econometric Topic

7/24/2019 econometric Topic

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ECONOMETRIC ANALYSIS

ASSIGNMENT

CIA

Submitted To:

Mr. Anand S

(Econometric Analysis)

Submitted By:

Sayon Das

1421328MBA-F2


2/20

Q1. We lea!ed Odi!ay Lea"t S#uae" o OLS i! t$e %la"". W$at ae t$e ot$e

e"timatio! te%$!i#ue" a&ailable' (o) ae t$ey "imila o di**ee!t *om OLS' W$e!

ae t$e"e e"timato" u"ed'

Ans). Te ordinary least s!"are metod is a statistical metod #ic is "tili$ed %or estimatin&

te 'ario"s "nno#n arameters in a linear re&ression model. Tis tecni!"e is alied to &et

te *est %it in a re&ression line and "sed to identi%y te oints #ic a'e te least s!"ared

distance %rom te re&ression line. +n ,S te c"r'e tat elains te relationsi *et#een

eected and o*ser'ed data set *y minimi$in& s"m o% s!"ares o% de'iation *et#een o*ser'ed

and eected 'al"es. Te oter estimation tecni!"es/-

1. 0ei&ted least s!"ares- A secial case o% least s!"ares metod

2. enerali$ed east S!"are3. Best linear "n*iased estimator (BE)4. Best linear "n*iased rediction (B). Minim"m Mean s!"are error (MMSE)5. 6oot mean s!"ares (6MS)

Wei+$ted lea"t "#uae":

A secial case o% least s!"ares #en te all te 'al"es ecet te dia&onal are n"ll. Te

#ei&ted ,S taes te ass"mtion tat #ei&t is "nno#n and cannot andle

a"tocorrelation.

Ge!eali,ed Lea"t "#uae:Tis metod can a'e 7eteroscedasticity #it a"tocorrelation

*"t te samle roerties are not no#n.

Be"t Li!ea -!bia"ed E"timato BL-E/:

+t in'ol'es alication o% "n*iased and e%%icient linear estimation #ic is el%"l in 'ario"s

statistical in%erences a*o"t arameters *ased on samle statistics estimators. al"e e!"al to

tr"e 'al"e o% o"lation arameters are ro'ide *y BE.

B is "sed #en random data is needed %rom te o"lation set

Mi!imum Mea! "#uae eo MMSE/: +tis an estimation metod #ic minimi$es te

mean s!"are error(MSE) o% te %itted 'al"es o% a deendent 'aria*le9#ic is a common

meas"re o% estimator !"ality.

Root Mea! S#uae"RMS/: +t is a statistical meas"re #ic can *e de%ined as te s!"are

root o% te mean o% s!"are o% a samle.
https://en.wikipedia.org/wiki/Mean_square_errorhttps://en.wikipedia.org/wiki/Dependent_variablehttps://en.wikipedia.org/wiki/Dependent_variablehttps://en.wikipedia.org/wiki/Dependent_variablehttps://en.wikipedia.org/wiki/Mean_square_error


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0e can "se tese estimators in order to identi%y te data set s"c tat roer 'aria*les are

"sed to reresent o"lation and identi%y te data sets #ic reresents in te re&ression line.

Q0./ I. W$at i" $eteo"%eda"ti%ity'

II. W$at oblem" )ould you *a%e i! you data a!aly"i" i* you $a&e

$eteo"%eda"ti%ity'

III. (o) do you dete%t it'

I2. W$at ae t$e emedie" to it'

Ans).

I/ Te eteroscedasticity is re%erred to sit"ation in #ic te 'aria*ility o% a %actor is

"ne!"al across te ran&e o% 'al"es o% a second 'aria*le #ic redicts it and resid"als

do not a'e a constant 'ariance.

A scatter lot o% te 'aria*les maes a cone str"ct"re or 'aria*ility o% deendent

'aria*le #idens or narro#s as 'al"e o% te indeendent 'aria*le increases.

Co!ditio!al (eteo"%eda"ti%ityidenti%ies 'aria*le 'olatility #ic cannot *e

identi%ies %or %"t"re eriods and te 'olatility cannot *e redicted s"c as stoc rices9*onds etc.

-!%o!ditio!al (eteo"%eda"ti%itycan identi%y te 'olatility %or %"t"re eriods. E&.

Seasonal 'aria*ility s"c as sale o% #oolen clots and s#eaters.

E3amle: 1. +ncome 's eendit"re on meals is a clear eamle o% eteroscedasticity. +% te

income increases 'aria*ility o% %ood cons"mtion #ill increase and oor erson #ill mae a

constant eense "rcasin& ineensi'e %ood. eole #it i&er incomes dislay &reater

'aria*ility o% %ood cons"mtion.

+n linear re&ression model #e tae te ass"mtion tat error term in normal distri*"tion #it

mean : and 'ariance ;29 i.e. ar("i) < ;2 is called omoscedasticity. #en te error term

does not a'e constant 'ariance9 i.e. ar("i) < ;2 i #e call it eteroscedasticity.

7eteroscedasticity 'aria*les lotted in &ra aear as tey %all into normal distri*"tion


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#ereas in eteroscedacity te scatter as i& 'aria*ility and does not %all into normal

distri*"tion c"r'e.

II/.Ass"mtions o% linear re&ression model are correct9 ,S &i'e "n*iased estimates9

7eteroscedasticity occ"rs #en 'ariance o% errors 'aries in o*ser'ations and i% errors are

7eteroscedasticity ,S estimator remains "n*iased #ere standard errors are inconsistent.

Te ro*lems %aced *y te data analysis o% 7eteroscedasticity are

1. = estimator is no lon&er BE (Best inear n*iased Estimators) #ic means tat

it as a i&er samlin& 'ariance.2. +t constantly o'erestimates te standard error.

III/. 4ete%tio! o* (eteo"%eda"ti%ity

a. Ga$i%al Met$od: lottin& resid"als in > ais and deendent 'aria*le ? ais te

attern o% 7eteroscedasticity can *e detected.

b. 5omal Met$od

W$ite Te"t"/ Te #ite test is a statistical test tat esta*lises resid"al 'ariance o% %actor

in a re&ression model in constant and is estimator %or eteroscedasticity consistent

standard errors. 6 s!"are


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+% te initial model is not selected 6 s!"are #ill *ecome si&ni%icant.

(6 : Model is omoscedastic(a : Model is eteroscedasticity

0en te -'al"e :.: 9

0e reect te 7: and accet 7a.

Gold*eld7Qua!dt Te"t

+n statistics te &old%ield !"andt test cecs te eteroscedasticity in re&ression analysis

*y di'idin& a dataset into t#o &ro"s called t#o &ro" test #ic o%%ers dia&nostic o%

eterosedastic errors in "ni'ariate or m"lti'ariate re&ression model.

6e!"ired test statistic T< C6SS2@(n-)@2 cG @ C6SS1@(n-)@2 cG

(6 : ;12 < ;22(a : ;12 H ;22

0en te -'al"e :.:9 #eIll reect 7: and accet 7a.

B8G Te"t:

Te Bre"s a&an Test is "sed to test te eterosedascity in linear re&ression model and

tests #eter te estimate 'ariance o% resid"als %rom a re&ression are deendent on

'al"es indeendent 'aria*les.

>


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d. Data Trans%ormation.

Q. Ta;e a!y data o* you %$oi%e )it$i! t$e built7i! R data"et. Illu"tate all t$at you

$a&e e3lai!ed i! #ue"tio! 0 )it$ t$i" data. E3lai! t$e R7e"ult" o* t$i" e3e%i"e.

Submit R7%ode" "%it alo!+ )it$ e"ult".

Ans:R-Script:p p library(lmtest)> bptest(p)

stdenti!ed "resc#-$agan test

data: p"$ = %&'*, d = , p-ale = .&.**

> plot(p)

/it to see ne0t plot:

1nterpretation: /2- 3#e 4ata #as #omoscedacity/5- 3#e data #as no #omoscedacity (#eteroscedacity e0ists)

Since p ale is greater t#an .&.% 6e re7ect nll #ypot#esis and accept alternate#ypot#esis i&e t#e data contains #eteroscedacity&


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Q4.Test weak-form eciency of the ecient markets hypothesis for anyIndian stock of your choice for the period 01-01-2014 to 30-10-2015usin! your know"ed!e of time series ana"ysis. #25 marks$5 %se the datainsurance.&"s attached with this mai" to 'ui"d a "inear re!ression mode"with the fo""owin! points in mind(

R7Code:

mydata - read.cs'(NL/@sers@a"ra'@Do#nloads@:::8O.cs'N)mydataPts-ts(mydataPLlose.rice9 %re!


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li*rary(!"antmod)&etSym*ols(NLila.SN9 src


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H &etSym*ols(NSE+N9 src


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Q5.%se the data insurance.&"s attached with this mai" to 'ui"d a "inearre!ression mode" with the fo""owin! points in mind(1. )ependent *aria'"e - +,har!es

2. ,reate the fo""owin! aria'"es( / se& 1 if ma"e and 0 if fema"e#fema"e as 'ase cate!ory$

/ ,onert re!ion to dummies with northeast as the 'ase cate!ory/ smoke1 if yes and 0 if no

/ ,reate a new aria'"e 'mi30 such that 'mi30 1 if 'mi 30 0otherwise

/ ,reate an interaction aria'"e / #'mi30 & smoke$/ ,reate a!e2a!e & a!e

3. Independent *aria'"es / a"" ori!ina" and user created aria'"es otherthan char!es4. &p"ain the 0 and 1 ino"ed in the -tests and t-tests and thecorrespondin! resu"ts #p-a"ues$5. 6onus points if you can 'ui"d some e&citin! !raphs and charts usin!any too" of your conenience. 6e sure to share the insi!hts from the

!raphs.

A!"./

data< read.cs'(NL/@sers@Sayon@Desto@crist@Lrist ttrimester@Econometrics@ins"rance.cs'N)H attac(data)HH se1


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n


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D% S"m S! Mean S! F 'al"e r(HF)n"ll 1 1.VeK11 1.VeK11 23V8.VV 2e-15 YYYcildren 1 2.VV:eK:5 2.VV:eK:5 :.351 :.481se1 1 3.35OeK:5 3.35OeK:5 :.4:5 :.23Vsmoer1 1 1.125eK:5 1.125eK:5 :.135 :.O124

*mi3: 1 2.8eK: 2.8eK: :.:31 :.85:re&ion1 3 1.V8OeK:O 5.522eK:5 :.OVV :.4V42

*mi3:.smoer1 1 1.11eK:O 1.11eK:O 1.345 :.2451a&e2 1 3.2:3eK:O 3.2:3eK:O 3.85O :.:4V Y6esid"als 132O 1.:VVeK1: 8.28eK:5---Si&ni%. codes/ : ZYYYI :.::1 ZYYI :.:1 ZYI :.: Z.I :.1 Z I 1

(yot$e"i" te"ti!+:1) 1.Te indeendent 'aria*le [n"ll\ as a si&ni%icant -'al"e #ic is less tan :.::1

i.e 2e-15 YYY. 7ence #eIll reect 7:and accet 7a. So9 [n"ll\ as si&ni%icant imacton te deendent 'aria*le [car&es\.

2) Te indeendent 'aria*le [cildren\ as an insi&ni%icant -'al"e o% &reater tan :.:

i.e.:.481 . 7ence #eIll accet 7: and reect 7a. So9 [cildren\ as no si&ni%icant

imact on te deendent 'aria*le [car&es\.

3) Te indeendent 'aria*le [se\ as an insi&ni%icant -'al"e o% &reater tan :.:. i.e.

:.23V 7ence #eIll accet 7: and reect 7a. So9 [se\ as no si&ni%icant imact on

te deendent 'aria*le [car&es\.

4) Te indeendent 'aria*le [smoer\ as an insi&ni%icant -'al"e o% &reater tan

:.:.i.e :.O124 7ence #eIll accet 7: and reect 7a. So9 [smoer\ as no si&ni%icant

imact on te deendent 'aria*le [car&es\.

) Te indeendent 'aria*le [*mi\ as an insi&ni%icant -'al"e o% &reater tan :.: i.e.

:.85: . 7ence #eIll accet 7: and reect 7a. So9 [*mi\ as no si&ni%icant imact

on te deendent 'aria*le [car&es\.

5) Te indeendent 'aria*le [re&ion\ as an insi&ni%icant -'al"e o% &reater tan

:.:.i.e. :.4V42 7ence #eIll accet 7: and reect 7a. So9 [re&ion\ as no

si&ni%icant imact on te deendent 'aria*le [car&es\.

O) Te +nteractin& 'aria*le *mi ? smoer as a si&ni%icant -'al"e o% &reater tan

:.:.i.e.:.2451 7ence #eIll accet 7: and reect 7a. So9 Te +nteractin& 'aria*le

*mi ? smoer as no si&ni%icant imact on te deendent 'aria*le [car&es\.

8) Te indeendent 'aria*le [a&e\ as an insi&ni%icant -'al"e o% &reater tan :.:.i.e

:.:4V Y 7ence #eIll reect 7: and accet 7a. So9 [a&e\ as si&ni%icant imact on

te deendent 'aria*le [car&es\.


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0it lot no.1 #e can in%er tat te n"ll and *mi are te indeendent 'aria*les #ilete car&es deendent 'aria*le co"ld *e redicted #it te el o% te n"ll. T"s #itte cart #e can say tat te tey *ot are correlated ositi'ely.0it lot no.2 #e can in%er tat tere is no correlation *et#een te car&es and te

*mi.

BIBLIOGRA8(Y

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http://www.statsmakemecry.com/smmctheblog/confusing-stats-terms-explained-heteroscedasticity-heteroske.htmlhttp://www.statsmakemecry.com/smmctheblog/confusing-stats-terms-explained-heteroscedasticity-heteroske.htmlhttp://www3.wabash.edu/econometrics/EconometricsBook/chap19.htmhttp://www.investopedia.com/terms/h/heteroskedasticity.asphttps://www.statisticssolutions.com/homoscedasticity/http://www.statsmakemecry.com/smmctheblog/confusing-stats-terms-explained-heteroscedasticity-heteroske.htmlhttp://www.statsmakemecry.com/smmctheblog/confusing-stats-terms-explained-heteroscedasticity-heteroske.htmlhttp://www3.wabash.edu/econometrics/EconometricsBook/chap19.htmhttp://www.investopedia.com/terms/h/heteroskedasticity.asphttps://www.statisticssolutions.com/homoscedasticity/

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