Application of Financial Econometrics

The assignment provides a report on the application of financial econometrics, which plays a crucial role in extracting useful information about significant economic policy issues using available data. It involves the evaluation of time series models and the use of sub-sample analysis to obtain in- and out-of-sample results with linear models. The document also discusses various topics such as economic policy uncertainty, financial markets volatility index, interest rate spread between corporate and government bonds, crude oil price changes, and stock market returns.

FINANCIAL
ECONOMETRICS

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
QUESTION 1...................................................................................................................................1
(a) Identifying and estimating time series model........................................................................1
(b) Using sub sample obtained in and out of sample forecasts and evaluating chosen models..4
QUESTION 3...................................................................................................................................7
(a) Calculating effect of shocks of oil prices on financial variables...........................................7
(b) Establishing that development in equity market impact volatility......................................12
(c) Impact of EPU on bond spread and volatility index............................................................13
QUESTION 4.................................................................................................................................16
(a) Testing the hypothesis that private consumption expenditure is related to financial wealth
and labour income.....................................................................................................................16
(b) Forecasting future private consumption expenditure.........................................................18
(c) Testing the hypothesis that ‘excess’ private consumption expenditure is a useful predictor
of excess equity returns.............................................................................................................20
CONCLUSION..............................................................................................................................21
REFERENCES..............................................................................................................................22

INTRODUCTION
Financial econometrics is known as application of statistical method to data of financial
market. It is considered as branch of financial economics and helps in studying quantitative
problems arise through management. The present report would identify and estimate time series
model and sub sample obtained in and out of forecasts of sample. It will consider series of
returns and examined about normality with important characteristic of distributions of returns. In
the same series, it will estimate model of conditional variance and motivation with use along
with incorporation of specification both sign and relative size of shock with impact in condition
volatility (Li and et.al., 2019). Moreover, it will extract impact of shocks to prices of oil on
particular financial variables and development in equity markets which impact volatility.
Simultaneously, it will show impact of EPU on spread of bond and affected through volatility
index. This report will test hypothesis that private consumption expenditure is related to two of
sources and way to predict future private consumption expenditure. Lastly, hypothesis would be
testes about excess private consumption expenditure as useful predictor of excess returns of
equity.
QUESTION 1
(a) Identifying and estimating time series model
On basis of identifying and determining time series model, there is evaluation of the least
square model which is form of mathematical regression that extracts line of best fit for particular
set of data, giving visual demonstration of relationship among different data points. Every point
of data is replicated as representative of relationship within independent variable and unknown
dependent variable. It gives overall rationale for placement of the line of appropriate fit within
data points being elaborated (Nguyen, 2019). The very common application of method of the
least squares which is replicated as linear or ordinary with objective of creating a straight line
that reduces sum of squares of errors produced by outcomes of associated equations like
associated equations like squared residuals from variations in observed value and anticipated on
basis of model. There is outcome with selection of X1 and X7 as initial one and last.
X1 and X7
Dependent Variable: X1
Method: Least Squares
Date: 04/29/19 Time: 10:49
Sample: 1 348
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Included observations: 348
Variable Coefficient Std. Error t-Statistic Prob.
C 0.300250 0.033813 8.879709 0.0000
X7 1.053131 0.033399 31.53165 0.0000
R-squared 0.741838 Mean dependent var 0.245242
Adjusted R-squared 0.741092 S.D. dependent var 1.238003
S.E. of regression 0.629933 Akaike info criterion 1.919324
Sum squared resid 137.2983 Schwarz criterion 1.941464
Log likelihood -331.9625 Hannan-Quinn criter. 1.928138
F-statistic 994.2452 Durbin-Watson stat 1.948666
Prob(F-statistic) 0.000000
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(b) Using sub sample obtained in and out of sample forecasts and evaluating chosen models
The sub sample obtained in and out of forecasts of sample with evaluation of the least
squares model with its advantages and disadvantages such as”
It has placed itself as initial tool for modeling of process due to completeness and
effectiveness. The types of data are described better with functions which are non linear in
parameters due to either processes are inherently linear or due to short ranges any process could
be approximated through linear model. Moreover, estimate of non parameters obtained through
linear least square are optimal estimate through broad class of estimates of possible parameter
with usual assumptions for process modeling. This undertakes efficient application of data and
good outcome could be obtained with very small data sets.
On the contrary, it could be assumed with long ranges with poor extrapolation properties
along with sensitivity to outliers (Luo and Chen, 2019). It is becoming difficult for extracting
particular linear model which fits data as range of data raises. The explanatory variables are very
extreme along with output of linear model. In simpler terms, linear models might be not very
effective to extrapolate the outcome of process for which data could not be gathered in region of
interest.
Dependent Variable: X1
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Method: Least Squares
Date: 04/29/19 Time: 10:55
Sample (adjusted): 1 72
Included observations: 72 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.263842 0.082425 3.200997 0.0021
X7 1.080041 0.077147 13.99980 0.0000
R-squared 0.736837 Mean dependent var -0.005276
Adjusted R-squared 0.733077 S.D. dependent var 1.316400
S.E. of regression 0.680113 Akaike info criterion 2.094268
Sum squared resid 32.37873 Schwarz criterion 2.157509
Log likelihood -73.39365 Hannan-Quinn criter. 2.119445
F-statistic 195.9944 Durbin-Watson stat 1.872276
Prob(F-statistic) 0.000000
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QUESTION 3
(a) Calculating effect of shocks of oil prices on financial variables
In the scenario, there is requirement of extracting impact of shocks to oil price on
particular financial variables comprises financial market volatility index and stock market returns
along with interest rate among government and corporate bonds along with Economic Policy
Uncertainty there is selection of VAR model to calculating it. VAR has numerous advantages as
compared to OLS model. The users must have to test that variable are exogenous and
endogenous because every variables are endogenous. Secondly, then VAR model as value of a
particular variable depends on more than associations of white noise terms as per own lags which
is very flexible compared to models to AR model (Goel and Mehra, 2019). Thus, comparison
with traditional models with accuracy of predict with VAR is very better. On basis of data and
variables, it could be written with statistical model with equation :
Spread=+Oil_r)
EPU = +Oil_r)
Vix = +Oil_r)
Nasdaq_r = +Oil_r)
The first step is required for testing that every variables as stationery or non stationery
with application Dickey-Fuller unit root test. It could be observed that prob* which is less than
5%. Moreover, P value could be reject that hypothesis and nasdaq_q is stationery.
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Null hypothesis: NASDAQ_R has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic- based on SIC, maxlag=16)
T-statistics Prob*
Augmented Dickey-
Fuller test statistics -3.381025 0.0123
Test critical values: 1% level -3.449276
5% level -2.869775
10% level -2.571226
Vix and oil_r variables and spread could test the similarity with nasdaq_r which could
follow the particular tables:
*T-statistic Pro.*
oil_R -17.01642 0.00000
vix -4.165239 0.0009
spread -3.381025 0.0123
EPU -3.373983 0.0126
It had been observed that VIX and oil_r, EPU as spread variables which is stationery.
(prob<5%). The second step it has been extracted from optimal lag length for purpose of VAR.
In the particular case, there is selected due to minimising value of criteria ODF information as
compared to other order of lag.
VAR Lag Order Selection Criteria
Endogenous variables: EPU NASDAQ_R OIL_R SPREAD VIX
Exogenous variables: C
Sample: 1990M01 2018M08
Included observations: 336
Lag LogL LR FPE AIC SC HQ
0 -5258.069 NA 27740517 31.32779 31.38459 31.35043
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1 -4344.81 1793.9 140248.7 26.04054 26.38135* 26.17640*
2 -4306.752 73.62466 129773.1 25.96281 26.58764 26.21188
3 -4276.028 58.52271 125456.2 25.92874* 26.83757 26.29102
4 -4257.022 35.63541 130072.7 25.96442 27.15727 26.43992
5 -4239.662 32.03423 136224 26.00989 27.48675 26.59861
6 -4218.647 38.15137 139645.2 26.03361 27.79448 26.73555
7 -4206.151 22.31444 150660.7 26.10804 28.15292 26.92319
8 -4182.589 41.37409 152257.2 26.1166 28.44549 27.04496
Furthermore, there is estimation of VAR model and outcome is followed as below:
Standard error in (); t-statistic in []
As a result with 4 equations:
EPU= -0.0576694424558*OIL_R(-1) -
0.0122138100727*OIL_R(-2) + 0.27276*Oil_r(-3) + 13.5961172805
NADAQ_E= -0.0335892399531*OIL_R(-1) + 0.0164369598691* OIL_R(-1) +
0.0164369598691*OIL_R(-2) + 0.046776846291*OIL_R(-3) – 0.677239638008
SPREAD= -0.00169663029816*OIL_R(-1) + 0.000313883854751*OIL_R(-2) +
0.000253942641175*OIL_R(-3) + 0.122360978702
VIX= 0.0138930821721*OIL_R(-1) – 0.0175911682117*OIL_R(-2)+
0.000769854610195*OIL_R(-3) + 2.52164784454
If there is increment in oil price of one unit, uncertainty of economic policy would raise by 0.202
unit. Apart from this, oil price raise with one unit, stock market return would raise by 0.0289%.
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If the oil price raise with single unit, interest rate among government and corporate would
decrease by 0.0012%. However, oil price increment single unit, financial market volatility index
would fall by 0.0028%.
The third step would run Grangrer causality test which would support for altering
variable in model is effected through variable. The outcome would follow a table below:
It reflects one way relationship among oil and price changes with uncertainty. The
Alpha=0.1, reflects of economic policy uncertainty reflects cause to movement of oil price.
Simultaneously, one way relationship among oil price and spread as with VIX. The movement of
return of stock market return would lead to alter in price of oil along with interpretation of VAR
model through impulse response.
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1st graph: It reflects response of EPU to oil price then it will have negative affect on EPU on
short time with positive effect on EPU had attained peak at period 4 compared to continous
reverse effect at following duration. In the same series, positive shock of oil price would dircetly
lead NADDAQ_R falls with significant amount for short time compared to oil price would have
positive impact on NASDAQ_R and attained at peak with period 4 with compared to effect of oil
price today decay to 0. The third graph with response of spread to price of oil reflects different
pattern, shock to oil price impacts to go down in short duration, but effect of this shock signifies
to revert approx to -0.04 (Guirguis, 2019). The response to VIX to price of oil is positive in near
future and effect of shock is about approx mean to -0.04.
Dependent Variable: OIL_R
Method: Least Squares
Date: 04/27/19 Time: 16:37
Sample (adjusted): 1 344
Included observations: 344 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 4.641946 1.722962 2.694166 0.0074
EPU -0.009081 0.017575 -0.516700 0.6057
VIX -0.075530 0.083401 -0.905628 0.3658
SPREAD -0.640209 0.947994 -0.675330 0.4999
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NASDAQ_R -0.005875 0.074254 -0.079121 0.9370
R-squared 0.018646 Mean dependent var 0.697213
Adjusted R-squared 0.007067 S.D. dependent var 8.462566
S.E. of regression 8.432612 Akaike info criterion 7.116518
Sum squared resid 24105.93 Schwarz criterion 7.172342
Log likelihood -1219.041 Hannan-Quinn criter. 7.138752
F-statistic 1.610271 Durbin-Watson stat 1.455157
Prob(F-statistic) 0.171239
Interpretation:
The above calculation defines the effect of stocks of oil prices [crude oil price changes
(oil_r)] on the financial variable which includes Economic Policy Uncertainty (EPU), financial
markets volatility index (VIX), the interest rate spread between corporate and government bonds
(spread), and stock market returns (nasdaq_r). The Coefficient comes out to be 4.641946. This
shows the fact that the all the financial variables have a different lelve of dependency go the
dependent variables. The dependent variable is taken as OIL_R. The dependently variable are
Economic Policy Uncertainty (EPU), financial markets volatility index (VIX), the interest rate
spread between corporate and government bonds (spread), and stock market returns
(nasdaq_r).The probability of OIL_R with EPU comes out to be 0.6057 which is more than the
standard value of p of 0.05. This shows the fact that there is not significant relationship between
the OIL_R and EPU, which means that there is no effect f the stock of oil prices on the financial
variable of Economic Policy Uncertainty.
(b) Establishing that development in equity market impact volatility
Dependent Variable: VIX
Method: Least Squares
Sample (adjusted): 1 344
Included observations: 344 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 19.53576 0.405700 48.15321 0.0000
NASDAQ_R -0.233488 0.064112 -3.641876 0.0003
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R-squared 0.037334 Mean dependent var 19.29319
Adjusted R-squared 0.034519 S.D. dependent var 7.554041
S.E. of regression 7.422517 Akaike info criterion 6.852711
Sum squared resid 18842.07 Schwarz criterion 6.875040
Log likelihood -1176.666 Hannan-Quinn criter. 6.861604
F-statistic 13.26326 Durbin-Watson stat 0.244471
Prob(F-statistic) 0.000313
Interpretation:
The above calculation shows a relation ship between the development in the equity market
and its effect on the volatility. For this calculation the VIX (financial markets volatility
index) have been taken as dependent variable and VIX is taken as independent variable. The
probability between these two factors have been calculated as 0.0003. With comparing it
with the standard value of p as 0.05 it can be seen that is far low from the set standard value.
This shows acceptance of alternative hypotheses which means that there is a significant
relation between the VIX and the equity market. The relationship between the two variable
that is the VIX (financial markets volatility index) and stock market returns (nasdaq_r) is
determined.
(c) Impact of EPU on bond spread and volatility index
Spread= +EPU)
The first step to extract optimal lag length for VAR. From the outcome, we would give lag order
equal 4 due to reducing value of criterion of information.
Moreover, with estimation of VAR model:
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Second estimation of VAR model:
The above table could be observed that T-statistic with absolute
NASDAQ_r= 4.22>z value(1.96) so this leads to reject null hypothesis as NASDAq_r is
significant. The presence of two equations:
VIX=-0.126941256324*NASDAQ_R(-1) + 2.65058943317
NASDAQ_R= 0.046583253.733*VIX(-1) + 0.069837081966
If there is increment in equity market with 1 unit then vix would fall by 0.1269 unit and vix
increase 1 unit, equity market would also raise by 0.0465 unit.
For purpose of testing interactions with application of pairwise Granger Causality test.
On the above table, it could be observed with one object to relationship among equity
market and VIX. The movement of equity market would be lead the alteration of VIX,
Furthermore, interpretation of impact of VIX on Nasdaq_r along with vice versa with impulse
response.
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The first graph reflects response of equity market to VIX, its shock of VIX lead the
equity market goes in large amount in short duration and this shock is reverting approx to 0. The
second graph reflects response of VIX to equity market. Moreover, shock of equity market
directly lead equity market goes to large amount in short time and effect of equity market on
VIX is positive is specified duration.
Dependent Variable: EPU
Method: Least Squares
Date: 04/27/19 Time: 16:40
Sample (adjusted): 1 344
Included observations: 344 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 43.65762 4.667586 9.353363 0.0000
SPREAD 26.74355 2.535962 10.54572 0.0000
VIX 0.014872 0.253798 0.058597 0.9533
R-squared 0.380291 Mean dependent var 107.0080
Adjusted R-squared 0.376656 S.D. dependent var 32.91023
S.E. of regression 25.98333 Akaike info criterion 9.361470
Sum squared resid 230220.6 Schwarz criterion 9.394964
Log likelihood -1607.173 Hannan-Quinn criter. 9.374811
F-statistic 104.6289 Durbin-Watson stat 0.563117
Prob(F-statistic) 0.000000
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QUESTION 4
(a) Testing the hypothesis that private consumption expenditure is related to financial wealth and
labour income
Null Hypothesis: H0- There is no significant relationship in private consumption expenditure and
financial wealth and labor income
Alternative hypothesis: H1- There is significant relationship in private consumption expenditure
and financial wealth and labor income
Dependent Variable: PCE
Method: Least Squares
Date: 04/27/19 Time: 16:23
Sample (adjusted): 1 187
Included observations: 187 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.873883 0.069659 -12.54522 0.0000
FINWEALTH 0.153996 0.022265 6.916566 0.0000
LABINC 0.922624 0.031469 29.31819 0.0000
R-squared 0.995591 Mean dependent var 10.08606
Adjusted R-squared 0.995543 S.D. dependent var 0.280505
S.E. of regression 0.018728 Akaike info criterion -5.101734
Sum squared resid 0.064532 Schwarz criterion -5.049898
Log likelihood 480.0121 Hannan-Quinn criter. -5.080730
F-statistic 20772.32 Durbin-Watson stat 0.208479
Prob(F-statistic) 0.000000
Interpretation:
From the above calculation it can be interpreted that the coefficient depicts the estimated
coefficients. The above figure measures the marginal contribution of the independent variable to
the dependent variable. For determining the relation between two variable, the dependent
variable is taken as private consumption expenditure and the independent variables in the
calculations are financial wealth and labour income, with keeping all others variable constant.
This factors shows that the slop of relation between the corresponding private consumption
expenditure and financial wealth and labour income. The comes out to be negative as -0.873883,
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which show the steep slop in the relation between two factors. The probability column depicts
the probability of drawing at statistics as the one which are actually observed. Under this there is
an assumption that the errors are normally distributed and there is an estimation that coefficient
are asymptotically normally distributed. The probability shown is also known as p value or the
marginal significance level. For the given calculation the value of P comes out to be 0.00, which
is less than 0.05 value. This results in acceptance of the alternative hypotheses. This depicts the
facts that there is significant relationship in private consumption expenditure and financial
wealth and labour income. The other value calculated are r- square, Adjusted R Square, S.E. Of
regression, sum square, log likelihood, F statistics, probability, mean dependent variable, S.D.
Dependent variable, Akaike info criterion, Schwarz criterion, Hannan-Quinn criter, Durbin-
Watson stat which comes out to be 0.995591, 0.995543, 0.018728, 0.064532, 480.0121,
20772.32, 0.000000, 10.08606, 0.280505, -5.101734, -5.049898, -5.080730, 0.208479,
respectively. All this factors shows the fact the there is all these three factors are related with
other have a high-level of dependency on each other. This can be started that the private
consumption expenditure of people means the money spent by people in their personal expenses
have a direct relation with financial health and labour income of that individual.
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(b) Forecasting future private consumption expenditure
Dependent Variable: PCE
Method: Least Squares
Date: 04/29/19 Time: 10:31
Sample: 1 187
Included observations: 187
Variable Coefficient Std. Error t-Statistic Prob.
C 9.856597 0.014045 701.7995 0.0000
EQUITYINDEX 0.008616 0.000362 23.78941 0.0000
R-squared 0.753641 Mean dependent var 10.08606
Adjusted R-squared 0.752309 S.D. dependent var 0.280505
S.E. of regression 0.139603 Akaike info criterion -1.089386
Sum squared resid 3.605480 Schwarz criterion -1.054829
Log likelihood 103.8576 Hannan-Quinn criter. -1.075384
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F-statistic 565.9360 Durbin-Watson stat 0.024768
Prob(F-statistic) 0.000000
(c) Testing the hypothesis that ‘excess’ private consumption expenditure is a useful predictor of
excess equity returns
Null Hypothesis: H0- There is no significant relationship in private consumption expenditure and
excess equity returns
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Alternative hypothesis: H1- There is significant relationship in private consumption expenditure
and excess equity returns
Dependent Variable: PCE
Method: Least Squares
Date: 04/27/19 Time: 17:33
Sample: 1 187
Included observations: 187
Variable Coefficient Std. Error t-Statistic Prob.
C 9.856597 0.014045 701.7995 0.0000
EQUITYINDEX 0.008616 0.000362 23.78941 0.0000
R-squared 0.753641 Mean dependent var 10.08606
Adjusted R-squared 0.752309 S.D. dependent var 0.280505
S.E. of regression 0.139603 Akaike info criterion -1.089386
Sum squared resid 3.605480 Schwarz criterion -1.054829
Log likelihood 103.8576 Hannan-Quinn criter. -1.075384
F-statistic 565.9360 Durbin-Watson stat 0.024768
Prob(F-statistic) 0.000000
CONCLUSION
From the above report, it had been concluded that financial econometrics plays very
important role as it offers tools which enables for extracting useful information about
significance economic policy issues with the data availability. It shows application of statistical
techniques for understanding economic issues and testing theories. It has reflected evaluation of
time series model and with use of sub sample obtain in and out with linear model which is very
vital. Simultaneously, with Economic Policy Uncertainty, financial markets volatility index,
interest rate spread among corporate and government bonds, crude oil price changes and stock
market returns. It has reflected development in equity markets which impacts volatility and
volatility index. Henceforth, it has shown private consumption expenditure and consumption
with wealth variables has been replicated.
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REFERENCES
Books and Journals
Goel, A. and Mehra, A., 2019. Analyzing Contagion Effect in Markets During Financial Crisis
Using Stochastic Autoregressive Canonical Vine Model. Computational Economics. 53(3).
pp.921-950.
Guirguis, M., 2019. Step-By-Step Application of Econometrics in Finance. A Practical Guide for
Postgraduate and Research Students. A Practical Guide for Postgraduate and Research
Students.(January 12, 2019).
Li, H., and et.al., 2019. The Relationship between Oil and Financial Markets in Emerging
Economies: The Significant Role of Kazakhstan as the Oil Exporting Country. Finance
Research Letters.
Luo, J. and Chen, L., 2019. Modeling and Forecasting the Multivariate Realized Volatility of
Financial Markets with Time-Varying Sparsity. Emerging Markets Finance and Trade,
pp.1-17.
Nguyen, H. P., 2019. Why Hammerstein-Type Block Models Are so Efficient: Case Study of
Financial Econometrics. BEYOND TRADITIONAL PROBABILISTIC METHODS IN
ECONOMICS. p.129.
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