EMBA Research Presentation

8/9/2019 EMBA Research Presentation

1/27

01/22/15

JANUARY 2015

FORECASTING BANGLADESHS INFLATIONUSING THE BOX-JENKINS (ARIMA)

METHODOLOGY

PRESENTED BY

JACKSON SHAUMEN BISWAS

ID 20031

DEPARTMENT OF FINANCE

FACULTY OF BUSINESS STUDIES

UNIVERSITY OF DHAKA


2/27

01/22/15

2

INTRODUCTION


3/27

INTRODUCTION

01/22/15

3

Con!o" o#$! %n&"'%on %( )$ *!%+$ o,-$.%#$ o& !$/"'o!( '( %n&"'%on %n.!$'($(

n.$!'%n ,o) %n Con(+$!( 'n P!o.$!( +%n C!!$n" )$ &%n'n.%'" !$/"'o! ')o!%%$( %n B'n/"'$() '!$ &'.%n/ )$ 4%n

.)'""$n/$ o& +'%n'%n%n/ *!%.$ (',%"% 4)%"$ '..o++o'%n/ )%/)$! /!o4) %n

)$ $.ono+

D!%n/ )$ *'( )!$$ $.'$(6 !'+'%. .)'n/$( %n )$ %n&"'%on'!

$n#%!on+$n )'#$ (%+"'$ ' 4$'") o& (%$( on $7'+%n%n/ 'n $#'"'%n/

%&&$!$n +$)oo"o/%$( %n &o!$.'(%n/ %n&"'%on On$ o& )$ ($#$!'" '**!o'.)$( o& %n&"'%on &o!$.'(%n/ %( (%n/ n%#'!%'$ %+$

($!%$( 'o !$/!$((%#$ %n$/!'$ +o#%n/ '#$!'/$ 8ARIMA9 +o$"(

T)%( 'n'"(%( '((%(( %n &o!$.'(%n/ &!$ #'"$( o& %n&"'%on 'n o $(%+'$

)$ %+*'. o& $#$n( o! *o"%. .)'n/$( R$("( &!o+ 'n'"(%( .'n /%#$

#'"',"$ %n&o!+'%on 4)$n &o!+"'%n/ &!$ *o"%.%$(


4/27

01/22/15

4

OBJECTIVE OF THE STUDY


5/27


6/27

01/22/15

6

DATA AND RESEARCH METHODOLO


7/27

DATA AND RESEARCH METHODOLO


8/27

01/22/15

8

E=AMINATION OF THE DATA SERIES


9/27

TIME SERIES PLOTTIN< AND TREND ANALYSIS

01/22/15

9

1126112988470564228141

300

250

200

150

CPI

Consumer Price Index

140126112988470564228141

300

250

200

150

100

MAPE

MAD

Accurc!

CPI

A

%

'rend An#!sis P#o" (or CPI)ro*"+ Cur,e Mode#

-" 117.425 / 1.00597"

> Time Series Plot and Trend Analysis Plot o!

Monthly "onsumer Price nde' Data o!

Bangladesh !rom anuary **+ Decem%er

*+ sho-s trend like %eha$ior

> #isual de.iction o! Time series .lot o! !irst

order di!!erence o! Monthly "onsumer Price

nde' Data sho-s a non trend data set1126112988470564228141

8

6

4

2

0

2

D4C

PI

$irs" Di((erence Consumer Price Index


10/27

AUTOCORRELATION AND PARTIAL AUTOCORRELATION ANALYSIS

01/22/15

10

> ! time series is stationary then its autocorrelation gra.h decays /uite ra.idly !rom its initial

$alue o! unity at 0ero lag1 s case o! no stationary data set autocorrelation dies out gradually

o$er time1

>Autocorrelation o! First order di!!erence data set to "onsumer Price nde' dro.s /uickly to 0ero

%ut has signi!icant seasonal .attern

302520151051

1.0

0.8

0.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

Au"ocorre#"ion

Au"ocorre#"ion $unc"ion (or CPI*i"+ 5 sini(icnce #imi"s (or "+e u"ocorre#"ions

302520151051

1.0

0.8

0.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

Pr"i#Au"ocorre#"ion

Pr"i# Au"ocorre#"ion $unc"ion (or CPI*i"+ 5 sini(icnce #imi"s (or "+e r"i# u"ocorre#"ions

302520151051

1.0

0.8

0.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

Au"ocorre#"ion

Au"ocorre#"ion $unc"ion (or DCPI

*i"+ 5 sini(icnce #imi"s (or "+e u"ocorre#"ions

302520151051

1.0

0.8

0.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

Pr"i#Au"ocorre#"ion

Pr"i# Au"ocorre#"ion $unc"ion (or DCPI

*i"+ 5 sini(icnce #imi"s (or "+e r"i# u"ocorre#"ions


11/27

SEASONAL ANALYSIS

01/22/15

11

> #isual de.iction o! the gra.hical re.resentation o! seasonal analysis sho-s Strong Seasonality

in monthly data series o! "onsumer Price nde' o! Bangladesh

1.02

1.01

1.00

0.99

12

8

4

1.2

1.1

1.0

0.9

20

10

0

10

Seson# An#!sis (or CPIMu#"i#ic"i,e Mode#

Seson# Indices

Percen" %ri"ion &! Seson

De"rended D" &! Seson

esidu#s &! Seson


12/27

01/22/15

12

UNIT ROOT TEST 8AU


13/27

UNIT ROOT TEST

01/22/15

13

> 2ere 3ull 2y.othesis 2* 4 Data set has a unit root and Alternati$e 2y.othesis 2+ 4

Data set does not !ollo- unit root1 ! P#alue !rom ADF5*1*6 then 2* acce.ted or 2*

Re7ected1

> 8riginal "P data series has a unit root (P#alue o! ADF -hich is *19999 5 *1*6) %ut the

Data set o! First 8rder Di!!erence o! "P does not !ollo- unit root (P#alue o! ADF -hich

is *1*****1*6)

> "P data o! Bangladesh has integrated at di!!erentiation order +1

ADF Te%t o, O'3"+l D+t+ Set o, CIE7o/$no(? Con('n

L'/ L$n/)? 2 8Ao+'%. @ ,'($ on SIC6 +'7"'/9

@S'%(%. P!o,

A/+$n$ D%.;$@F""$! $( ('%(%. 215312 0

T$( .!%%.'" #'"$(? 1 "$#$" @3GG1

5 "$#$" @21G

10 "$#$" @25GGGG

ADF Te%t o, F'%t D,,e'e"ce D+t+ Set o, CIE7o/$no(? Con('n

L'/ L$n/)? 0 8Ao+'%. @ ,'($ on SIC6 +'7"'/9

@S'%(%. P!o,

A/+$n$ D%.;$@F""$! $( ('%(%. @G200 00000

T$( .!%%.'" #'"$(? 1 "$#$" @3G05

5 "$#$" @2130

10 "$#$" @25GG


14/27

01/22/15

14

IDENTIFICATION OF ARIMA MODEL


15/27

IDENTIFICATION OF ORDER OF DIFFERENTIATION IN ARIMA

01/22/15

15

R&le o, T#&!0

R&le /4 I& )$ ($!%$( )'( *o(%%#$ 'o.o!!$"'%on( o o ' )%/) n+,$! o&"'/(6 )$n % *!o,'," n$$( ' )%/)$! o!$! o& %&&$!$n.%n/

R&le 4 I& )$ "'/@1 'o.o!!$"'%on %( $!o o! n$/'%#$6 o! )$ 'o.o!!$"'%on(

'!$ '"" (+'"" 'n *'$!n "$((6 )$n )$ ($!%$( o$( no n$$ ' )%/)$! o!$!

o& %&&$!$n.%n/ I& )$ "'/@1 'o.o!!$"'%on %( @05 o! +o!$ n$/'%#$6 )$ ($!%$(

+' ,$ o#$! %&&$!$n.$

R&le 54I& )$ ($!%$( )'( ' (!on/ 'n .on(%($n ($'(on'" *'$!n6 )$n o()o" ($ 'n o!$! o& ($'(on'" %&&$!$n.%n/@@, n$#$! ($ +o!$ )'n on$

o!$! o& ($'(on'" %&&$!$n.%n/ o! +o!$ )'n 2 o!$!( o& o'" %&&$!$n.%n/

8($'(on'" 'n non ($'(on'"9

R&le 64T)$ o*%+'" o!$! o& %&&$!$n.%n/ %( o&$n )$ o!$! o& %&&$!$n.%n/ '

4)%.) ('n'! $#%'%on %( "o4$(


16/27

IDENTIFICATION OF ORDER OF DIFFERENTIATION IN ARIMA

01/22/15

16

A&toco''el+to" o, Re%&+l% o, + "o" %e+%o"+l ARIMA (.7/7.) Moel

A&toco''el+to" o, Re%&+l% o, + %e+%o"+l ARIMA (.7/7.) (.7/7.)/ Moel

>Autocorrelation o! Residuals o! ARMA (*,+,*) sho-s strong seasonal .attern1

> ;ag + Autocorrelation o! Residuals in ARMA (*,+,*) model is $ery high1 So a !irst order seasonal

di!!erentiation should %e introduced1

> ;ag + Autocorrelation o! Residuals in ARMA (*,+,*) (*,+,*)+ model is *1*9 (;o-est)

Autocorrelation0.4593

Strong SeasonalPattern

Autocorrelation0.0935

"se a #on Seasonal $irst %rder and a Seasonal $irst %rderDifferentiation


17/27

IDENTIFICATION OF ORDER OF AR AND MA

01/22/15

17

R&le o, T#&!0

R&le 84 I& )$ PACF o& )$ %&&$!$n.$ ($!%$( %(*"'( ' ()'!* .o&& 'no! )$"'/@1'o.o!!$"'%on %( *o(%%#$@@%$6 %& )$ ($!%$( '**$'!( ("%/)" n$!

%&&$!$n.$@@)$n .on(%$! '%n/ 'n AR $!+ o )$ +o$" T)$ "'/ ' 4)%.)

)$ PACF .( o&& %( )$ %n%.'$ n+,$! o& AR $!+(

R&le 94 I& )$ ACF o& )$ %&&$!$n.$ ($!%$( %(*"'( ' ()'!* .o&& 'no! )$

"'/@1 'o.o!!$"'%on %( n$/'%#$@@%$6 %& )$ ($!%$( '**$'!( ("%/)" o#$!

%&&$!$n.$@@)$n .on(%$! '%n/ 'n MA $!+ o )$ +o$" T)$ "'/ ' 4)%.))$ ACF .( o&& %( )$ %n%.'$ n+,$! o& MA $!+(

R&le :4 I& )$ 'o.o!!$"'%on ' )$ ($'(on'" *$!%o %( *o(%%#$6 .on(%$!

'%n/ 'n SAR $!+ o )$ +o$" I& )$ *'!%'" 'o.o!!$"'%on ' )$ ($'(on'"

*$!%o %( n$/'%#$6 .on(%$! '%n/ 'n SMA $!+ o )$ +o$" T! o '#o%

+%7%n/ SAR 'n SMA $!+( %n )$ ('+$ +o$"6 'n '#o% (%n/ +o!$ )'n

on$ o& $%)$! ;%n


18/27


01/22/15

18

A&toco''el+to" o, Re%&+l% o, + %e+%o"+l ARIMA (.7/7.) (.7/7.)/ Moel

> 3on Seasonal AR Term and MA Term should %e incor.orated in the model as ;ag + PA"F is

.ositi$e and A"F sho-s shar. cuto!!1

> Seasonal MA Term should %e incor.orated in the model as Seasonal ;ag o! PA"F is negati$e1

Partial Autocorrelation isPositive

"se #on Seasonal AR& MR termand Seasonal MR term in the model

+'t+l A&toco''el+to" o, Re%&+l% o, + %e+%o"+l ARIMA (.7/7.) (.7/7.)/ Moel

Sharp CutofNegative Autocorrelation in

Seasonal ag

Negative Partial Autocorrelation inSeasonal ag


19/27


01/22/15

19

A&toco''el+to" o, Re%&+l% o, + %e+%o"+l ARIMA (7/7/) (.7/7/)/ Moel

>Akaike n!ormation "riterion is lo-est (=61=), estimated -hite noise (Standard De$iation) is +1


20/27

01/22/15

20

COMPARISON OF MODELS


21/27

MODEL COMPARISON

01/22/15

21

ARIMA Moel AIC SBC SSE ;+'+"ce S


22/27

01/22/15

22

BEST FITTED MODEL


23/27

BEST FITTED MODEL

01/22/15

23

ARIMA '2&1&1( ')&1&1(12 model has high !redicti-e !oer that means act+al -al+es

and !redicted -ales has high le-el of close match

T$1e Coe, t R+to 'o0 > ?t@

AR 16 1 1013 1255 001

AR 162 @0223GG @252 131

MA 161 100 133 001

MA 26 12 0201 001

In$!.$* 0130 1002 001


24/27

01/22/15

24

FINDIN


25/27

FINDIN


26/27

01/22/15

26

UESTION AND ANSWER SESSION


27/27

01/22/15

27

THANKS YOU ALL

EMBA Research Presentation

Documents

Transcript of EMBA Research Presentation