termpaper in multivariate statistics


    Click here to get an A+ paper at a Discount

    Project description
    I only want assignment 3 to be done.
    Unfortunately, there is a misprint in 3a: In the final line of this assignment, the formula that you are to conclude with should not have an x but a y in it. That is, it should be (y-mu)^2 and not (x-mu)^2 in the exponent
    1
    Term paper
    :
    GRA 60
    393
    Multivariate Statistics with Econometrics
    Examination start date:
    1
    4
    Nov
    ,
    201
    3
    09
    :
    00
    Total no. of pages:
    12
    excl
    . a
    ttachments
    Examination end date:
    0
    2
    Dec
    ,
    201
    3
    12
    :
    00
    No. of a
    ttachments:
    4
    , with file names
    specified on the
    next
    page
    Counts
    4
    0 % of GRA 60
    3
    9
    The weighting
    of the
    exam
    problems
    is
    specified on the next page.
    Responsible department:
    Economics
    F
    ORMAL REQUIREMENTS

    READ THIS CAREFULLY
    The examination
    must
    be solved
    individually or in groups of up to three
    (3)
    students. Collaboration between
    groups
    (
    on the preparation of the
    exam paper)
    is regarded as cheating or attempting to cheat and is covered under
    “Regulations relating to Admissions, Studies and Examinations”. All students
    are responsible
    to
    familiari
    se
    themselves with these rules and regulations.
    Group submission requires exam registration in identical exam code
    and at the same exam location.
    This
    means that students taking this exam for the first time
    cannot
    be on a group together with the students taking the
    exam as a re

    take
    (as they are taking
    the exam with exam code GRA6039
    1
    )
    The exam paper
    has a page

    limitation that is described on the next page, and
    must be adequately stapled, or
    bound, and submitted in
    three (3)
    copies. Please
    refrain from using plastic covers, or similar binders.
    The front page must contain the following information:

    Student ID number
    (7 digits
    placed in the
    top right corner
    . The students’ names
    must not
    be written on
    the front page.)

    Examination code, course
    name and subject title

    Date of submission and deadline

    Examination location

    Marked “Confidential”, if applicable
    G
    uidelines for layout:

    Type

    written on A4 size paper with 5 cm. left margin, 2 cm right margin, 2 cm. at the top and bottom
    of
    the page

    Font
    Times New Roman
    in size 12, and line spacing of 1½. (Approx
    .
    300

    350 words per page)
    .
    All
    pages must be numbered
    .
    Submission:
    The
    exam
    paper must be
    submitted
    within the deadline at the candidate’s examination location.
    O
    nly students at BI Nettstudier and
    BI Bank og
    Forsikring
    may submit their papers
    by postal mail
    to their
    examination location. This also applies for candidates from our Bachelor of Management programmes, Master of
    Management programmes and customized progr
    ammes.
    Y
    our exam
    paper must be sent as “Express

    Over night cash”.
    Minimum dimension
    required
    : 23x13x1 cm.
    From abroad DHL, TNT etc must be used. The shipment must be registered at the distributor within the deadline
    of handing in the paper.
    For exact postal address to your examination location, see
    www.bi.edu
    .
    Postal ad
    d
    ress for examination location
    s
    BI Oslo, BI Nettstudier
    and
    BI
    Bank og Forsikring is:
    Handelshøyskolen BI
    i
    Oslo, Eksamenskontoret, 0442 OSLO
    ,
    Norway.
    N
    B!
    The deadline is absolute. Late
    exam
    papers will not be graded
    .
    Please remember to fill
    in
    the Student Declaration.
    Good luck!
    HOME EXAM IN GRA6039
    MULTIVARIATE STATISTICS WITH ECONOMETRICS
    FALL 2013
    STEFFEN GR�NNEBERG
    The exam is divided into two parts, and consists of in all four problems. The �rst
    part, comprising two problems, is entirely practical and concerns applied statistics.
    The second part, also comprising two problems, is entirely theoretical.
    Part I of the exam contains 85 % of the total points on the exam, and part II
    therefore contains the remaining 15 %. In each problem, each sub-problem carry
    equal marks.
    The page limit for the
    rst and second
    problem is
    6 type-written pages
    . You
    must solve these problems using Stata, and you must include the source code for
    your complete analysis. The Stata-code is to be included in an appendix which does
    not have a page limit.
    This appendix must not include anything other than
    the Stata source code.
    The exam has four attachments relating to the data that is to be analyzed in the
    rst part of the exam, with �le names as follows.
    US
    macro
    data.dta”
    Assignment1
    data
    source
    links.pdf”
    All
    data
    generation
    steps.zip”
    Lothian
    Taylor
    96.dta”
    Detailed descriptions of these �les are given in the exam text.
    There is no page limit for
    the second part of the exam
    (i.e. the third and fourth
    problem), which concerns theory. For part II of the exam, you may choose freely
    whether you write your solution in a word processor or by hand. If you write the
    solution by hand, do be careful to write as clearly as possible. Obscure passages
    will simply be ignored.
    You will be severely penalized for breaking these rules.
    While the home exam is a group project, it is strictly forbidden to collaborate
    between groups. Groups that collaborate with other groups not only face the dire
    consequences of being caught as a cheater, they are watering out their own grade:
    The grade limits depend in part on the overall performance of all the groups, so
    sharing your hard earned answers decreases the likelihood of getting the best grade
    that you can.
    I hope that while working through these problems, you will �nd them interesting,
    and end up learning much from them. Good luck on the exam!
    PART I: Applied statistics
    (2 assignments, counting 85 % in total)
    Assignment 1.
    (Counts 42.5 %)
    In Lecture 6, we followed Stock & Watson’s discussion in their Chapter 14 of Intro-
    duction to Econometrics” through modeling the in ation rate using an ADL-model
    using lagged values of the in ation rate and the unemployment rate. The motivation
    for including the unemployment rate was the Phillips curve. However, much more
    2




    HOME EXAM { GRA6039, FALL 2013 3
    data { which may be highly relevant for forecasting in ation { is available in pro-
    prietary and even open databases online. Can we improve our forecast capabilities
    through including many more covariates?
    The research paper Di�usion indexes” by Stock & Watson (1998) suggests a
    methodology for incorporating many, many covariates in an ADL-model by using
    some of the principal components of a large set of potentially relevant covariates.
    They provide a mathematical framework that justi�es this use under fairly general
    conditions, even quite far away from the IID setting we worked with when we
    studied PCA during the fourth part of our course. The basic PCA idea is very
    general: identify rotations of a data-matrix so that their columns have zero empirical
    covariance and sort the rotated data columns according to their empirical variance.
    While we followed Johnson & Wichern in interpreting this statistical tool when the
    data-generating mechanism has no time-dependence, it is also often valid when the
    data-generating process is allowed to have time-dependence.
    The paper can be read at
    http://www.nber.org/papers/w6702.pdf
    . This is an
    important paper, and the technical version of the paper together with the actual
    published paper has a massive 2 000 citations according to Google Scholar. Note
    that you need not read the (quite advanced) technical details of this paper in order
    to answer this exam.
    We will in this assignment study a small-scale replica of a part of their paper’s
    empirical example by assessing if using principal components to forecast in ation
    yields improvements compared to the forecast capabilities of an AR-model and a
    na
    
    �ve ADL-model.
    Note that the ideas contained in Stock & Watson’s paper are part of a much larger
    framework in modern econometrics, which includes so-called dynamic factor models,
    which are based on the factor models we studied in our treatment of Exploratory
    Factor Analysis. However, our perspective will here be based exclusively on the
    PCA idea.
    The exam’s appendix describes the data-set which we will use as the basis for
    our experiment. Note that you are not asked to test the structural stability or test
    for unit roots in this assignment.
    (A) Run a PCA analysis on all variables, except for the in ation variable (and,
    of course, the time-variable).
    Stata hint:
    Because there are so many variables, it may be easier to
    read the PCA output after requesting that only loadings whose absolute
    values exceed a pre-speci�ed number are printed. For example,
    pca d*,
    blanks(0.25)
    will only print loadings with an absolute value exceeding
    (the arbitrarily chosen) 0
    :
    25, and where
    d*
    is a short-hand for all variables
    with names starting with d”.
    (B) We will here compare the performance of the following three types of models.
    I) An AR-model for the in ation measure.
    II) An ADL-model using autoregressive terms of the in ation measure
    and lags of principal components as covariates.
    III) An ADL-model where autoregressive terms of the in ation measure
    and lags of all other variables (excluding the time-variable) are covari-
    ates. All covariates, except lags of the in ation measure, are to be
    included with the same number of lags.
    For all three models, you must choose the appropriate number of lags of
    the in ation measure to include.
    For model II you must choose the number of principal components to
    include and the number of lags to include for the selected principal compo-
    nents. You may assume that the AIC/BIC methodology is valid as a model
    selection tool also in model II (even though, as explained in the paper,

    Click here to get an A+ paper at a Discount


    Order This Paper Now

                                                                                                                                      Order Now