時間序列分析及var模型-文庫吧資料
2025-07-02 18:30本頁面
【正文】 u 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。 however, I don’t obtain clear results.Given the extreme increase in volatility in prices, it might be likely that there are structural breaks in an alleged cointegration vector. Structural breaks are difficult to handle.Another way to look at this problem is to test whether price ratios or logprice ratios are stationary time series. If they are stationary, then the two underlying time series are cointegrated and the ratio indicates the cointegration vector. Again DickeyFuller tests cannot reject the null hypothesis。 however, the (S)BIC prefers only one lag. I would prefer HQIC and try two lags first. If the second lag does not exhibit significant coefficient, we could try to reduce the lag length in line with (S)BIC.We run a VAR with two lags to explain current price changes in gold and silver. Table 2 provides the OLS estimates.Table 2: VAR model with two lagsWe see that silver prices (lag 2) affect current gold prices, and we can establish autocorrelation in both time series. To test whether gold Granger causes silver or vice versa, we run Granger causality tests reported in Table 3.Table 3: Granger causality testsHence, we confirm that past changes in silver prices can predict future gold price changes. This is very interesting, as it can be used to develop a trading strategy. Finally, we need to show that the VAR is stable (see Table 4).Table 4: Stability condition of the VARFinally, we can illustrate the impact of silver price changes on future gold price changes using an impulse response function. Figure 2 shows the impulse response function and confidence intervals derived from bootstrapping. If silver prices increase today by 1%, we should expect a significant decline in gold prices in two years by %.Figure 2: Impulse response function CointegrationWhen we explore Figure 1 a bit more carefully, we can see that silver and gold prices exhibit a certain degree of comovement. We could almost argue that they share a mon stochastic trend. The limitation of ARIMA and VAR models is that they can be only used if the time series are stationary. In our case, we had to firstdifference your time series to ens
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