Jim Gatheral Scholarship Report. Training in Cointegrated VAR Modeling at the. University of Copenhagen, Denmark

Transcription

1 Jim Gatheral Scholarship Report Training in Cointegrated VAR Modeling at the University of Copenhagen, Denmark Xuxin Mao Department of Economics, the University of Glasgow December 2, 213 I. Background Information Before coming to Glasgow in December 21, I obtained my BSc in Economics from Renmin University of China and graduated with an MSc s in Mathematics, Economics and Applied Modeling from several European Universities. Besides numerous volunteering activities, I worked as a Research Economist at UOB Investment (China) Limited (29-21). Funded by a Glasgow University Postgraduate Scholarship and a Scottish Overseas Research Student Award, My PhD research is supervised by Professor Ronnie MacDonald and Professor Joseph Byrne. My research interests lie in the fields of applied macro-econometrics and international finance. The main stream macro-econometric modeling is based on a vector autoregressive (VAR) model analyzing data integrated of order one (I(1)). However, in my research, some of the important variables may be weakly integrated of order two (I(2)). Under this condition, 1

2 the traditional I(1) modeling may cause huge loss of information and even the invalidity of data analysis results. One of key research areas in international finance is to explain the changes in the exchange rate. Numerous fundamental researches have failed to explain the abnormal exchange rate movements. My research is to consider the effects of currency intervention, speculation and sentiment in a microstructure framework, which may shed some light on the related researches. Professor Katarina Juselius and her co-researchers in the University of Copenhagen have developed a modeling approach to analyze I(2) data systematically in a VAR framework. The modeling technique has been successfully applied in many research areas. To learn and develop the related advanced modeling technique would fill the gap of modeling I(2) processes in the foreign exchange market and hugely boost my research progress. Therefore I decided to apply for the Jim Gatheral Postgraduate Travel Scholarship. and was awarded 3, to visit the University of Copenhagen and work with Professor Katarina Juselius from 1 September to 31 December 212. The purpose of the trip was to take training in cointegrated VAR modeling on I(2) processes, and analyze the currency intervention, speculation and sentiment in a microstructure framework. II. Research Undertaken in Copenhagen During my visit at the University of Copenhagen, a cointegrated VAR modeling framework was built to analyze the effects of intervention, speculation and sentiment on the changes of the exchange rate. The modeling technique can also be used to test the hypotheses of a microstructure model I built, and provide results related to the long-run relations and short-run dynamics of the foreign exchange market. 2

3 A. Cointegrated VAR modeling on I(2) Processes Under the I(1) hypothesis, a simplified cointegrated VAR model is given by: (1) X t = αβ X t 1 + Γ X t 1 + ε t where β X t 1 is an r 1 vector of stationary cointegration relations and ε t N p (, Ω ), t = 1,..., T. The model can also be expressed as: (2) R t = αβ R 1t + error terms where the residuals R t and R 1t are obtained from auxiliary regressions of X t on X t 1 and X t 1 on X t 1. It is not unusual to find I(2) data was analyzed in a cointegrated VAR I(1) model. The reason was either the author forgot to check the existence of I(2) features in the data or ignored the I(2) properties for the sake of simplicity. However, in Equation (1), X t 1 and X t 1 may contain a I(2) an I(1) trend respectively. Consequently, the I(2) trend of R 1t may not be canceled out. The connection between β X t 1 and β R 1t can be expressed as follows: (3) R t }{{} I() = αβ (X }{{} t 1 B 2 X t 1 ) + ε } {{ } t I(2) I(1) = α(β X } {{ t 1 β B } 2 X t 1 ) + ε } {{ } t I(1) I(1) = α(β X t 1 ω X } {{ t 1 ) + ε } t I() where ω = β B 2. Therefore, β ir 1t = β ix t 1 + ω x t 1,where i = 1,..., r. There are different types of relations β ir 1t I(). One type is that ω i = and β ix t 1 I(), which means directly stationary long run relations can be achieved. The other type is that β ix t I(1) cointegrates with ω i x t 1 I(1), which means only polynomially 3

4 cointegrated relations can be found. There might be a mixed case that some relations of β x t are I(1) while the others are stationary. The rank of the model, r, can be determined by a likelihood test of the hypothesis H(r ) : r r for some number r against the general unrestricted model H(p) : r p: (4) T (r ) = 2lnQ[H(r ) H(p)] = T Σln(1 ˆλ i ) where the asymptotic distribution of the statistic T (r ) is a multivariate type of the Dickey- Fuller tests. An identified long-run structure of β can then be obtained after asymptotically χ 2 -distributed likelihood ratio tests. After the determination of long run relations, a simple short-run adjustment equation may be presented as follows: () A x t = A 1 x t 1 + a(ˆβ c ) x t 1 + µ,a + µ 1,a t + v t where A 1 = A Γ 1, a = A α, and v t = A ε t IN p (, Σ). By removing insignificant variables, a parsimonious short-run dynamics representation may be achieved. As the short-run dynamic structure does not impose identifying restrictions on the residuals, a moving average representation is adopted to impose identifying restrictions on the common driving trends, a Σε i, and their weight β.the corresponding moving-average representation is given by: (6) x t = C t ε i + +tcµ + C (L)(ε t + µ + αβ 1 t) + X, i=1 where C(L) = β (α Γβ ) 1 α. The C matrix can be expressed as a matrix of two matrices similar to Π = αβ : (7) C(L) = β α, 4

5 where β = β (α Γβ ) 1. By this means, the p (p r) matrix β denotes the loadings to the p r common stochastic trends α ε i. With the moving average structure, the long-run impact of shocks from different variables can be interpreted. In summary,a cointegrated VAR model has been presented to analyze the effects of currency intervention, speculation and sentiment even when there exist some I(2) variables. The cointegrated VAR model provides us with a potential structure to identify possible long-run parity relations in international finance. Meanwhile it may test the effectiveness of intervention after considering the effects from speculation and sentiment, and macroeconomic fundamentals. It also provides a way to analyze the short-run effects and identify the longrun impacts of the above variables. B. Empirical Tests and Findings In the cointegrated VAR framework, a detailed analysis has been implemented for the Japanese foreign exchange rate market between 1991 and 28. The whole period can also be separated in different regimes of currency interventions. The long-run structures, short-run dynamics, long-run impacts are presented to identify the effective channels of the currency interventions, and the impacts of currency speculation, sentiment and volatility on the exchange rate. Between 1991 and 28, the Japanese exchange interventions had significant effects on the long-run and short-run JPY-USD movements through the coordination channel. One billion of the Japanese currency intervention, coordinated with the % decrease of JPY speculation and sentiment, was correlated with around 3.3% monthly JPY depreciation in the long run. In the short run, the Japanese interventions also managed to reduce JPY speculation and sentiment in the following month by about 4.3%. With distinctive intervention sizes and frequencies, there were regime shifts of Japanese interventions between 1991 and 28. The analysis of first Japanese intervention regime spaned from April 1991 to June 199, and were featured with small but frequent interven-

6 Figure 1: Main Variables in the First Regime, USD/JPY Change Rate 1. Forward Premium Rate... Short Term Interest Rate Differential Long Term Interest Rate Differential Japanese Currency Intervention 2. Net Yen Speculation tions. The Japanese monetary authorities reacted with leaning against the wind interventions to sharp JPY appreciation. Although there were short-term effects from the interventions, there was no long-run effectiveness. Meanwhile, the JPY speculation and sentiment shocks had large and significant impacts on the JPY-USD exchange rate movements. Large but infrequent interventions happened in the second intervention regime between June 199 and January. The Japanese monetary authorities reacted to the JPY appreciation with leaning against the wind interventions in clusters, but they failed to react to large exchange rate volatility and speculation and sentiment. While there exist short-term intervention effects and long-run effectiveness relationship through the coordination channel, the cumulative shocks to the interventions and speculation and sentiment have no long-term impacts on the exchange rate. It was the shocks to the long-term interest rate differential that drived the exchange rate. In the third regime between January 23 and March 24, the Japanese interventions were frequent and in large scale. The Japanese monetary authorities also reacted with leaning with the wind interventions to sharp JPY appreciation. The interventions were effective 6

7 Figure 2: Main Variables in the Second Regime, Rate of JPY USD Change Forward Premium Rate.. 4. Short Term Interest Rate Differential 4. Long Term Interest Rate Differential Rate of Implied Volatility Change 1 Japanese Currency Intervention 1 Net Long JPY Speculation Figure 3: Main Variables in the Third Regime, Rate of JPY USD change. Forward Premium Rate. 2. Short Term Interest Rate Differential Rate of Implied Volatility Change 1 Net Long JPY Speculation.. 2. Long Term Interest Rate Differential Japanese Currency Intervention

8 through the portfolio and coordination channels. As the main driving force in the model, the cumulative shocks to the long-term interest rate differential stimulated speculation and sentiment on JPY appreciation, which caused more interventions. Although the cumulative shocks to interventions increased the rate of the exchange rate volatility, one billion of Japanese intervention had long-run impacts of 1.1% weekly JPY depreciation. In summary, the latter period of my visit at the University of Copenhagen was devoted to reveal the power the Cointegrated VAR modeling technique to explain a complex economic phenomena. The empirical analysis with the cointegrated VAR models provided detailed results with respect to different intervention regimes between 1991 and 28. It is novel as the first research to test three different intervention channels jointly in a structural framework with various factors, i.e., speculation and sentiment, exchange rate volatility and forward rate biasedness. The empirical research also involved testing an innovative microstructure framework, with findings potentially helpful to unfold the myths of JPY-USD exchange rate movements. III. Impact of Jim Gatheral Scholarship Without the scholarship, I could not have the opportunity to learn the advanced cointegrated VAR I(2) modeling technique in another country, work with distinguished researchers in the field of applied macro-econometrics, and find some interesting empirical results for my further international financial research. The findings may have not only theoretical research significance but also prospective policy implications for central banks. It might also provide the agents of the foreign exchange market with a profitable trading strategy. The academic communications between me and Professor Katarina Juselius prevails even after the funded academic trip. I met her again in Copenhagen in January 213 to discuss my progress of the research on the modeling. Although my research progress was deferred due to unexpected heath problems between January and November this year, I am confident to pursue the research again and finish a paper on the findings in the near future. 8

9 The Jim Gatheral scholarship does have a profound impact on my PhD studies. I am indebted to Dr. Jim Gatheral for his great consideration and generous donation. Note: JPY-USD is the abbreviation for the U.S. dollar (USD) and Japanese yen (JPY) pair for the currencies of the United States and Japan. The currency pair shows how many JPY (the quote currency) are needed to purchase one USD (the base currency). 9