last srinath first krishna - transportation research...

Graduate Research Award Program Application: 2010-2011 Page 2 of 11

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Application Checklist and Application Packaqe Gover Sheet

Applicant's name: Ravulaparthy Srinath Krishna Dale _0511712010_Last First Middle

A completed application checklist and application package cover sheet

Personal information of applicant

Qualifications of applicant

Research project proposal

Reference letter #1

Reference letter #2

Research advisor form

Unofficialtranscripts from:Arizona State University and UC Santa BarbaraThe Otficialtranscripts have been ordered and will be sent separately,

Writing Sample

(The writing sample should be submitted with the application. An appropriate writingsample might be a previous publication, a paper written for a class assignment, aresearch project report, or similar example of professional writing. lf papers were co-authored, the role of the applicant must be clearly described. writing samples may notbe longer than 25 pages.)


APPLICATION FORM

GRADUATE RESEARCH PROGRAM ON PUBLIC-SECTOR AVIATION ISSUES

Sponsored By: Administered By:FederalAviat¡on Administration Airport Cooperative Research ProgramU.S. Department of Transportat¡on Transportation Research Board, National Academies

PART I- PERSONAL INFORMATION OF APPLICANT

(Please Type)

1. Full legal name:Ravulaoarthv Srinath KrishnaLast First Middle Former name (if any)

2.Dateofbirth:-01/09/1984Placeofbirth:-Hyderabad,lndia

3. Citizenship:_lndia

4. Gender: [X]Male [ ]Female

5. Ethnicity (optional) :

American lndian or Alaskan Native: origin in any of the original peoples of North AmericaBlack: origin in any of the black racial groupsHispanic: Mexican, Puerto Rican, Central or South America, or other Spanish culture or origin,regardless of race

X I Asian or Pacific lslander: origin in any of the original peoples of the Far East, Southeast Asia,or the pacific lslands. lncludes China, Japan, Korea, the Philippine lslands, Samoa, and thelndian Subcontinent

lWhite: origin in any of the original peoples of Europe, North Africa, or the Middle East

6. Mailing address: 1832 Ellsion Hall, Department of Geography, UC Santa Barbara, Santa BarbaracA 931 06

7. Permanent address: C-319, Dattasai Apartments RTC X Roads, Hyderabad 500020, AndhraPradesh, lndia

8. Telephone numbers - Mailing:805-455-381727674243

Permanent:91-40-

9. Email address: [email protected]

10, College or University currently enrolled at: University of California, Santa Barbara

11. Major Field: GeographyDegree objective: [ ] Maste/s [X ] DoctorateExpected month and year of graduation: _051201

12. Names of two people from whom you are requesting reference letters.a. Dr. Kostas Gouliasb. MichaelGorton

13. Name and title of faculty research advisor for this project:Dr. Kostas Goulias, Professor

-a_


PART II _ QUALIFICATIONS OF APPLICANT

(Please Type)

14. Education: ln reverse chronological order, list colleges or universities attended.

15. Professional Experience. ln reverse chronologicalorder,list professional experience, includingsummer and term{ime work.

16. Awards, honors, and publications: List fellowships, scholarships, and other academic and/orprofessional positions, held since entering college or university.

College / University

Please explain any interruption(s) of training, illness, etc.)

Name of Employer Location Dates Nature of Work

Arizona State University Tempe, AZ 01/2006 - 05/2006 Teaching Assistant:Teaching undergraduatecourse in "TestingMaterials for Construction"

Arizona State University Tempe, AZ 05/2006 - 01/2008 Research Assistant:Research in traffic safety,statistics, travel behaviorand traffic enoineerino

HDR Engineering lnc. Phoenix, AZ 01/2008 - 06/2009 Transportalion Planner:Worked on airtransporlation planning,travel demand modeling,and traff ic enoineerino

UC Santa Barbara Santa Barbara, CA 08/2009 - till dale Research Assistant:Researching on travelbehavior, demographicsimulation

Award, Honor, or publication Date(s) Description

ffashington.S., Ravulaparthy.S et al )1/20093ayesian lmputaÌion Method in Revealed)reference Survevs. oresented at TRB 2009.


17. Describe your career goals and how this research will contribute to achieving those goals (you

may add page(s) if necessary):

A large majority of Metropolitan Planning Organizations (MPO's) consider airports in a simplified mannerby treating them as special generators as part of their regional travel demand models, As a result regionalmodels usually provide little help in analyzing policies involving changes or improvements to the airportsin terms of service and ground transportation access. The dynamic changes in the demographics of airtravelers is an important component in regional air travel demand modeling.

My research would focus on building a demographic spatial micro-simulator with detailedinformation at person and household level. The new techniques being carried out in panel surveys andactivity-based surveys help in the design of such a simulator. The research on socio-demographicforecasting in travel demand modeling has been progressing slowly which does not provide sufficienttools for policy makers. Within these issues, my research addresses the need for a socio-demographicmicro-simulator tool which can forecast social, economic and demographic data more precisely at personand household level, while integrating changes in land-use over time and accounting for migrationpatterns in the region.

Furthermore, thís research also gives me an opportunity to collaborate with experts in other fieldsin academia, who would provide valuable input which eventually would lead to a successfulinterdisciplinary collaboration in solving problems in aviation and air travel demand modeling. Thisresearch project also provides opportunities for undergraduates with flair of research in this field.

After completing my PhD, I intend to pursue a career in academia and research, as academicsform the right platform in communicating my research. This would provide me with an opportunity of beingat the forefront in this vast expanding field of travel demand modeling and travel behavior. I am especiallyexcited for being part of the transportation community, when people from both industry and academia areadvocating in a paradigm shift from the current transportation planning practices primarily focused onsustainable transportation systems in making the world a better place to live.

Graduate Research Award Program Applicationl 2010-2011 Page 6 of 11

I atfirm that the information

Signature of the Applicant:

is true and complete to the best of my knowle{ge.

D,-" !{]ftf øro[NOTE: This applÍcation Ís not complete wìthout a signature.]


APPLICATION FORM

GRADUATE RESEARCH AWARD PROGRAM ON PUBLIC-SECTOR AVIATION ISSUES

Sponsored By: Administered By:Federal Aviation Administration Airport Cooperative Research ProgramU.S. Department of Transportat¡on Transportation Research Board, National Academies

PART III -RESEARCH PROJECT PROPOSAL

(Please Type)

Name:_RavulaparthySrinathKrishna Dale_0511712010Last First Middle

Title of Research Projecl:

Dynamic Social and Demographic Microsimulation for Airport Travel Demand

ln 500 words or less, describe the proposed research project. lnclude project objectives,methodology, and expected outcomes. Also indicate how this research work could benefit theaviation community, and contribute to your career goals.

[Please attach additional sheets as needed.]

ACRP Graduate Research Program Application : 2010 -201 I Srinath K Ravulaparthy

Research Project Proposal

A large majority of Metropolitan Planning Organizations (MPO's) consider airports in a

simplified manner by treating them as special generators as part. of their regional travel demand

models. Specific features like the composition of the air travelers' demographics, travel behavior

and their attitudes towards current airport facilities and accessibility are rarely analyzed or

explicitly modeled. As a result regional models usually provide little help in analyzing policies

involving changes or improvements to the airports in terms of service and ground transportation

access. Having worked as a Transportation Planner in a private industry and interacting'with the

MPO's has made me realize the scope and need for such research and development in the field oftravel demand forecasting with special emphasis on air travel.

Innovative methods in travel demand forecasting have laid foundations to capture and

predict travel behavior more reaiistically than ever before. One of the important input

components for any travel demand modeling process are the social, economic and demographic

data at the person and household level. Moreover, the forecasts from these new travel demand

models are highly sensitive to input information provided. The research on socio-demographic

forecasting in travel demand modeling has been progressing slowly which does not provide

sufficient tools for policy makers. Within these issues, ffiy research addresses the need for a

socio-demographic micro-simulator tool which can forecast social, economic and demographic

data more precisely at person and household level, while integrating changes in land-use over

time and accounting for migration pattems in the region.

My research would focus on building a demographic spatial micro-simulator with

detailed information at person and household level. The new techniques being carried out inpanel surveys and activity-based surveys help in the design of such a simulator. This research

would conduct an agent based simulation, where the agent (an individual) is evolved over time

(human life cycle evolution) and the various decision making processes that are undertaken

during these periods are also simulated in both time and space. Accounting for such fine detail

would provide potential opportunities in improving airport related services and ground access

transportation. The prediction in land-use changes over time is also an important factor that is

considered in the simulator, which can dictate future improvements surrounding the airport

services in providing sustainable transportation opportunities. Incorporating immigration into

this simulator would provide the changes in regional travel needs and spatial patterns that would

be important as these would be serving as potential air travelers, who have higher propensity to

return to their of origin for family and vacation visits. The simulation of such fine detail is

possible with advances in micro-analytic simulation models and related programming languages.

Thus, for a successful implementation of this research it would be very helpful to have

external funding. This funding would definitely encourage in successful implementation of this

ACRP Graduate Research Program Application:2010-2011 Srinath K Ravulaparthy

research, which would ultimately contribute to the field of Transportation Planning and Travel

Demand Modeling.

Thank you for considering my application.

Srinath KRavulaparthy Date: 05llll20l0

UNIVERSITY OF CALIFORNIA Sarìta Barbara

Y. DAVIS .lR\¡¡M. LæANGELES ' MEÌ.CED ' Rñ:ERSIDE. SÀNDIEGO . S¡{N¡ffi-*CISC-o SANTA B.ARBARA . SANTA CRÜZ

DEPARn¿ENT oF GEoGRA?HY -ì61I Ellison HallSanta Bar'Þara, CA 9310ó-4060Phoûe: (805) 893-36ó3Fax: (805) 893-7782http ;//iv$l&'. geog,ucsb.edu

N4ay I4,20I0

Airport Cooperative Research Program

Dear Colleagues:

It is with grêat enthusiasm that I am writing this letter of recommendation for one of my current

Ph.D. students Srinath Rawlaparthy. Srinath is uniquely talented and extremely energetic in his

approach to research. He continues his graduate studies at the Ph.D. level after receiving an MS

in engineering from Arizona State University and very good studies in engineering from India.

Srinath decided to come back to graduate school after a short period of consulting practice giving

up the comfort of a well paying job for the hard life of a graduate student. At UCSB Srinath is

taking during this year a series of courses in Econometrics and he is excelling in every aspect.

He is also an inspiration for other graduate students with his phenomenally positive attitude and

genuine curiosþ. Of course these are the traits that brought him here at UCSB as the

recommendation letters from his past mentors testiff and make him one of the best students I

could ever recommend for his airport related research on developing a new forecasting model

system.

Srinath's research is on the development of a demographic spatial micro-simulator with

detailed information at person and household levels. He is using agent based simulation to

develop personal histories of change using software. This software contains statistical models oflof3

individuals and their households that are based on travel surveys. We expect these demographic

simulators to become a standard tool for regional travel demand forecasting after the hard

fundamental research is complete but certainly within the next three to four years. Before

moving these methods to widespread practice, a variety of design options need to be considered,

tested, and validated. Particularly important for this proposed research is the travel behavior

aspect of long distance travel and the propensity of households and individuals to travel long

distances by air. As we see in other forecasting models for travel behavior dynamic

microsimulation of households and individuals is becoming the premier tool and aviation should

not be left behind in this new and exciting development. The research work to do all this

requires excellent background in statistics and econometrics, programming skills, and deep

understanding of the social and demographic processes that are reflected in the simulator. In

addition, understanding oftravel demand and its determinants is equally important.

Srinath has many of these skills and the talent to creatively develop new methods and

techniques. As an MS student at ArizonaState, Srinath worked on discrete choice models using

Bayesian statistics. He is combining that background with other economehic methods to

develop the models needed in the microsimulator and in a very short time he already produced

many useful results. This is anamazingproductivity and takes very smart individuals to make

something like this happen in such a short time. Knowledge, creativity, energetic enthusiasm,

and skills of this type are of paramount importance as we move to 'ogreener" policies at every

jurisdictional level and as we prepare for the new transportation legislation. In fact, in

California we already experience the impact of "greener" legislation and many planning agencies

are required to use better modeling and simulation tools. I believe Srinath's work will be at the

center stage of this development and will become a uniquely qualifìed leader.

There is more to say about Srinath. In the past few months working in a project with

other graduate students, Srinath gave proof of his ability to work with other students that is

2of 3

admirable. He is motivated by other students but he also motivates them to think harder, faster,

and better leading by the example of an amazing work ethos and contagious positive energy.

I am convinced Srinath is uniquely qualified to receive a research grant from ACRP for

many reasons. First, he has completed a truly impressive anay of preparatory work in India,

Arizona State, and he continues doing this at UCSB with outstanding performance and

enthusiasm. Second, Srinath has a consistent record of excellence in everything he does. Third,

he is extremely dedicated and through his resourcefulness made already substantial progress

towards his goal. Fourth, Srinath has the right attitude to achieve great results and is willing to

make the necessary sacrifices to achieve academic excellence. Fifth, the methods he proposes to

use to predict airport demand is at the highest levels of excellence and is feasible within the time

frame proposed.

Srinath is matching perfectly the purpose of this competition as his previous

achievements demonstrate making him a truly outstanding candidate. The ACRP grant will

complete his portfolio of accomplishments and enable him to continue unobstructed this

challenging course to complete his Ph.D. I am convinced we will all be very proud to have

Srinath as a colleague in transportation for many years tô come.

Konstadinos G. Goulias, Ph.D., Professor, University of California Santa Barbara

3of3

()N1: (.()Ml'r\NY |,ll,rtt.¡' \'olttt itttt'

May 14,2010

To Whorn It May Concern:

I am pleased to recommend Srinath Ravulaparthy for the Airport Cooperative Research Program

Graduate Research Program Award in Aviations Issues. I was Srinath's mentor during his tenure

at HDR Fngineering, ¡ic., in Phoenix, Arizona, and workeC closel¡, rryith hirn cn the develoPrrent

of Arizona's first statewide travel demand model.

I first became acq¡ainte{ with Srinath when we studied together under Dr. Ram Pendyala at

Arizona State University. He is a serious student of travel behavior forecasting. I was impressed

with his aptitude and curiosity and invited him to join our travel demand modeling team at HDR

upon his graduation.

As Srinath came on board, HDR was beginning a six-month effort to develop an Arizona

statewide travel demand model to support an Arizona Department of Transportation planning

framework study with a}}S}vision. ihe pace of work was furious but Srinath's cheerfulness and

diligence helpeá carry us through challenging elements of model development' Srinath evaluated

,u.i"y clata, àevelopéA trip genération and attraction models, and worked to develop the

statewide model socioeconomic database.

In addition to applying his skills in modeling travel behav-ior, Srinath never hesitated to jump into

unfamiliar waters. He-set to work willingly on airpoft traffic engineering projects and other traffic

impact study projects making him an asset to the office'

It was a great pleasure to work with Srinath. I cannot imagine a better recipient for this award. I

enthusiastically recommend him to you.

Sincerelv./1

ru/"/ r&r-Michael E. Gorton, AICPSenior Transportation Planner

5CI"'r\n¡rslvERSÄRY. ,.j, i,t ,::i,, ¡ t: ., ..'1' t ''.:

. ..:; r I

32û0 East Camclhack lÌoad

surte 350

Phrrr:nix. AZ 85018-23 I 1

Phone: i602) 522'77110

fãx 16021527-:11Ð1

v.¡¡''v.hdrinc.corl

HDR Engineeting, lnc.


APPLICATION FORM

GRADUATE RESEARCH AWARD PROGRAM ON PUBLIC-SECTOR AVIATION ISSUES

Sponsored By. Administered BY.

FederalAviation Administration Airport Cooperative Research ProgramU.S. Department of Transportation Transportation Research Board, National Academies

PART V - FACULTY RESEARCH ADVISOR

To be completed bv the applicant:

NOTE: ln order to enrich the educational experience gained from your proposed research proiect, it isnecessary for you to request a faculty member from your university who is familiar with your researchproject to act as a research advisor to you during the course of the proiect. Please provide the followinginformation and ask the faculty member to complete the form. You should submit it with your application.The researÇh advisor may also be a reference respondent.

Applicant's Nam e: _Bavu laparthy Srinath-Date: May 1 4, 2010Last First Middle

Title of Proposed Research Project:

Dynamic Social and Demographic Microsimulation for Airport Travel Demand

To be completed by the facultv research advisorNOTE: The research product of research award recipients can be considerably enhanced if a facultymember at the applicant's university acts as an advisor to the applicant during the conduct of theresearch. Therefore, each applicant is required to designate such an advisor who will be available to

him/her throughout the course of the research project to provide advice as it progresses. When researchpapers by award winners are published by the Transportation Hesearch Board, the faculty member will beidentified as the research advisor.

Faculty Research Advisor's Name: Konstadinos G GouliasTitle: Professor_Department: GeographyUniversity: University of California Santa BarbaraMailing Address: 1832 Ellison Hall, Department of Geography, UCSB, Santa Barbara CA 93106Email: [email protected] Phone: 805-308-2837

1. Have you examined the applicant's proposed research plan? Yes -X No

2. Do you consider the applicant's research plan reasonable? Yes -X- No ,-lf no, please comment.


PART V: Page 2

3. Do you believe that this applicant can complete the proposed research within the time frame

indicated? Yes -X-

No

-.

lf no, please comment'

4. Will the applicant receive academic credit for this work? Yes X- No

-.

lf yes, please

indicate the nature of this academic credit. [Note: Receiving academic credit in no way counts

against the applicant.l

-He will receive credit for independent research Geog 598

5. Please indicate briefly how you plan to monitor and advise on the work of the applicant on thisproject.

_We will meet individually every week lor 2-3 hours and he will also share his research in our

weekly meetings with the entire research group. ln addition, we willjointly define research milestones

and a detailed schedule of deliverables.

6. I am willing to be the research advisor to the applicant if the applicant receives this research

award. Yes -X- No -,;Z-;4- -'- -2 -'\Signature: -=t-- '*--u-Ç-C Date:

--May 14,2010

Name: SrinathKrishnaRavulaparthyStudent lD: 100090¿1402

Print'Date; O31O2J2010External DegreesJawaharlal Nehru Technological Un¡vers¡tyBachelorofTechnology 06/01/2005

Degrees Awarded

Degree: l\4aster ofsdenæConfer Date: 05/08/2008Degree GPA: 3.63Plan: Civil and Environmental Eng¡neering

fra A, Fulton Schooì of Eng¡neer¡ng

Beginning of Graduate Record

2006 Spr¡ng

Course SegÊrjplig! Attemoted Earned

CEE 515.M Properties ofconcrete 3.000 3.000CEE 580.M Pract¡cum 3.000 3.000CEE 598-M Special Top¡æ 3.000 3-000Course Top¡c: ST:Sustainable Trans SysCEE 598-M Spec¡al Top¡cs 3.000 3.000Course Top¡c: ST:Sustainable Urban Engrg¡,ilCEE598 GRADEB+ TOA- EFF010307

Cum GPA; 3.63 Cum Totals 36.000 98.001

Page 1 of 1

2007 Summer 1

Attemoled Earned Grade Po¡nts

1.000 1.000 Y 0.000

Atlempted Earned Po¡nts

1.000 1.000 0.000

37.000 37.000 98.001

2007 Summer 2

AttomÞted Earned Grade Points1-000 1.000 Y 0.000

Attemoted Earned Points1.000 1.000 0.000

38.000 38.000 98.001

2007 Fall

Attempted Earned Grade Po¡nts

3.000 0.000 x 0.000

6.000 6.000 Y 0.0006.000 6.000 Y 0.000

Attsmpted Earnsd

'12.000 12.000

50.000 50.000

Points

0.000

98-001

Arizona State UniversityUnofficial Transcript

Course Descr¡ot¡on

CEE 592-M Rêsêarch

Têrm GPA:

Cum GPA;

0.00 Term Totals

3.ô3 Cum Totals

Grade

BY

Points9.0000.000

1'1.001

'12.000

Po¡nts

32.001

32.001

Points0.0009.999

9.000

12.000

Points30.999

63.000

Po¡nts

35.001

Gourse Descr¡pt¡Òn

CEË 592.M Rêseãrch

Term GPA: 0.00 TermTotals

Cum GPA: 3.63 Cum Totals

Course Descriotion

CEE 573 TransportationOperations

CEE 580 PracticumCEE 592 Rêsêa¡chThes¡s; The Feasibility of Bayesian lmputation ofNon-Chosen Attrìbute Values ¡n Revealed PreferenceChoice Surueys

Term GPA: 3.56

Cum GPA: 3.56

Attemotêd Earned

Term Totals 12.000 12.000

Cum Totals 12.000 12.000

2006 Fall

Descr¡plion Attempted Earned

Research 3.000 3.000Spec¡al Topi6 3.000 3.000ST:St¿t & Eæn ¡/odelin CeSpecial Topiæ 3.000 3.000ST;Dâtabâse l\rgmntConferênce and 3.000 3.000Workshop

CourseTopic: Cw:FundamentlsGiscience

Course

cEE 592-McEE 598-MCourse Topic:csE 598.MCourse Topic:GPH 594-M

Grade

Bt

B

Term GPA: 0.00 TermTotals

Cum GPA; 3.63 Cum Totals

END OF TRANSCRIPT

Term GPA:

Cum GPA:

course Descr¡ption

CEE 590.M Read¡ng andConference

CEE 598.M Special Top¡GCEE 599-M ThesisPUP 598.M Special Topic

Attempted Eamed

Term Totals 12.000 '12.000

Cum Totals 24.000 24.000

Attêmptêd Earned

Term Totals 12.000 12.000

2007 Spr¡ng

Attempted Earned Grade Points3.000 3.000 A 12.000

A- 11.001Y 0.000A 12.000

3.44

3.50

3.000 3.0003.000 3.0003_000 3.000

Term GPA:

5/17/2010

Univers ity of California, Santa Barbara

Unofficial Transcript

Srinath RawlaparthyPerm Number:3844974

Fall2009

course Grade

ECON 2414-ECONOMETRICS A+GEOG 2ol-SEMINAR GEOGRAPHY S

GEOG 2BBKG-SPECIAL TOPIC GEOG APSTAT 274-TIME SERIES B+

Quarter Total (Grad) GPA 3.76

Cumulative Total (Grad) GPA 3.76

Wìnter 2010

course Grade

ECON 241B-ECONOMETRICS AGEOG 2OOB-INTRO GEOG RESRCH AGEOG 2o1-SEMINAR GEOGRAPHY S

GEOG 211B-TRANSPORT MOD&SIM A+

Quarter Total (Grad)Cumulative Total (Grad)

GPA 4.OO

GPA 3.88

Spring 2010

Course

ECO N 241C-ECONO METRICSGEOG 2OOC-INTRO GEOG RESEARCH

GEOG 201-SEMINAR GEOGRAPHY

GEOG 21IA-TRANSP PLAN & MOD

Unofficial Transcript - Printable Version

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511712010 2:03:25 PM

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EnrlCd

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Grade EnrlCd

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Att CompUnit Un¡t4.0 4.02.0 2.04.0 4.04.0 4.0

14,0 L4.0

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15,0 15.029.0 29.0

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Transfer Work Undergraduate Ïotal: 0.0

UC & Transfer Work Undergraduate Total: 0.0

UC Work Graduate Ïotal: 29.0

,..ucsb.edu/.../UnofficialTranscri ptPrinta... 1/L

PSTAT 274 - Time Series

Final Project

Vehicle Miles Traveled in California: A Time Series Analysis

December 7,2009

Submitted by:

Srinath Ravulapanhy

Department of Geography

UC Santa Barbara

Summary and ConclusionsThe increasing motorized travel trend in California over the past years is measured in billionsVehicle Miles Traveled (VMT). This data was obtained from Caltrans measured over 20 years

from January 1989 through December 2008, the data suggests an increasing trend with a strong

seasonal effect. This data can be analyzed in the domain of time series, which accounts for both

the increasing trend and seasonal effects observed in the data (see Figure i).

As the data is measured monthly with an increasing trend, this trend is eliminated by differencingthe original VMT time series at lag 1. There is a strong seasonal component presence which isevident from the ACF plot for the differenced series (see Figure 5), where ACF decays slowlyfor every 12'h lag. Differencing further at lag 12 eliminates the seasonal component, but PACF ofthis series suggests a strong spike at lag 12 (see Figure 9), which indicates the presence of an

Autoregressive (AR) component. In order to account for this strong seasonal effect and

increasing trend, SARIMA models were chosen to fit the original data series.

Potential SARIMA models were compared based on the model goodness of fit statistics like,AICC, log-likelihood, model variance, and model AIC values (refer to Appendix-A for model

outputs). From the potential models compared, SARIMA (2, 1,0) x (2, 1,0) (12) represents a

better model fit for the data, with lowest AICC being -274.33 and maximum log-likelihood value

of 141.27. Standard residual analysis like: ACF and PACF plots, test statistics like Portmanteau

and Ljung-Box tests also suggest that the residuals follow a white noise sequence.

The forecasting of the VMT data is pivotal in regional planning process and policy analysis

which helps planners make informed decisions. This forecasting process is undertaken from the

SARIMA model fit to the data series. The forecasted data (refer to Appendix-A for forecasted

values) for the next 12 months (see Figure 11) are within the confidence intervals, suggesting the

model estimated is a good fit to the current data series.

The VMT time series data can also be analyzed using spectral analysis expressed as a linear

combination of uncorrelated white noise sequences plus the deterministic trend component,

which is composed of sine and cosine waves of different frequencies. There is a strong seasonal

component evident from the periodogram (see Figure 13), with an estimated period of 12

months, which is the time required for one complete cycle.

The increasing trend in the time series data is fitted by the linear combination of sine and cosine

waves for time r plus a third degree polynomial (refer to Appendix-A for model outputs), for the

frequencies IlI2 and 3/12 which are predominant for the estimated periodogram (see Figure 13).

The residuals from the model fit have a strong seasonal component as observed from ACF and

PACF plots (see Figure 16 and Figure 17), and this indicates a presence of AR and MAcomponents.

Potential SARIMA models were compffed based on the goodness of fit statistics. SARIMA (3,

0, 0 x (2, 0, 1) (12) represents a better model fit with an AICC of -250.23 and log-likelihood of

133.11(refer to Appendix-A for model outputs). Standard residual analysis is also conducted for

the model residuals as fitted from the SARIMA model. The tests are performed based on the

residual ACF ptot (see Figure 20), test statistics like Portmanteau and Ljung-Box tests and

cumulative periodogram (see Figure 19) of the fitted residuals, which suggest that the residuals

follow a white noise sequence.

Time Series Analysisl,.L Introduction:

Over the past years, there has been an increase in motorized travel in the state of California, and

this trend can be studied using the measure, Vehicle Miles Traveled (VMT) which is estimated

for motorists traveling on California state highways. This data was obtained from California

Department of Transportation (Caltrans), and provides an insight about this incremental trend.

Since, the data is observed over time; it can be analyzed using appropriate time series methods,

which involve: data analysis, model fitting, and forecasting.

l.2DataDescription:

VMT data from January 1989 through December 2008 was obtained from Caltrans, Traffic Data

Branch. VMT is a measure to indicate the total motorized travel on California state highways.

VMT measured in billion vehicle miles traveled is calculated according to the equation [1] given

as follows, where 7C denotes the traffic counts recorded along each roadway section and LM

represents the total number of lane miles for each roadway section.

VMT : TC * LM t1l

This data can be represented as a time series plot shown in Figure 1; time series model can be fitto this dataset which can explain the affects of time on motorized travel like: seasonality effects

and increasing trends in travel; the modeling also helps in forecasting the VMT data into the

future. This modeling effort is necessary to understand and explicitly capture dynamics of the

travel over time, as this forecasted VMT data is useful in regional planning and policy

applications, which helps planners to make informed decisions'

L.3 Data Analysis:

Based on the plot from Figure 1, it can be said that the data represents a seasonality effect with

an increasing trend. Typically, we would prefer to have a stationary time series with constant

variance, absence of any trend and seasonality effects. Sample Auto Correlation Function (ACF)

and Partial Auto Conelation Function (PACF) for the data are also plotted as in Figure 2 and

Figure 3 respectively.

Upon close observation, there is a strong seasonal component effect at 12th Lag for sample PACF.

Thus, based on these plots it would be appropriate to transform the data to achieve the

aforementioned requirements: stationary time series, elimination of trend, and seasonality

effects. Therefore, this can be achieved by differencing the original time series at first lag, whichresults in the elimination of a trend. Figure 4 shows this data series along with sample ACF and

PACF for the differenced time series in Figure 5 and Figure 6 respectively.

As seen from the above plots, sample ACF slowly decays at every l}'h lag, and a spike in sample

PACF at l2th lag, which indicates a seasonality effect with periodicity of 12. Thus, in order to

stabilize this effect and eliminate seasonality, the series is again differenced allag 12. Figure 7,

shows the time series plot for this difference, with corresponding ACF and PACF plots inFigure-8 and Figure-9 respectively. Sample ACF and PACF plots still indicate the presence ofseasonality; therefore, we need to explicitly model this effect through Seasonal Autoregressive

Integrated Moving Average (SARIMA) models.

L.4 Preliminary Model Identifïcation:

The VMT time series data indicates the presence of strong seasonal component, and this can be

evidently seen from the above sample ACF and PACF plots. Based on these plots, the time series

can be model with Autoregressive Moving Average (ARMA) of order p and q respectively

denoted as ARMA(p, q). As seen from the sample ACF and PACF plots for the differenced timeseries at lag 12, there seems to be a presence of both MA and AR components leading to an

ARMA model which may seem plausible for this non-seasonal component. Similarly, from the

differenced time series at first lag, the sample ACF decays slowly at every l}th lag,but the PACF

slowly decays after l't Iag, this indicates modeling the seasonal component with an

autoregressive (AR) of order 1 or either 2.

L.5 Model Fit:

Seasonal ARIMA models are estimated, with the integration component being "1", since we

differenced once to eliminate the trend in the data and the second difference at lag 12

corresponds reduced the effect of seasonality. SARIMA models are generally represented as

SARIMA (p, d, q) x (P, D, Q) þeasonality), wherc p is order of the AR component; d number ofdifferences applied, and q is the order of MA for the non-seasonal component, and P is the order

of AR component; D is the number of differences applied, and Q is the order of MA for the

seasonal component, with a periodicity as observed from the seasonality effect. Seasonality forthe VMT data series is 12.

Thus, the general form of SARIMA models that can be formulated is represented as in equation

[2], which accounts for both the trend and the seasonality effects for an observed time series

process. Let Xt correspond to the original time series, then according to equation [2], SARIMAmodel as described with AR component as a functioî ç(B) and seasonal AR component as a

function of Ø(Ê); similarly, with a MA component as a function 0(B) and seasonal MA

component as a function @(B') for seasonality s, with B represented as a back shift operator,

where Ê(X,) - Xn,.In the equation below, Z is white noise, where Zt-WNP,ær)'

ç(B)ø(Bs)Yt = 0(B)@(B')Z' l4

where Yt = (!.- B)dQ - B)DXt

Potential models are fit to the original VMT time series data, in R-software using maximum

likelihood estimation (MLE). The potential models that were compared are Model-l: SARIMA

(2, l, O) x (1, 1, 0) (12); Model-2: SARIMA (2, 1,0) x (2, L,0) (12); Model-3: SARMA (3, 1, 0)

x (1, 1, 0) (12) and Model-4: SARIMA (3, i, 0) x (2,1,0) (12) . The model outputs along with

estimated coefficients and goodness of fit statistics are provided in Appendix-A.

L.6 Residual Analysis:

Test for residuals are performed for the fitted models, to check that the residuals resemble a

white noise with constant vadance, and are IID. Residual plots along with Ljung-Box statistic

probabilities are plotted for residuals of Model-2 are shown in Figure-l0 respectively. Based on

the plots it can be said that, the residuals for the model resemble an iid white noise process, with

negligible correlation structure. Necessary statistical tests are also performed on residuals for the

fitted models.

Portmanteau Test: This statistic is represented al Qo which is given by equation [3], large value

of the statistic suggests that sample ACF of the data are too large for the data to be an iid

sequence and this statistics is 12 distributed with h degrees of freedom. Therefore, if Qo> f at

a=0.05 we reject the null hypothesis, that they represent an iid sequence'

t3lQp = nll o'(Ð

Therefore, this statistic is computed for h = 15 for all the four models in R-software, with values

for Model-l being23.74 at probability (p) = 0.069; Model-2 being23.63 at p = 0.071, Model-3

being22.51at p = 0.095, and Model-4 being 22.9 atP = 0.086

Ljung-Box Z¿sf: This statistic is an enhanced version of Portmanteau test, and is given as in

equation t3l. Simila¡ to that of Portmanteau test, a large value of the statistic suggests that

sample ACF of the data arctoo large for the data to be an iid sequence, and this statistic is also fdistributed with h degrees of freedom. Thus, we accept the null hypothesis, that they represent an

iid sequence if Qø< t' at o=0.05.

Similarly, this statistic is also calculated at lag h=15, with values of the probabilities for the

models being: Model-l is p - 0.052, Model-2 is p = 9'954, Model-3 is p = 0'073 and Model-4 is

p = 0.066 Therefore, based on the residual plots and statistical tests it can be said that the

residuals from the model fits are an iid sequence with white noise distribution.

L.7 Model Selection:

Based on the aforementioned discussion with reference to fitted models and residual analysis, allthe models are compared with each other for final model selection on the basis of goodness of fitmeasures which are described as follows:

AICC value: AICC value for each model fit is calculated based on the original data. The

parameters that determine the AICC value are: order of the ARMA(p, q) model,length ofthe time series, and the loglikelihood function as obtained from the model output. The

criteria, is the model with lowest AICC value is preferred over the other, which indicates

a parsimonious model. Thus, the calculated AICC values are, Model-l is -273.38, Model-2 is -274.33, Model-3 is -271.85 and Model- is -272.49

Model AIC value: Model AIC value is obtained from the model output, and similarly, the

model with least AIC value is preferred over the others. The model AIC values are,

Model-1 is -271.51, Model-2 is -272.54, Model-3 is -270.06 and Model-4 is -270.8

LogJikelihood value: Model log-likelihood function as obtained from the model output is

also used for the model selection. The model with a high logJikelihood value is selected

over the other models. Thus, the log-likelihood values are, Model-l is 139.76, Model-2 isI41.27, Model-3 is 140.03 and Model-4 ís 14I.4

Estimated rnodel variance: The estimated model variance as obtained from the fittedmodels, the one with the lowest is preferred over the other models. The estimated modelva¡iances are, Model-1 is 0.01699, Model-2 is 0.01675, Model-3 is 0.01695 and Model-4is 0.01672

Therefore, based on these above model selection criterions, the model that best describes the

VMT time series dataset is Model-2 which is of the form: SARIMA (2, I,0) x (2,1, 0) (12) . krgeneral the SARIMA models are given in the following form with a non-seasonal and seasonal

component explaining the time series process.

The confidence intervals for Model-2 coefficients g and (Þ as shown in Appendix-A is calculated

as g+1.96*SE and (Þ+1.96SE, where SE is the model standard error. These confidence intervals

are given by upper boind and lower bound as shown in Table 1.

Table 1 Conlidence Intervals for the SARIMA model coefficients

Coefficients(<p, o)

Upper bound(<o+1.96*SE. O+ 1.96SE)

Lower bound(<p-1.96*SE, O-1.9658)

<o r = -0.581 -0.454 -0.707

o r = -0.309 -0.184 -0.434Qt = -0.278 -0.t43 -0.4t4(Þr = -0.135 0.016 -0.288

1,.8 Model Forecasting:

The VMT time series data is used in forecasting into the future with the fitted model. The data is

forecasted for the îext12 intervals, which indicates the next 12 months of the time series data.

Figure 11 illustrates the forecasting indicated by red line, and bounded by 95Vo prediction

intervals indicated in blue dotted lines. Based on the forecasts, it can be said that the predictions

are within the confidence intervals, indicating that Model-2 is a good model fit better explaining

the VMT time series phenomenon. The forecasted values for the next 12 months are provided in

Appendix-A along with the standard effors.

Spectral Analysis2.1 Introduction:

,In spectral analysis, the approach is based on the assumption that the time series can be

represented as a linear combination of uncorrelated noise series plus the deterministic trend

component. The deterministic component in spectral analysis, assumes that the time series is best

regarded as a sum of periodic sine and cosine waves of different frequencies or periods. The

general linear combination form can be represented as in equation [4], for k = n/2, and f¡, = An,

for fr = l, 2,...,nn where n is length of the time series.

Xt= a.o+\i!2t@¡rcos2ttf¡rt *bvsínLrf¡rt) + 4 t4l

2.2DataAnalysis:

VMT time series data plot as observed from Figure 1, a corresponding spectral analysis can be

performed based on spectrum of the data. A cycle is defined a sine or cosine wave over a defined

interval l0,2nl; for example xt = sin(2nl't) for frequency / over time I The function of the

formf -1, is called period, which is defined as the length of time required for one full cycle. This

frequency can be identified as from the periodo grarn Py(f¡,) given by equation [5] which can be

generated for a given time series process Xr. The periodogram for the YMT time series is shown

as plotted in Figure 12, this periodogtam is further smoothened to better represent the

frequencies observed in the data as observed from Figure 13.

Px(fù =|@ln+bll tsl

where, ãu = |nül'=r. X ¡c o sLn f¡rt and ß y = |LT=, x rs ínLn f¡rt

The height of the periodogram shows the relative strength cosine-sine pairs at various

frequencies in the overall behavior ofthe series. As observed from Figure 13, it can be said that

there exists strong peaks at frequencies Il!2,2112,,.,6112, with dominant peaks at 1'll2 and 3ll2

contributing significantly to the periodogram. Thus, from this it can be said that the period of this

time series is 12, which means, that it takes 12 months to complete one cycle. Furthermore, the

cumulative periodogram is also plotted in Figure 14 to examine if the data is white noise. Based

on Figure 14, we reject the hypothesis, that the observed data is not white noise as the

cumulative periodogram falls outside the Kolmogorov-Smirnov confidence intervals.

2.3 Model Estimation for trend in data:

A linear model is fit to the VMT time series data to eliminate the linear trend and account for the

periodic effects as observed from the data, a linear model of the following form as represented inequation [6] is fitted to the data.

Xt: &o* at* þt'+yf + arcosLnflt*b6in2rf1t* ø2cosLnf2t+brsinLtfrt+Y, [6]

In equation 16l, Y, are the residuals of the model fit, and the coefficients estimated are significant

as obtained from model output. The model ouþut is provided as in Appendix-A This linear

model eliminates the trend as observed to the original VMT data, with an R-square of 0.974.

2.4 Model fit to the Residuals:

Residual analysis on Y, suggests that they follow SARIMA (p, d, q) x (P, D, Q) þeasonality)process, with a seasonal component of 72. This can be observed as from Figure 15 which plots

the residuals, along with ACF and PACF plotted in Figure 16 and Figure 17 respectively.

Furthermore, the cumulative periodogram of the residuals suggests that they are not white noise,

which needs to be modeled.

Thus, based on the ACF and PACF plots of the residuals (I) from the linear model as

represented in equation [6], it can be said that ACF decays for every l2'h lag and a peak at the

l2th lagfor PACF, suggests both AR and MA component with strong seasonality of 12. Potential

models where tested based on these assumptions against various model comparison statistics as

discussed in the previous section. Therefore, a SARMA (3, 0, 0 x (2,0, l) (12) was fit to the

residuals (f). The goodness of fit statistics for the fïtted model is: log-likelihood of 133.11, withan AICC of -253.81, model AIC of -250.23 and model variance is 0.01575, along with parameter

estimates having low standard errors. The model output for the fitted model is provided as inAppendix-A

2.5 Residual Analysis from SARIMA mode fit:

Analysis of residuals is conducted as obtained from the SARIMA model fit. Figure 18 plots the

residuals of the model fit, with Figure 20 showing the ACF along with the standard residuals

from the model. As seen from Figure 20, Ljung-Box statistic probabilities suggest that the

residuals follow a white noise process; this fact is further strengthened from Portmanteau test,

which accepts the hypothesis that the residuals follow an iid white noise sequence as, Qois 20.60

at probability 0.\49, which is less than f at s=0.05; furthermore, the Ljung-Box statistic with

Qø = 28.102 at probability 0.107, which is less than f at a=0.05, also suggests that the residuals

follow an iid white noise sequence. From Figure 19 which illustrates the cumulative periodogram

of the model fit residuals, it can be concluded that they follow a white noise process, as they lie

within the Kolmogorov-Smirnov confidence intervals.

References:

1. Brockwell.P., Davis.R., (2002) Introd.uction to Time Series Fareeasting. Springer, New

York.2. Califomia Department of Transportation, Traffi.c Data Branch, httçllir¿ffrc-

counts.dot.câ.govl

3. Cowpertwait. P,, Metcalfe. 4., (2009). Intoductory Time Series wíth R. Springer' New

Yorlc4. Cryer. J., Chan. K., (2008) Time Series Anølysis with Applications in R. Springer, New

York.5. 'Walter.Z., Nenadic.O ., Time Series AnøIytis with R - Pørt I.

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