時(shí)間序列分析及var模型-預(yù)覽頁(yè)
【正文】 es。金融時(shí)間序列及面板數(shù)據(jù)往往都有很強(qiáng)的自相關(guān)性，假定解釋變量影響因變量。 Cointegration Vector autoregression (VAR) hence, there is no serial correlation between error terms and any realisation of any independent variable (lead or lag). As we discovered, serial correlation (or autocorrelation) is very mon in financial time series and panel data. Furthermore, we assumed a predefined relation of causality: explanatory variable affect the dependent variable. 傳統(tǒng)的線性回歸模型假設(shè)嚴(yán)格的外生性，誤差項(xiàng)與可實(shí)現(xiàn)的獨(dú)立變量之間沒(méi)有序列相關(guān)性。 however, we can use a more relaxed concept, namely weak exogeneity. As we use lagged values of both dependent variables, we can argue that these lagged values are known to us, as we observed them in the previous period. We call these variables predetermined. Predetermined (lagged) variables fulfil weak exogeneity in the sense that they have to be uncorrelated with the contemporaneous error term in t. We can still use OLS to estimate the following system of equations, which is called a VAR in reduced form.(3) yt=α1+i=1pβ11iyti+i=1pβ12ixti+ε1t(4) xt=α2+i=1pβ21iyti+i=1pβ22ixti+ε2tThe beauty of this model is that we don’t need to predefine whether x or y are endogenous (the dependent variable). In fact, we can test whether x (y) is endogenous or exogenous using Granger causality tests. The idea of Granger causality is that past observations (lagged dependent variables) can influence current observations – but not vice versa. So the idea is rather simple: the past affects the present, and the present does not affect the past. STATA provides Granger causality tests after conducting a VAR analysis, which is based on testing the joint hypothesis that past realisations do not Granger cause the present realisation of the dependent variable.In many applications, VAR models make a lot of sense, as a clear direction of causality cannot be predefined. For instance, there is a substantial literature on the benefits of internationalisation (. entering foreign market through crossborder Mamp。 thus, in the long run it tends to go back to its longterm equilibrium (mean). Based on the ratio, we could argue that gold seems to be overvalued pared to silver at the moment. Of course, taking the ratio suggests a very simple cointegrating vector – in fact we assume a onetoone relationship. Before we can use the Johansen procedure, we have to make sure that the time series have the same order of integration I(p). We already know that gold and silver prices are both I(1) time series. Table 5 shows the results of the Johansen test for cointegration. In line with the VAR model, we use two lags.Table 5: Johansen testThe null hypothesis that there is no cointegration (r=0) can be rejected if we use the trace statistic. However, the null hypothesis that we have one cointegrating vector (r=1) cannot be rejected. The problem is that the maxlambda statistic does not support cointegration. I also tried logprices instead, which is mon in analysing goldsilver ratios。 Sons.15Dr Gerhard Kling, Quantitative Research Methods in Finance, University of Southampton
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