I. Overview
Vector autoregression (VAR, Vector Auto regression) commonly used to predict the dynamic effect on variable system of time-series systems are connected and analyzing random disturbance. The method of the system by VAR each endogenous variable hysteresis value as a function of all system variables to the endogenous structural model, thereby bypassing the requirement of the structural model. Engle and Granger (1987a) pointed out two or more linear combinations of nonstationary time series may be smooth. If such a smooth linear combination of the presence or, between the non-stationary (with root unit) is considered to have the time series cointegration. This combination is referred to as a smooth linear cointegration equation and may be interpreted as a long-term equilibrium relationship between the variables.
For the time series variable VAR model systems are connected prediction model is valid, while a vector autoregressive model is also frequently used to analyze the effect of different types of dynamic random error of system variables. If the delayed impact not only exists between variables, without affecting the relationship between the presence of the same period, for the VAR model, because the VAR model is actually implicit relationship to the current random disturbance among the items.
Second, note
1, a stationary unit root test test sequence, if not directly stationarity test sequence OLS easily lead to false regression.
2, when the data test is stable (ie, there is no unit root), in order to further examine the causal link variables can be used Granger causality test, but only if done Granger test is that the data must be stable, or can not do.
3, when the test data is non-stationary (i.e., unit root), and each sequence is (provided cointegration test) with the order integration, to further determine whether there cointegrated variables with cointegration, Co EG whole test mainly two-step method and test JJ:
a, EG-step test method is based on regression residuals, the residuals can test its stability through the establishment OLS model
B, JJ test is based on regression coefficient test, provided that VAR model (ie model in line with ADL model)
4, when there is cointegration relationship between the variables can be set up to further investigate ECM casual dating, Eviews there is also provided a Wald-Granger test, but this time is not the Granger causality test, but the variable nature outside inspection Please note recognition.
5, Granger test can only be used for stationary series! This is the premise Granger test, and its cause and effect relationship is not due to the relationship with the fruit, but that we usually understand the change of preliminary x can effectively explain the change in y, so called "Granger cause."
6, non-stationary series is likely to occur spurious regression, cointegration meaning is to test whether a causal relationship described their regression equation is spurious regression, the existence of a stable relationship between the variable that is tested. So, causality test is non-stationary sequence of co-integration test.
7, stability test has three functions:
1) test the smooth, if smooth, do Granger test, non-stationary, CWA positive test.
2) cointegration in order to use a single integer for each sequence.
3) the time is determined by the sequence of the data generation process.
ADF test:
. 1 --- View the root Test Unit, a dialog box, the default option for the original sequence order of the variable stability test, after confirmation, if the P-value less than 0.05 ADF test, reject the null hypothesis, the sequence described is stationary when the P value is greater than 0.5, to accept the null hypothesis, non-stationary sequence of instructions;
2 repeat the steps, view --- unit root test, a dialog box, select the 1st difference, i.e., a first difference of the variables do stationarity testing, and the same test of the first step, if the P-value of less than 5%, which is a first order stationary, if P is greater than 5%, the test proceeds smoothly second order difference sequence.
Do first unit root test to see whether the variable sequence steady, if stable, can be constructed regression model classic econometric model; if not steady, differential, when stationary series when the i-th difference to be, i obey the order integration (Note that the trend, intercept select different circumstances, and it is determined based on the P value of the null hypothesis). If all tests are subject to the same sequence order integration, VAR models can be configured to do co-integration test (note the lag phase selection), to determine whether there is inter-model internal variable co-integration relationship, that is, the existence of long-run equilibrium relationship. If so, you can construct VEC model or by Granger causality test, test variables between "who cause who change", that a causal relationship.
First, Granger causality test is chronologically the test statistic, which does not mean that the true causal relationship, whether in a causal relationship needs to be determined based on theory, and empirical models.
Second, Granger causality test variables should be smooth, if the unit root test found two variables is unstable, then, can not be directly Granger causality test, so a lot of people do not smooth variable grid Granger causality test, this is wrong.
Third, co-integration results only indicate the presence of long-run equilibrium relationship between variables, then, in the end still do first is to do first Granger cointegration it? Because the variable does not only need to smooth co-integration, so, first of all because of the variable differential, after a smooth, you can use a differential term Granger causality test, to determine the timing variable has changed, then, cointegration, see variable exists long-run equilibrium.
Fourth, the long-term equilibrium does not mean the end of the analysis should also consider short-term fluctuations, do error correction testing.
8. The stationary unit root test is test data, or that a single integer order.
9. cointegration is said to have long-term stability relationship between two or more variables. But a necessary condition for cointegration between variables is the same order integration between them, which means that the unit must be tested before proceeding with the co-integration test.
10. cointegration say is that there is long-term and stable relationship between the variables, this is only derived from the number of conclusions, but can not determine who is the cause and who is the fruit. The causality test solution is to this problem.
Unit root test is the test of time sequence is stable, co-integration analysis is done on the basis of long-term trend stationary time series on, and Granger test is generally short term causal relationship is established after error correction model established. Therefore, the natural order is to do first unit root test, cointegration another, and finally Granger test.
Unit root test is the test of the time series stationary, only stationary time series, to quantitative analysis, there would be spurious regression; co-integration is a long-term stable relationship between two or more variables of the study, both study the co-integration test usually Engle - Granger test, with more than both the Johansen test; Granger causality test is a causal relationship between the study variables, cointegration explain the long-term stable relationship is not necessarily a causal relationship, so it is necessary test to determine the causal relationship between the two by Granger. Unit root test sequence is generally, by the same order if a single whole, during cointegration and causality test is performed. Pay special attention: only cointegration same order to the whole.
Lag intervals for when 11.VAR modeling endogenous to fill lag, but this time you can not determine which lags behind the best time, so to try and choose a different lag, AIC or SC to the minimum, with the corresponding hysteresis is optimal lag, this time made out of VAR model was more reliable.
12. The reason for doing co-integration test before the VAR is co-integration test is very sensitive to lag test and inspection forms, you first need to determine the optimal lag. Since the VAR is unconstrained, and co-integration is constrained, and therefore the optimal lag co-integration test is generally the optimal lag VAR subtract 1 to determine the optimal lag, go to the form of diagnostic tests, and ultimately to do Cointegration.
13. When it is determined the number of cointegrated look down, there is a result of standardization, the result is cointegration equation, since the results are the variables on one side of the equation, so if the coefficient is positive, it indicates that the negative relationship, and vice versa.
14. The co-integration represents a long-run equilibrium relationship between variables, seemingly with your OLS is not contradictory.
(1) If the test does not co-integration, shows no long-term stability off first, VAR model can be done, but the model to do stability analysis
(2) VAR VEC relationship is: VEC is co-integration constraints (ie, long-term stability relationship) of VAR model, used for non-stationary time cointegrated sequence modeling
15. Simply put when VAR model:
The first step: how not smooth sequence can establish initial VAR model
(the process of establishing the data may be pre-stationary series, it could be part of the stable, and may be of the same order the whole relationship does not co-stationary series, it may be of different orders the sequence is not smooth, the lag order arbitrarily specified. All sequences are typically considered to endogenous vector)
Step 2: Perform After the initial VAR established
a lag order tests to determine the final model lags
2 causality test for determining the lag order to determine which sequences exogenous variables
point to rebuild VAR model (At this time lag order has been set, the inner and outer endogenous variable has been set), then the root AR chart analysis,
such as the root mean less than 1 unit, can be pulsed on VAR been constructed and variance decomposition
the unit has a root greater than 1, consider the original order to a lower order (order one sequence processing method: differential or logarithmic, second order single whole sequence: the theoretically logarithmic differential may be performed simultaneously, but the sequence of lost economic implications, should give up this process, consider the sequence of the trend can be decomposed, after decomposition as still can not meet the requirements, you can strike, does not create any model, relax or thwarted by the computer), after repeated treatment of the new sequence (which includes the first stationary series) first step and second step until it meets the stability far
The third step, after the establishment of final VAR, SVAR model could be considered
if the variable is not only lagged effect, there is also affect the relationship the same period, the VAR model is not appropriate, the need for structural analysis in this case
Reference:
15 attentional point of VAR Model
Reproduced in: https: //www.jianshu.com/p/6622114b24b6