時(shí)間序列分析及var模型-文庫(kù)吧在線文庫(kù)
【正文】 transaction costs. In pairs trading, you go long in one stock and short in the second stock to hedge your position. We need to avoid that we have to trade too frequently to reduce transaction costs. The following figure cumulates the deviations from the longterm equilibrium and shows periods of over an undervaluation.In practice, you would run different scenarios and determine losses and profits from following different trading rules. Moreover, you need to test your model outofsample to ensure that it holds. Currently, we assume that we update the model every day, which is not necessarily the case. Exercises Interpretation of VECMInterpret the following VECM result. In particular, discuss whether there is a longterm equilibrium between gold and silver prices and highlight the shortterm dynamics. ReferencesEnders, W. (2004) Applied econometric time series, 2nd edition, John Wiley amp。Let’s look at a standard AR(p) process for two variables (yt and xt).(1) yt=α1+i=1pβ1iyti+ε1t(2) xt=α2+i=1pβ2ixti+ε2tThe next step is to allow that lagged values of xt can affect yt and vice versa. This means that we obtain a system of equations for two dependent variables (yt and xt). Both dependent variables are influenced by past realisations of yt and xt. By doing that, we violate strict exogeneity (see Lecture 2)。Page | 15Lecture 66. Time series analysis: Multivariate models Learning outesWe now relax both assumptions using a VAR model. VAR models can be regarded as a generalisation of AR(p) processes by adding additional time series. Hence, we enter the field of multivariate time series analysis. VAR模型可以當(dāng)作是在一般的自回歸過(guò)程中加入時(shí)間序列。 hence, both ratios don’t seem to be stationary. Vector errorcorrection model (VECM)The VECM bines VAR and cointegration into one framework. The VAR is extended by including deviations from the longterm equilibrium defined by the cointegration vector. The coefficient of the deviation from the longterm equilibrium indicates the speed of adjustment back into equilibrium.The VECM capture the longterm relationship and the shortterm dynamics of two or more time series. Let’s see how it works in the case of gold and silver prices. Table 6 reports the VECM specification, which resembles the VAR with two lags. It also contains the CE ponent。 hence, we can assess the dynamic impact of a marginal change of one variable on another. The standard OLS regression provides coefficients, and coefficients refer to the partial impact of an explanatory variable on the dependent variable. In the case of VAR models, the relationship bees dynamic, as a change of one variable (say x) in t can affect x and y in t+1. The impact on x and y in t+1 in turn affects x and y in t+2 and so on until the impact dies out. Impulse response functions are very useful in illustrating the shortterm dynamics in a model.Let’s look at an example to see how VAR modelling works. In Lecture 5, we tried very hard to understand gold prices. We extend our univariate model by exploring the relat
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