1. Impact Of Nasdaq , Hang Seng ,
Nikkei On Sensex Using
Granger’s Causality Test
By Group 9
2. Flow Of Presentation
• Introduction- Time Series
• Challenges
• Stationarity
• Correlogram
• Random Walk
• Unit root
• Dicky Fuller Unit Root Test
• How to remove non stationarity
• The Granger Test
• Limitations
3. Introduction- Time Series
• Use to make investment decisions
• It is a set of observations on a variable’s outcomes in
different time periods
• E.g., daily returns on a traded security
• Time series models: to explain the past
• To predict the future of a time series
4. Challenges
• In time series, assumptions of linear regression do not
apply
• The residual errors are correlated unlike linear regression
model
• This is more critical for TS as in it dependent and
independent variables are not distinct
• The mean and/or variance changes over time
5. Stationarity
• A series is stationary, if
1. Mean is constant
2. Variance is constant ,over time
3. Value of covariance between two time periods depends
only on the lag between them
• For linear regression models to be applicable first a series
should be stationary
6. Correlogram
• It is test of stationarity and is based on autocorrelation
function(ACF)
• ACF at lag k is the division of covariance at lag k and
variance
• ACF is unit less and lies between -1 to +1
• When we plot ACF against the lag K, the plot is said to be
correlogram
7.
8. Unit root
• In simple regression : y = a + bx , and if we take
y = X(t), value at time ‘t’
x = X(t-1) , value at time ‘t-1’
• Series become time series
• And if b or the slope is equal to ‘1’ then it is said the model
has unit roots
• In econometrics every series which has unit root said to be
random walk
9. Random Walk
• The change in value of series from one period to another-
random or follows a pattern.
• In RW, value in one period is the value in previous period plus
an unpredictable random error
• Equation: X(t) = B0 + X(t-1) + Ep
• E.g., currency exchange rates follow a random walk
• Sophisticated exchange rate forecating models are no better
than random walk models and best estimation: current
exchange rate
10. Continued…..
• Ep is stochastic errorterm with classical assumptions-
1. Zero mean
2. Constant variance
3. Non autocorrelated
And is also referred as white noise error terms, enginnering
terminology
11. • Two types –
1. Random walk without drift
2. Random walk with drift
• Without drift: simple one with B0 = 0
• In it best predictor , is current values
• RW with drift increase or decrease by a constant amount
in each period with B0 ≠ 0
• We first transform with drift to without drift by taking first
difference
12. Dicky Fuller Unit Root
Test
• Now, X(t) = bX(t-1) + Ep
negating both sides by X(t-1)
• ΔX(t) = (b-1) X(t-1) +Ep
• And b-1= δ
• For Dickey fuller test:
μ(0): δ = 0, random walk
μ(1): δ ≠ 0, no random walk
13. Continued….
• Under the null hypothesis, the conventionally computed t-
statistic is tau statistic
• In literature tau test is also known as dickey fuller test
• If the error term is autocorrelated, we use augemented
dickey fuller test
14.
15. How to remove non
stationarity
• By taking differencing
• By continuously compounding returns
• By taking ratios
• By taking simple returns
16.
17.
18. The Granger Test
• Regression analysis deals, dependence of one on another
• But dependence doesn’t mean causality
• E.g., we know GNP and money supply are
interdependent
• But that doesn’t define whether M->GNP or GNP->M or
M<->GNP, i.e. the direction of causality
• For Granger test:
μ(0): There is no causality
μ(1): There is causality
19. Continued…..
• The test assumes:
GNP(t)= a1 GNP(t-1) + a2 GNP(t-2) +…..+ b1 M(t-1) + b2 M(t-
2) +……..+ u1t
M(t)= c1 M(t-1) + c2 M(t-2) +…..+ d1 GNP(t-1) + d2 GNP(t-2)
+……..+ u2t
• Disturbances u1t and u2t are uncorrelated
• Equations mean that current GNP value depends upon
past values of GNP and Money supply and ,vice versa
20. • Unidirectional causality from M to GNP
• Conversely, Unidirectional causality from GNP to M
• Feedback, or bilateral causality
• Independence, no causality at all
• Since, future cannot predict the past, if variable X cause Y
• Changes in X => Changes in Y, therefore, in regression
when we include past values of X and it improves the
prediction then it is said to be X cause Y, and vice versa
23. Limitations
• Since the direction of causality may depend critically on
the no. of lags included
• How many lags should be optimal
• It is a pairwise test so we can take only two variables at a
time
