Time Series Analysis for Model, Structural Analysis, Granger Causality and ARMA Model

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Time Series Analysis,
December 2017
[Pick the date]
Com

Question 1
Part I : Model
a) In order to complete the model, we first found the number of lags to be included in the
analysis. To Do so, we took a time series analysis. All variables were taken for this
analysis. We have taken maximum lag as 1 since the data is given as yearly. First, an
informal analysis of stationarity was conducted by looking at the time series plot. All the
variables are around the mean, implying that the variables are stationary. (See Appendix
: Graphs 1-3) We also identified if the data has a constant and no trend.
b) Next we conducted a formal Analysis of Unit roots using the Advanced Dicky Fuller Test
and KPSS tests to test the non-stationarity and stationarity.
The OLS Estimates are as follows
Equation 1: gdp
coefficient std. error t-ratio p-value
------------------------------------------------------------
const 0.0453425 0.0455777 0.9948 0.3204
gdp_1 0.556470 0.0434717 12.80 1.30e-031 ***
infl_1 −0.286246 0.0538757 −5.313 1.81e-07 ***
rate_1 −0.149610 0.0590711 −2.533 0.0117 **
time −1.58047e-05 0.000195764 −0.08073 0.9357
Equation 2: infl

coefficient std. error t-ratio p-value
-----------------------------------------------------------
const 0.0310928 0.0412172 0.7544 0.4511
gdp_1 0.276891 0.0393126 7.043 8.42e-012 ***
infl_1 0.529129 0.0487213 10.86 3.27e-024 ***
rate_1 0.0473744 0.0534196 0.8868 0.3757
time −0.000165645 0.000177035 −0.9357 0.3500
Equation 3: rate
coefficient std. error t-ratio p-value
----------------------------------------------------------
const 0.0314197 0.0293796 1.069 0.2855
gdp_1 0.206096 0.0280220 7.355 1.12e-012 ***
infl_1 0.324573 0.0347285 9.346 6.89e-019 ***
rate_1 0.482056 0.0380774 12.66 4.68e-031 ***
time 1.40105e-05 0.000126190 0.1110 0.9117

Part II: Structural analysis: Impulse Responses
Test 1 Impulse Response Results
c) Interpretation using the transmission mechanism of monetary policy:
a) As seen in the above mentioned picture, the impulse response of GDP to GDP is
greatest, followed by Rate of Interest and Inflation. However, in the next stage, with a
shock, the GDP declines the greatest, followed by Interest Rate.
b) Inflation increases. Thus, for the given data, the economy tends to gain inflation in case,
of a change in monetary policy and the GDP tends to shrink.
c) With a shock in inflation, the GDP and Inflation tend to decline and at the same time,
implying an economic structure with high liquidity.
The combined graph of the two impulse response is gives in Graph 4 in Appendix
Part III Granger Causality
To understand whether there is a Granger Causality, we set the null hypothesis as . The F tests
with Zero Restrictions help identify whether there is a Granger Causality. Since, the P- value is
statistically significant, the there is a causality.