+
P transit exp
exp exp exp
V
VVV
t
atw
( )=
+
P walk exp
exp exp exp
V
VVV
w
atw
Notice the probability function carefully where I am still dealing with the difference in
utilities. Lets divide both the denominat
respondents. Approximately 96% identified themselves as heterosexual.
Surveys often ask questions to determine the state-of-mind of the respondents. The Pew
online dating survey asked respondents to report their self-assessed quality of life (see Table
9.
covariate.labels=c("Female", "Midwest","South", "West", "Living With A
Partner", "Divorced", "Separated", "Widowed", "Never Been Married", "No
Children", "Does Not Use Internet", "No Email", "No Internet On Mobile
Phone", "Respondent Reached On Cellular")