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Impact Of Nasdaq , Hang Seng , Nikkei On Sensex Using Granger’s Causality Test By Group 9
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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
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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
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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
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Stationarity• A series is stationary, if1. Mean is constant2. Variance is constant ,over time3. 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
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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
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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
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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
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Continued…..• Ep is stochastic errorterm with classical assumptions-1. Zero mean2. Constant variance3. Non autocorrelatedAnd is also referred as white noise error terms, enginneringterminology
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• Two types –1. Random walk without drift2. 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
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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
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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
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How to remove nonstationarity• By taking differencing• By continuously compounding returns• By taking ratios• By taking simple returns
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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
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Continued…..• The test assumes:GNP(t)= a1 GNP(t-1) + a2 GNP(t-2) +…..+ b1 M(t-1) + b2 M(t-2) +……..+ u1tM(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
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• 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
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Results• Sensex -> Nasdaq• Nikkei -> Sensex• Sensex -> Hang Seng
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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
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