Exchange Rate Prediction Euro vs NOK from financial and commodity information
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Transcript of Exchange Rate Prediction Euro vs NOK from financial and commodity information
Evaluation of Models for predicting the average monthlyEuro versus Norwegian krone exchange rate from financial
and commodity information
Raju RImal
Norwegian University of Life Sciences(NMBU)
April 22, 2015
Raju RImal (NMBU) Masters Thesis April 22, 2015 1 / 23
Table of Contents
1 The BIG picture2 Part I
Exchange rate determinationFactors affecting exchange rateForeign currency and ExchangerateBalance of Payment AccountRelevant Variables
3 Part IIStatistical Models
Linear ModelsMulticollinearity ProblemPCR and PLS regression ModelRidge RegressionCross-validation and Prediction
4 Part IIIComparison of ModelsComments on ModelComparisonDiscussions and Conclusions
Raju RImal (NMBU) Masters Thesis April 22, 2015 2 / 23
The BIG picture
The BIG picture
1 Identify functional relationship of Exchange rate with financial andcommodity variables
2 Make prediction using different models
3 Compare the models
Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
The BIG picture
The BIG picture
1 Identify functional relationship of Exchange rate with financial andcommodity variables
2 Make prediction using different models
3 Compare the models
Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
The BIG picture
The BIG picture
1 Identify functional relationship of Exchange rate with financial andcommodity variables
2 Make prediction using different models
3 Compare the models
Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
Part I
Identify functional relationship of Exchange ratewith financial and commodity variables
Raju RImal (NMBU) Masters Thesis April 22, 2015 4 / 23
Part I Exchange rate determination
Exchange rate determination
Exchange Rate is a price of one currency in terms of another
Determined from the demand and supply of the currency in MoneyMarket (ForEx)
Raju RImal (NMBU) Masters Thesis April 22, 2015 5 / 23
Part I Exchange rate determination
Exchange rate determination
Exchange Rate is a price of one currency in terms of anotherDetermined from the demand and supply of the currency in MoneyMarket (ForEx)
−1. 1. 2. 3. 4. 5. 6. 7. 8.−1.
1.
2.
3.
4.
5.
6.
7.
0
Demand of Currency
Supply of Currency
Quantity
Exchange
Rate
Equilibrium Point
Raju RImal (NMBU) Masters Thesis April 22, 2015 5 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf,∆Int,∆Inc,∆Gc,∆Exp) (1)
∆Inf = Inflation differential betweentwo countries
∆Int = Interest Rate differential be-tween two countries
∆Inc = Income differential betweentwo countries
∆Gc = Government Control differen-tial between two countries
∆Exp = Expectation differential be-tween two countries
Consumer Price Index(CPI)Interest Rate (Norwayand Euro Zone)Loan Interest Rate
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf,∆Int,∆Inc,∆Gc,∆Exp) (1)
∆Inf = Inflation differential betweentwo countries
∆Int = Interest Rate differential be-tween two countries
∆Inc = Income differential betweentwo countries
∆Gc = Government Control differen-tial between two countries
∆Exp = Expectation differential be-tween two countries
S0
D0
Valueof
EURO
per
NOK
Quantity of EURO
9.10
9.97
S1
D1
QEuro
Upward shift in Demand
of Euro due to inflation in
Norway
Downward shift in supply
of Euro purchasing NOK
Consumer Price Index(CPI)Interest Rate (Norwayand Euro Zone)Loan Interest Rate
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf,∆Int,∆Inc,∆Gc,∆Exp) (1)
∆Inf = Inflation differential betweentwo countries
∆Int = Interest Rate differential be-tween two countries
∆Inc = Income differential betweentwo countries
∆Gc = Government Control differen-tial between two countries
∆Exp = Expectation differential be-tween two countries
Quantity of Euro(purchasing Norwegian Krone)
Price
ofEuro
(EUR/N
OK)
S0
S1
D0
D1
QEuro
NOK8.72
NOK9.10
Demand Shift
Supply Shift
Consumer Price Index(CPI)Interest Rate (Norwayand Euro Zone)Loan Interest Rate
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf,∆Int,∆Inc,∆Gc,∆Exp) (1)
∆Inf = Inflation differential betweentwo countries
∆Int = Interest Rate differential be-tween two countries
∆Inc = Income differential betweentwo countries
∆Gc = Government Control differen-tial between two countries
∆Exp = Expectation differential be-tween two countries
Quantity of Euro(purchasing Norwegian Krone)
Price
ofEuro
(EUR/N
OK)
S0
D0
D1
Q◦(Euro)
NOK8.72
NOK9.10
Increased demand of for-eign goods due to in-creased income levels
Consumer Price Index(CPI)Interest Rate (Norwayand Euro Zone)Loan Interest Rate
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf,∆Int,∆Inc,∆Gc,∆Exp) (1)
∆Inf = Inflation differential betweentwo countries
∆Int = Interest Rate differential be-tween two countries
∆Inc = Income differential betweentwo countries
∆Gc = Government Control differen-tial between two countries
∆Exp = Expectation differential be-tween two countries
Variable Selected:Consumer Price Index(CPI)Interest Rate (Norwayand Euro Zone)Loan Interest Rate
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf,∆Int,∆Inc,∆Gc,∆Exp) (1)
∆Inf = Inflation differential betweentwo countries
∆Int = Interest Rate differential be-tween two countries
∆Inc = Income differential betweentwo countries
∆Gc = Government Control differen-tial between two countries
∆Exp = Expectation differential be-tween two countries
Variable Selected:Consumer Price Index(CPI)Interest Rate (Norwayand Euro Zone)Loan Interest Rate
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
ExchangeRate Involve
during
Foreign InvestmentTrading of Goodsand Services
Travelling andmany otheractivities
Import Export
All these activities involve exchange of currency. These activities arerecorded as Balance of Payments account.
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
ExchangeRate Involve
during
Foreign InvestmentTrading of Goodsand Services
Travelling andmany otheractivities
Import Export
All these activities involve exchange of currency. These activities arerecorded as Balance of Payments account.
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
ExchangeRate Involve
during
Foreign InvestmentTrading of Goodsand Services
Travelling andmany otheractivities
Import Export
All these activities involve exchange of currency. These activities arerecorded as Balance of Payments account.
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
ExchangeRate Involve
during
Foreign InvestmentTrading of Goodsand Services
Travelling andmany otheractivities
Import Export
All these activities involve exchange of currency. These activities arerecorded as Balance of Payments account.
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
ExchangeRate Involve
during
Foreign InvestmentTrading of Goodsand Services
Travelling andmany otheractivities
Import Export
All these activities involve exchange of currency. These activities arerecorded as Balance of Payments account.
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
ExchangeRate Involve
during
Foreign InvestmentTrading of Goodsand Services
Travelling andmany otheractivities
Import Export
All these activities involve exchange of currency. These activities arerecorded as Balance of Payments account.
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
ExchangeRate Involve
during
Foreign InvestmentTrading of Goodsand Services
Travelling andmany otheractivities
Import Export
All these activities involve exchange of currency. These activities arerecorded as Balance of Payments account.
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Current AccountPayments for merchandise and servicesFactor Income paymentsTransfer payments
Capital and Financial AccountDirect foreign investmentPortfolio investmentOther Capital InvestmentErrors, Omissions and Reserves
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Current AccountPayments for merchandise and services
I Imports and Exports of Merchandise (tangibleproducts) and Services(tourism, consultingservice etc)
I The difference is referred as Balance of tradeI Import and Export of Good (Merchandise)
which are only availiable in Monthly formatare considered in this thesis
Factor Income paymentsTransfer payments
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Current AccountPayments for merchandise and servicesFactor Income paymentsIncome as Interest and Dividents
I received by domestic investors on foreigninvestments
I payed to foreign investors on domesticinvestments
Transfer payments
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Current AccountPayments for merchandise and servicesFactor Income paymentsTransfer paymentsRepresents aid, grands and gifts from one country toanother
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Capital and Financial AccountDirect foreign investment
I Includes investment in fixed assets in foreigncountries
Portfolio investmentOther Capital InvestmentErrors, Omissions and Reserves
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Capital and Financial AccountDirect foreign investmentPortfolio investment
I Includes long term transaction of long termfinancial assets such as bonds and stocks
Other Capital InvestmentErrors, Omissions and Reserves
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Capital and Financial AccountDirect foreign investmentPortfolio investmentOther Capital Investment
I Includes short term financial assets such asmoney market securities
Errors, Omissions and Reserves
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Capital and Financial AccountDirect foreign investmentPortfolio investmentOther Capital InvestmentErrors, Omissions and Reserves
I Includes adjustment for negative balance incurrent account
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and CapitalAccount;
Current AccountPayments for merchandise and servicesFactor Income paymentsTransfer payments
Capital and Financial AccountDirect foreign investmentPortfolio investmentOther Capital InvestmentErrors, Omissions and Reserves
Variable SelectedImportOil Platform, Old Ship,New Ship, Excluding Oiland Ship PlatformExportCondense Fuel, Crude oil,Natural gas, Oil platform,Old and new ships,Excluding Ships and oilplatform
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Relevant Variables
Some relevant variables selected for analysis
Financial VariablesKey Policy Rate of Norway (KeyIntRate)Overnight lending rate (LoanIntRate)Money market interest rates of Euro Area(EuroIntRate)Consumer Price Index (CPI)
Price VariableEurope Brent Spot Price (OilSpotPrice)
Lagged VariablesFirst lag of Exchange Rate (ly.var)Second lag of Exchange Rate (l2y.var)First lag of Consumer Price Index (l.CPI)
Import VariablesOld Ship (ImpOldShip)New Ship (ImpNewShip)Oil Platform (ImpOilPlat)Excluding Ship and Oil Platform(ImpExShipOilPlat)
Export VariablesCrude Oil (ExpCrdOil)Natural Gas (ExpNatGas)Condensed Fuel (ExpCond)Old Ship (ExpOldShip)New Ship (ExpNewShip)Oil Platform (ExpOilPlat)Excluding Ship and Oil Platform(ExpExShipOilPlat)
Raju RImal (NMBU) Masters Thesis April 22, 2015 9 / 23
Part II
Making prediction using different models
Raju RImal (NMBU) Masters Thesis April 22, 2015 10 / 23
Part II Statistical Models
Models in use
Following models are used for prediction of Exchange Rate,Multiple Linear Model
Y = β0 + β1X1 + . . .+ βpXp
The OLS estimate of β is,
β̂ =(XtX
)−1 XtY
Ridge RegressionPrincipal Component RegressionPartial Least Square Regression
Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
Part II Statistical Models
Models in use
Following models are used for prediction of Exchange Rate,Multiple Linear ModelRidge Regression
I Larger estimates due to multicollinearity is settled by using modifiedOLS estimate in case of Ridge Regression as,
β̂ridge =[λIp + XtX
]−1 XtY
I Here, ridge parameter λ is estimated by minimizing RMSEP throughcross validation
Principal Component RegressionPartial Least Square Regression
Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
Part II Statistical Models
Models in use
Following models are used for prediction of Exchange Rate,Multiple Linear ModelRidge RegressionPrincipal Component Regression
I A new set of variables Z1, . . .Zk called principal components areconstructed from linear combination of predictor variables
I The variation present on predictor variables are accumulated on firstfew principal components
Partial Least Square Regression
Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
Part II Statistical Models
Models in use
Following models are used for prediction of Exchange Rate,Multiple Linear ModelRidge RegressionPrincipal Component RegressionPartial Least Square Regression
I A new set of latent variables Z1, . . . ,Zk are constructed.I The variables tries to capture most information in predictor variable
that is useful for explaining response.
Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results withfew significant variables (EuroIntRate, ly.var and l2y.var).Subset models are created from the full model using following criteria,
Minimum Mallow’s Cp and Maximum adjusted R2
Minimum AIC and BIC
Stepwise procedure (Forward and Backward) based on F-value
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results withfew significant variables (EuroIntRate, ly.var and l2y.var).
Subset Model with criteria of
Minimum Mallow’s Cp and Maximum adjusted R2
1.2
0.04
0
0
−0.2
3 −0.0
3
1.1
R−Sq = 0.914 Adj R−Sq = 0.911
Sigma = 0.112 F = 264.8 (6,149)
0
5
10
15
(Int
erce
pt)
Eur
oInt
Rat
e
Exp
Crd
Oil
ImpO
ldS
hip
l2y.
var
Loan
IntR
ate
ly.v
ar
T−
Val
ue
0.65
0.06
0
0 0
0
0.01
−0.2
2−0
.03
1.08
0
R−Sq = 0.917 Adj R−Sq = 0.912
Sigma = 0.112 F = 160.9 (6,149)
0
5
10
15
(Int
erce
pt)
Eur
oInt
Rat
e
Exp
Crd
Oil
Exp
OilP
lat
ImpN
ewS
hip
ImpO
ldS
hip
l.CP
I
l2y.
var
Loan
IntR
ate
ly.v
ar
OilS
potP
rice
T−
Val
ue
Subset of linear model selected from criteria of minimum Mallow’s Cp (left) and maximumadjusted R2 (right)
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results withfew significant variables (EuroIntRate, ly.var and l2y.var).
Subset Model with criteria of
Minimum AIC and BIC
0.65
0.06
0
0 0
0
0.01
−0.2
2−0
.03
1.08
0
R−Sq = 0.917 Adj R−Sq = 0.912
Sigma = 0.112 F = 160.9 (6,149)
0
5
10
15
(Int
erce
pt)
Eur
oInt
Rat
e
Exp
Crd
Oil
Exp
OilP
lat
ImpN
ewS
hip
ImpO
ldS
hip
l.CP
I
l2y.
var
Loan
IntR
ate
ly.v
ar
OilS
potP
rice
T−
Val
ue
0.67
0
−0.2
2
1.14
R−Sq = 0.91 Adj R−Sq = 0.909
Sigma = 0.114 F = 514.1 (6,149)
0
5
10
15
(Int
erce
pt)
ImpO
ldS
hip
l2y.
var
ly.v
ar
T−
Val
ue
Subset of linear model selected from criteria of minimum AIC (left) and BIC (right)
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results withfew significant variables (EuroIntRate, ly.var and l2y.var).
Subset Model with criteria of
Stepwise procedure (Forward and Backward) based on F-value
0.67
0
−0.2
2
1.14
R−Sq = 0.91 Adj R−Sq = 0.909
Sigma = 0.114 F = 514.1 (6,149)
0
5
10
15
(Int
erce
pt)
ImpO
ldS
hip
l2y.
var
ly.v
ar
T−
Val
ue
1.2
0.04
0
0
−0.2
3 −0.0
3
1.1
R−Sq = 0.914 Adj R−Sq = 0.911
Sigma = 0.112 F = 264.8 (6,149)
0
5
10
15
(Int
erce
pt)
Eur
oInt
Rat
e
Exp
Crd
Oil
ImpO
ldS
hip
l2y.
var
Loan
IntR
ate
ly.v
ar
T−
Val
ue
Subset of linear model selected from F-test based criteria through forward selection procedure(left) and backward elimination procedure (right)
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results withfew significant variables (EuroIntRate, ly.var and l2y.var).
Following pairs of model are found equivalent as they constitute of sameset of variables,
Model selected from minimum AIC (aicMdl) and maximum AdjustedR2 (r2.model)Model selected from F-based backward elimination procedure(backward) and minimum Mallow’s Cp (cp.model)Model selected from minimum BIC (bicMdl) and F-based Forwardselected procedure (forward)
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Multicollinearity Problem
Multicollinearity Problem
Linear model with full set of predictor variable has seriousmulticollinearity problemsubset model selected from minimum AIC and Maximum Adjusted R2
criteria also have problems with multicollinearity.
0.0e+00
2.5e+08
5.0e+08
7.5e+08
1.0e+09
Key
IntR
ate
Loan
IntR
ate
Eur
oInt
Rat
eC
PI
OilS
potP
rice
ImpO
ldS
hip
ImpN
ewS
hip
ImpO
ilPla
tIm
pExS
hipO
ilPla
tE
xpC
rdO
ilE
xpN
atG
asE
xpC
ond
Exp
Old
Shi
pE
xpN
ewS
hip
Exp
OilP
lat
Exp
ExS
hipO
ilPla
tTr
Bal
TrB
alE
xShi
pOilP
lat
TrB
alM
land
ly.v
arl2
y.va
rl.C
PI
Variables
VIF
Linear Model
0.0
2.5
5.0
7.5
10.0
Loan
IntR
ate
Eur
oInt
Rat
e
OilS
potP
rice
ImpO
ldS
hip
ImpN
ewS
hip
Exp
Crd
Oil
Exp
OilP
lat
ly.v
ar
l2y.
var
l.CP
I
Variables
VIF
Model selected (criteria:AIC)
Using models such as PCR and PLS can solve this problem
Raju RImal (NMBU) Masters Thesis April 22, 2015 13 / 23
Part II PCR and PLS regression Model
PCR and PLS Regression
0
25
50
75
100
0 5 10 15 20Components
Var
iatio
n E
xpla
ined
X PerEURO
Variation Explained by PCR Model
25
50
75
100
0 5 10 15 20Components
Var
iatio
n E
xpla
ined
X PerEURO
Variation Explained by PLS Model
More than 90 percent of variation present in Exchange Rate isexplained by 16 components of PCR model while PLS has explainedthat much of variation by 6 components.However, PCR model has captured most of the variation present inpredictor with fewer components than PLS model.
Raju RImal (NMBU) Masters Thesis April 22, 2015 14 / 23
Part II Ridge Regression
Ridge Regression
Also known as shrinkagemethods as it shrinks theestimate that are enlarged byMulticollinearity.
The ridge parameter λ isestimated by minimizing theRoot mean square error(RMSECV) usingcross-validation technique.
Here, λ is found to be 0.005
0.1350
0.1375
0.1400
0.1425
0.0000 0.0025 0.0050 0.0075 0.0100λ
RM
SE
P
Setting up λ that minimize the RMSEP
Raju RImal (NMBU) Masters Thesis April 22, 2015 15 / 23
Part II Cross-validation and Prediction
Cross-valudation and Prediction
All the models seemed to work fine with observations included, but how itbehave with new observation – here comes the role of cross-validation.
Jan 2000 – Dec 2012
Training dataset
Jan 2013 – Nov 2014Test dataset
Dataset is splitted into calibration set and test set as in figure aboveModels fitted with training set were analysed for its behaviour withnew observations through cross-validation with consecutive segment oflength 12
2000 2001 . . . 2012Training Set
Raju RImal (NMBU) Masters Thesis April 22, 2015 16 / 23
Part III
Compare the models
Raju RImal (NMBU) Masters Thesis April 22, 2015 17 / 23
Part III Comparison of Models
Comparison of Models
Linear Models are compared on the bases of their goodness of fit
Model AIC BIC R.Sq R.Sq.Adj Sigma F.valuelinear -207.178 -133.982 0.919 0.906 0.116 68.594cp.model -230.323 -205.925 0.914 0.911 0.112 264.849r2.model -227.995 -191.397 0.917 0.912 0.112 160.906aicMdl -227.995 -191.397 0.917 0.912 0.112 160.906bicMdl -229.234 -213.985 0.910 0.909 0.114 514.106forward -229.234 -213.985 0.910 0.909 0.114 514.106backward -230.323 -205.925 0.914 0.911 0.112 264.849
Selected Linear Models, Ridge Model, PCR model and PLS models arethen compared on the basis of predictability
Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
Part III Comparison of Models
Comparison of Models
Linear Models are compared on the bases of their goodness of fit
Model AIC BIC R.Sq R.Sq.Adj Sigma F.valuelinear -207.178 -133.982 0.919 0.906 0.116 68.594cp.model -230.323 -205.925 0.914 0.911 0.112 264.849r2.model -227.995 -191.397 0.917 0.912 0.112 160.906aicMdl -227.995 -191.397 0.917 0.912 0.112 160.906bicMdl -229.234 -213.985 0.910 0.909 0.114 514.106forward -229.234 -213.985 0.910 0.909 0.114 514.106backward -230.323 -205.925 0.914 0.911 0.112 264.849
As prediction is objective, aicMdl or r2.model can be selected since theyhave smallest residual standard error and explain the variation in exchangerate better than otherSelected Linear Models, Ridge Model, PCR model and PLS models are thencompared on the basis of predictability
Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
Part III Comparison of Models
Comparison of Models
Linear Models are compared on the bases of their goodness of fitSelected Linear Models, Ridge Model, PCR model and PLS models arethen compared on the basis of predictability
OO
O
O OO
RMSEP R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Line
ar
AIC
Mod
el
BIC
Mod
el
Bac
kMod
el
Rid
ge
PC
R.C
omp1
5
PC
R.C
omp1
6
PC
R.C
omp1
7
PLS
.Com
p6
PLS
.Com
p7
PLS
.Com
p8
PLS
.Com
p9
Line
ar
AIC
Mod
el
BIC
Mod
el
Bac
kMod
el
Rid
ge
PC
R.C
omp1
5
PC
R.C
omp1
6
PC
R.C
omp1
7
PLS
.Com
p6
PLS
.Com
p7
PLS
.Com
p8
PLS
.Com
p9
Models
Val
ue (
RM
SE
P/ R
−sq
pre
d)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
Part III Comments on Model Comparison
Some Comments on model comparison
Figure alongside shows that,Linear Models predicts well for observationsincluded in the model
Ridge regression perform moderately buthas predicted closer than some linearmodels for new observationsPCR and PLS models have made moreaccurate prediction than other linear modelsboth in the case of cross-validation and testdatasetPLS model with 7 components has leastRMSEP while PCR model with 16components ave least RMSECV
OO
O
O O
O
RMSEP
R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Line
ar
AIC
Mod
el
BIC
Mod
el
Bac
kMod
el
Rid
ge
PC
R.C
omp1
5
PC
R.C
omp1
6
PC
R.C
omp1
7
PLS
.Com
p6
PLS
.Com
p7
PLS
.Com
p8
PLS
.Com
p9
Models
Val
ue (
RM
SE
P/ R
−sq
pre
d)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
Part III Comments on Model Comparison
Some Comments on model comparison
Figure alongside shows that,Linear Models predicts well for observationsincluded in the modelRidge regression perform moderately buthas predicted closer than some linearmodels for new observations
PCR and PLS models have made moreaccurate prediction than other linear modelsboth in the case of cross-validation and testdatasetPLS model with 7 components has leastRMSEP while PCR model with 16components ave least RMSECV
OO
O
O O
O
RMSEP
R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Line
ar
AIC
Mod
el
BIC
Mod
el
Bac
kMod
el
Rid
ge
PC
R.C
omp1
5
PC
R.C
omp1
6
PC
R.C
omp1
7
PLS
.Com
p6
PLS
.Com
p7
PLS
.Com
p8
PLS
.Com
p9
Models
Val
ue (
RM
SE
P/ R
−sq
pre
d)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
Part III Comments on Model Comparison
Some Comments on model comparison
Figure alongside shows that,Linear Models predicts well for observationsincluded in the modelRidge regression perform moderately buthas predicted closer than some linearmodels for new observationsPCR and PLS models have made moreaccurate prediction than other linear modelsboth in the case of cross-validation and testdataset
PLS model with 7 components has leastRMSEP while PCR model with 16components ave least RMSECV
OO
O
O O
O
RMSEP
R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Line
ar
AIC
Mod
el
BIC
Mod
el
Bac
kMod
el
Rid
ge
PC
R.C
omp1
5
PC
R.C
omp1
6
PC
R.C
omp1
7
PLS
.Com
p6
PLS
.Com
p7
PLS
.Com
p8
PLS
.Com
p9
Models
Val
ue (
RM
SE
P/ R
−sq
pre
d)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
Part III Comments on Model Comparison
Some Comments on model comparison
Figure alongside shows that,Linear Models predicts well for observationsincluded in the modelRidge regression perform moderately buthas predicted closer than some linearmodels for new observationsPCR and PLS models have made moreaccurate prediction than other linear modelsboth in the case of cross-validation and testdatasetPLS model with 7 components has leastRMSEP while PCR model with 16components ave least RMSECV
OO
O
O O
O
RMSEP
R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Line
ar
AIC
Mod
el
BIC
Mod
el
Bac
kMod
el
Rid
ge
PC
R.C
omp1
5
PC
R.C
omp1
6
PC
R.C
omp1
7
PLS
.Com
p6
PLS
.Com
p7
PLS
.Com
p8
PLS
.Com
p9
Models
Val
ue (
RM
SE
P/ R
−sq
pre
d)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
Part III Discussions and Conclusions
Discussions and Conclusions
This thesis has attempted to make prediction in time series dataSome subset of linear model considered are free from multicollinearityIn case of multicollinearity problem, latent variable models like PLSand PCR can deal with the situationPLS and PCR models also outperformed in predicting newobservations that are not included in the modelAutocorrelation is inevitable in time series data, including laggeddependent variable in the model has corrected the problemResiduals obtained from selected model (pls.comp7) does not containany autocorrelation PACF plot
More practices are recommented to study the performance of latentvariable model in time-series data
Next
Raju RImal (NMBU) Masters Thesis April 22, 2015 20 / 23
Part III Discussions and Conclusions
Partial Autocorrelation Function
Linear Ridge
PCR.16 PLS.7
−0.1
0.0
0.1
0.2
−0.1
0.0
0.1
0.2
0 5 10 15 20 0 5 10 15 20Var1
PAC
F
Partial Autocorrelation Function (PACF)
Raju RImal (NMBU) Masters Thesis April 22, 2015 21 / 23
Part III Discussions and Conclusions
Acknoledgement
Thanks to my Supervisors,Ellen Sandberg and Trygve Almøy
and professorSolve Sæbø
for their guidance and encouragements
Raju RImal (NMBU) Masters Thesis April 22, 2015 22 / 23
THANK YOU