This post illustrates Vector Auto Regression (VAR) technique that can be used to analyses impulse response of indices in different regions (Australia, Hong Kong, Europe and United States) when there is a shock in anyone of the market. It makes use of VAR model with simple recursive structure to analyse the impulse response.Vector auto regression (VAR) is an ordinary least square regression where each variable is regressed on lag value of itself and other variables in the set.
$Au{{s}_{t}}={{A}_{0}}+HK{{G}_{t-1}}+E{{U}_{t-1}}+US{{A}_{t-1}}+{{\mu }_{t}}$
In above equation u(t) is the VAR disturbance vector and is serially uncorrelated. VAR disturbance vector have variance covariance matrix, distrubance vector is assumed to be related to the underlying economic shocks, ${{\varepsilon }_{t}}$, by
${{\mu }_{t}}=D{{\varepsilon }_{t}}$
D is lower triangular and ${{\varepsilon }_{t}}$ has covariance matrix analogous to the identity matrix.
$\left( \begin{matrix} {{u}_{Australia}} \\ {{u}_{HongKong}} \\ {{u}_{Europe}} \\ {{u}_{usa}} \\ \end{matrix} \right)=\left( \begin{matrix} {{t}_{11}} & 0 & 0 & 0 \\ {{t}_{21}} & {{t}_{22}} & 0 & 0 \\ {{t}_{31}} & {{t}_{32}} & {{t}_{33}} & 0 \\ {{t}_{41}} & {{t}_{42}} & {{t}_{43}} & {{t}_{44}} \\ \end{matrix} \right)\left( \begin{matrix} {{\varepsilon }_{Australia}} \\ {{\varepsilon }_{HongKong}} \\ {{\varepsilon }_{Europe}} \\ {{\varepsilon }_{usa}} \\ \end{matrix} \right)$
We construct Financial market interdependence matrix to derive the impulse response of prices in different regions. We arrange the matrix based on financial market opening time, which states that Australian Market opens first, which is followed by HongKong Market, European market and then at at last by United States ( for the shake of illustration we ignore China and India market).
The data are extracted from world stock price indices (Yahoo Finance) and dates are arranged in ascending order. We extract the date from January 1st 2013 to December 31st 2014, and run the regression in Eviews software.
Data sources:
For (US and World Indices)
USA (us): S&P 500,
Australia (au):S&P ASX 200
Hong-Kong (hk): HANG SENG INDEX
EU(eu): FTSE 100
The model is estimated as a structural recursive VAR using Cholesky decomposition. The derived short run restriction matrix is structure in such a way that, in equation one Australian market does not react to change in other markets. In second equation, HongKong market reacts to Australian market, in third equation European market reacts to Hongkong market and Australian market; in equation four United States market reacts to HongKong, Euroepan Market and Australian market, contemporaneously. We take lag 5 which denotes working week days (we test the lag length and co-integration, you can refer the process in this link).
Stability test-AR root table shows that no root lies outside the unit circle, and VAR satisfies the stability condition. If you want to follow the process in E-views please click here.
First row shows how Australian market reacts to shock in rest of the region, second row shows Hong Kong market, third row shows European market and fourth row shows US market. We find that Australian market is less sensitive to HongKong market, however it is more responsive to US and European market in second day of trading (14 units and 15units positive response to one standard deviation shock in the residuals) . If we analyse Hongkong market we find that it responds instantaneously to Australian market as it climbs up 85 units as a response to one standard deviation shock in residuals (of Australian market share indices). In next row when we analyze European market we find that it responds significantly to US market, and shows 18 units positive increment. Further it quickly dies out when it responds to US and Australian market, and the absorption of the shock is more rapid when it responds to HongKong market.
We can extend this study and compare how the transition has been changing throughout the years. It will be interesting to see how response of Australian, US and HongKong market has changed overtime when there is shock in European market and compare the scenario before 2010 (first) Greece Bailout.
We analyze the impulse response of rest of region (third column) when there is shock in European market in the period 2005 to 2006. The results shows that impulse response to the shock on European market doesn't die out quickly when compared to 2013-2014, for example S&P 500 (US) market is back to normalcy within 12 days in the year 2013-14, while it continued above '6' even after 20th day in the period 2005-2006. The reason behind this could be that after late 2009 GREECE (first) bailout most of the vulnerable GREECE/EU stocks were sold out by the investors/companies, making respective markets relatively insulated and enabling them recover (back to normalcy '0' ) from shocks in European market within very short time.
$Au{{s}_{t}}={{A}_{0}}+HK{{G}_{t-1}}+E{{U}_{t-1}}+US{{A}_{t-1}}+{{\mu }_{t}}$
In above equation u(t) is the VAR disturbance vector and is serially uncorrelated. VAR disturbance vector have variance covariance matrix, distrubance vector is assumed to be related to the underlying economic shocks, ${{\varepsilon }_{t}}$, by
${{\mu }_{t}}=D{{\varepsilon }_{t}}$
D is lower triangular and ${{\varepsilon }_{t}}$ has covariance matrix analogous to the identity matrix.
$\left( \begin{matrix} {{u}_{Australia}} \\ {{u}_{HongKong}} \\ {{u}_{Europe}} \\ {{u}_{usa}} \\ \end{matrix} \right)=\left( \begin{matrix} {{t}_{11}} & 0 & 0 & 0 \\ {{t}_{21}} & {{t}_{22}} & 0 & 0 \\ {{t}_{31}} & {{t}_{32}} & {{t}_{33}} & 0 \\ {{t}_{41}} & {{t}_{42}} & {{t}_{43}} & {{t}_{44}} \\ \end{matrix} \right)\left( \begin{matrix} {{\varepsilon }_{Australia}} \\ {{\varepsilon }_{HongKong}} \\ {{\varepsilon }_{Europe}} \\ {{\varepsilon }_{usa}} \\ \end{matrix} \right)$
We construct Financial market interdependence matrix to derive the impulse response of prices in different regions. We arrange the matrix based on financial market opening time, which states that Australian Market opens first, which is followed by HongKong Market, European market and then at at last by United States ( for the shake of illustration we ignore China and India market).
The data are extracted from world stock price indices (Yahoo Finance) and dates are arranged in ascending order. We extract the date from January 1st 2013 to December 31st 2014, and run the regression in Eviews software.
Data sources:
For (US and World Indices)
USA (us): S&P 500,
Australia (au):S&P ASX 200
Hong-Kong (hk): HANG SENG INDEX
EU(eu): FTSE 100
The model is estimated as a structural recursive VAR using Cholesky decomposition. The derived short run restriction matrix is structure in such a way that, in equation one Australian market does not react to change in other markets. In second equation, HongKong market reacts to Australian market, in third equation European market reacts to Hongkong market and Australian market; in equation four United States market reacts to HongKong, Euroepan Market and Australian market, contemporaneously. We take lag 5 which denotes working week days (we test the lag length and co-integration, you can refer the process in this link).
Stability test-AR root table shows that no root lies outside the unit circle, and VAR satisfies the stability condition. If you want to follow the process in E-views please click here.
Stability check
Impulse response (2013-2014)
First row shows how Australian market reacts to shock in rest of the region, second row shows Hong Kong market, third row shows European market and fourth row shows US market. We find that Australian market is less sensitive to HongKong market, however it is more responsive to US and European market in second day of trading (14 units and 15units positive response to one standard deviation shock in the residuals) . If we analyse Hongkong market we find that it responds instantaneously to Australian market as it climbs up 85 units as a response to one standard deviation shock in residuals (of Australian market share indices). In next row when we analyze European market we find that it responds significantly to US market, and shows 18 units positive increment. Further it quickly dies out when it responds to US and Australian market, and the absorption of the shock is more rapid when it responds to HongKong market.
We can extend this study and compare how the transition has been changing throughout the years. It will be interesting to see how response of Australian, US and HongKong market has changed overtime when there is shock in European market and compare the scenario before 2010 (first) Greece Bailout.
Impulse Response (2005-2006)
We analyze the impulse response of rest of region (third column) when there is shock in European market in the period 2005 to 2006. The results shows that impulse response to the shock on European market doesn't die out quickly when compared to 2013-2014, for example S&P 500 (US) market is back to normalcy within 12 days in the year 2013-14, while it continued above '6' even after 20th day in the period 2005-2006. The reason behind this could be that after late 2009 GREECE (first) bailout most of the vulnerable GREECE/EU stocks were sold out by the investors/companies, making respective markets relatively insulated and enabling them recover (back to normalcy '0' ) from shocks in European market within very short time.
