Describing impact of trading in the global FX market

Describing impact of trading in the global FX market Anatoly B. Schmidt *) ICAP Electronic Broking LLC One Upper Pond Rd., Bldg F, Parsippany NJ 07054 email address: alec.schmidt@us.icap.com Market impact in the global FX market is described using the structural VAR model. The model is derived in terms of return, signed trading volume, signed order book volume, and signed inside-market order flow. The EBS market data for EUR/USD (with typical bid/offer spread of one pip) and EUR/JPY (with typical spread of two three pips) are used on one-second and ten-second time grids. The samples with whole-pip pricing and decimal pip-pricing are considered separately. The results show that market impact is determined primarily with the signed trading volume and it decays on the ten-second time scale. *) The information presented in this work is provided for educational purposes only and does not constitute investment advice. Any opinions expressed in this work are those of the author and do not necessarily represent the views of ICAP Electronic Broking LLC, its management, officers or employees. Electronic copy available at: http://ssrn.com/abstract=1978977

1. Introduction Impact of trading on price (often called market impact (MI)) is an important concept that is widely used in models of optimal trade execution (Amgren & Chriss, 2000; Kissell & Glantz, 2003). It is usually assumed that MI has a permanent component. The roots of this assumption may be traced to a typical behavior of monopolistic dealer who is primarily concerned with maintaining preferable bid/offer spread (Amihud & Mendelson, 1980). Consider a case when a large buy order wipes out entire inventory at the best offer price. As a result, the spread widens and the dealer responds to increase of demand by lifting the best bid price. However in modern limit order book (LOB) markets, multiple traders use market making strategy and fiercely compete for occupying the top of the order book. This competition may result not only in lifting the best bid but also in filling the liquidity gap on the offer side, which reduces MI. Negative autocorrelations of highfrequency FX returns that lead to mean reversion (Hashimoto et al, 2008; Chaboud et al, 2009), too, do not support the concept of permanent MI. Indeed, empirical findings in equities (Bouchaud et al, 2006)) and in FX (Schmidt, 2010) indicate that MI has powerlaw decay. There has been growing interest in describing MI in equities using the cumulative impulse response (CIR) that can be estimated using the structural vector autoregressive (VAR) equations (Hasbrouck, 1991; Engle & Patton, 2004; Mizrach, 2009; Hautsch & Huang, 2009). While the original Hasbrouck s model has two variables, returns and signed trading volumes 1), Mizrach (2009) and Hautsch & Huang (2009) have also included the variables describing the order book structure. Here I apply this approach to the global FX market. I Electronic copy available at: http://ssrn.com/abstract=1978977

introduce also a new variable, the inside-market signed order flow, for describing the competition among market makers. I apply the VAR model to EUR/USD and EUR/JPY for two distinct time periods. The first sample contains data for four weeks in February/March 2011 when whole-pip pricing was still used in the EBS market 2). The decimal-pip pricing was introduced later in March 2011 and the second sample contains data for four weeks in June 2011 when the EBS customer usage of decimal-pip pricing had rather stabilized. I consider one-second and ten-second time scales that have qualitatively different CIR. The main conclusion of this work is that the structural VAR yields power-law decay of MI at longer time intervals. While the signed trading volume determines most of MI, other market microstructure effects may also influence it. In the following Sections 2 5, I describe the model, data, results, and conclusions, respectively. 2. The model The structural VAR offered by Hasbrouck (1991) is derived in terms of two variables. The first one is log return for mid-point between the best bid price, b p t, and the best offer price, o p t b r t = log(( o b o p t + pt ) / 2) - log(( p + ) / t 1 pt 1 2) (1) The second variable is the signed trading volume x t n r x r t = H r (r, x) + ε r,t, H r (r, x) = ar, krt k + ax, k xt k (2) k= 1 k= 0 n

n r x x t = H x (r, x) + ε x,t, H x (r, x) = br krt k + n b x, x, k t k (3) k= 1 k= 1 The specific of the Hasbrouck s model (denoted here as VAR2(r, x)) is that the equation for r t includes contemporaneous value of x t (the term with k = 0), which implies an instant effect of trading volume. In this work, two variables are chosen to characterize the LOB effects. The first one is the signed order volume at best price, V 1 (the signed LOB top volume). The second variable is the signed LOB bulk volume, V a. For the whole-pip pricing, V a is chosen to be the signed aggregated order volume at the next four price levels behind the best price, regardless of whether they are populated. After introducing decimal-pip pricing, the orders that would be placed in the past at a single best price may be spread across several decimal levels. Therefore V a is chosen to be the signed order volume aggregated over first nine levels behind the best price. An alternative model derived in terms of the signed order counts N 1 and N a (as opposed to order volumes) was also briefly considered. A four-variable model, VAR4(r, x, V 1, V a ) has the following equation for r t r t = H r (r, x) + W r (V 1,, V a ) + n v 1 n v 5 ε r, t, W r (V 1,, V a ) = v + 1, kv1, t k k= 1 k = 1 a a V (4) Finally, the five-variable model, VAR5(r, x, V 1, V a, d), includes the signed aggregated volume of all orders, d t, that were submitted within the time interval [t-1, t] inside the market (i.e. with prices that are lower than the best offer at time t-1 and higher than the best bid at time t-1). r t = H r (r, x) + W r (V 1,, V a ) + D r (d) + ε r, t n d v 1 5, k a, t k, D r (d) = a d, k dt k (5) k= 0

Note that this model contains the contemporaneous term d t. The VAR equations for x, V 1, V a, and d have the similar form z t = H z (r, x) + W z (V 1,, V a ) + D z (d) + ε z, t (6) It is assumed that all shocks ε z, t have zero means and are jointly and serially uncorrelated. When the contributions of V 1 and V a were qualitatively similar, VAR4(r, x, V 1 +V a, d) was used instead of VAR5(r, x, V 1, V a, d). The CIR of return is calculated for the shock of x 0 = 1 assuming that V 1,0 = V a,0 = d 0 = 0 m CIR(m, x 0 ) = E[ r i x0 ] (7) i= 0 3. Data The EBS trading system (owned by ICAP Plc) is the major electronic institutional FX brokerage that has several specifics relevant for this work. First, EBS is essentially a limit-order market where transactions occur only when takers submit marketable limit orders. Hence the signed trading volume is calculated as the difference between the volume of trades initiated by takers submitting marketable bids and volume of trades initiated by takers submitting marketable offers. In limit order markets, MI depends not only on the order size but also on the order price. Indeed, a very large bid submitted at the best offer price can be matched only with the current inventory at this price. The rest of the order, depending on the trading workstation setup, may be either cancelled or stored in the order book as the new best bid.

There is a notable difference between the realized MI and expected MI (Schmidt, 2010). The former is smaller than the latter since those traders who do not have strict execution time constraints submit their orders at times of higher liquidity 3). Orders in the EBS market are submitted in units of millions of the base currency 4), 5). Therefore the trading volume of x 0 = 1 to EUR/USD or EUR/JPY has a meaning of a filled order with the size of one million of Euros. Two EBS market data samples for EUR/USD and EUR/JPY within the most liquid trading time 7:00 17:00 GMT on Mondays Fridays were used in this work. The first sample covers four weeks with whole-pip pricing: 7-Feb-2011 4-Mar-2011. Decimalpip pricing was introduced in Mid-March of 2011 and the second sample covers four weeks 6-Jun-2011 1-Jul-2011. EUR/USD is one of the most liquid currency pairs (on par with USD/JPY) with the bid/offer spread of about one pip. EUR/JPY has a higher spread of about 2 3 pips. There were 720020 and 72020 data records in each data set on the one-second and 10-second timescales, respectively. 4. Results All variables in the VAR models considered in this work had 20 lags. The VAR coefficients were estimated using the 3SLS/SUR method implemented in the RATS software package. The VAR coefficients in the equation for returns in VAR4(r, x, V 1 +V a, d) are listed in Table 1 and Table 2 for one-second and ten-second timescales, respectively. Many of these coefficients are statistically significant and their values decay rather slowly. In particular, negative autocorrelations in return are relatively strong on the ten-second timescale.

Table 1. The VAR coefficients for EUR/USD, 6-Jun-2011 1-Jul-2011 on the onesecond timescale. Table 2. The VAR coefficients for EUR/USD, 6-Jun-2011 1-Jul-2011 on the 10-second timescale 4.1 The one-second timescale While Mizrach (2009) indicated that the number of orders in the NASDAQ market is more informative than their aggregated volume, it is not the case in the FX market. Indeed the effect of signed order counts N 1 is much smaller than that of signed order volume V 1 (cf. CIR for VAR3(r, x, N 1 ) and VAR3(r, x, V 1 ) in Fig.2). This may be explained with that the counts of orders at given price are not observable in the EBS market while the aggregated order volumes are observable. Fig.1 Cumulative impulse response for EUR/USD with whole-pip pricing on one-second timescale. Fig.2 Cumulative impulse response for EUR/USD with decimal-pip pricing on onesecond timescale. The results on the one-second timescale for whole-pip pricing and decimal-pip pricing are qualitatively similar (cf. Fig.1 and Fig.2). First, the contribution of the LOB bulk

volume V a is much smaller than that of the LOB top volume V 1 (cf. CIR for VAR3(r, x, V a ) and VAR3(r, x, V 1 ). It seems that high-frequency traders (who usually trade with order size not exceeding 2MM) base their decisions on the volume at best price rather than on the order book depth. Somewhat paradoxical effect of V a in high-frequency market is that it actually decreases CIR. Hence while growing LOB top volume pushes price across the bid/offer spread, growing LOB bulk volume pulls price outside the market 6). The LOB push is actually described in the market microstructure literature. It is often worded in the following form: growing order volume at the best bid (offer) price increases probability that the next buyer (seller) submits a market order and hence fills the order at the best offer (bid) price (Parlour, 1989). Indeed, impatient traders may prefer to lose the spread for immediacy of execution. The LOB pull implies an opposite behavioral effect: if buyers (sellers) expect price to go down (up), they submit limit orders below (above) current best bid (offer) price. Then impatient sellers (buyers) may submit market orders. While the LOB pull is very subtle for EUR/USD with the bid/offer spread of about one pip, it is more pronounced for EUR/JPY with the spread of about 2 3 pips (see Fig.3). Fig.3. Cumulative impulse response for EUR/JPY with decimal-pip pricing on onesecond timescale. For EUR/USD, the effects of the inside-market signed order flow d and of the LOB top volume are comparable but their joint effect does not exceed 5% of CIR for whole-pip pricing and mere 1% for decimal pricing. Hence the Hasbrouck s model VAR2(r, x)

describes most of CIR. Yet for EUR/JPY, the inside-market signed order flow may increase CIR by about 20%. The VAR model on the one-second timescale does not exhibit decay of CIR. However, as it is shown below, this is a result of the limited model s memory (20 lags). 4.2 The ten-second timescale The 20-lag VAR model on the 10-second timescale covers significantly longer time interval and demonstrates pronounced decay within its memory span for both whole-pip pricing (Fig.4) and decimal pricing (Fig.5 and Fig.6). A power-law asymptote describes this decay with high degree of determination R 2 > 0.8. Fig.4. Cumulative impulse response for EUR/USD with whole-pip pricing on the 10- second timescale: a) entire time span; b) asymptotical behavior Fig.5. Cumulative impulse response for EUR/USD with decimal-pip pricing on the 10- second timescale: a) entire time span; b) asymptotical behavior Fig.6. Cumulative impulse response for EUR/JPY with decimal-pip pricing on the 10- second timescale: a) entire time span; b) asymptotical behavior

On the ten-second timescale, the LOB bulk pull disappears. For the whole-pip pricing in EUR/USD, the contributions of various order book factors into CIR satisfy the following condition (see Fig.5) CIR(d) < CIR(V a ) < CIR(V 1 ) (8) For decimal-pip pricing, the LOB top push practically disappears while the role of the inside-market signed order flow increases (see Fig.6). The condition (8) is now replaced with the following CIR(V 1 ) < CIR(V a ) < MI(d) (9) In general, the LOB volume and the inside-market signed order flow contribute about 5% into CIR of EUR/USD while the trading volume determines the rest. For the less liquid EUR/JPY, the LOB effects are negligible. However, the inside-market signed order flow may add about 15% to the total CIR (see Fig.6). 5. Conclusions The main conclusion in this work is that the structural VAR model exhibits decay of MI in the FX market. This decay becomes transparent at the time horizon of about 100 seconds and it seems to be determined by negative autocorrelations in returns. It should be noted that the power-law exponent in the range of ~ -0.04 that describes the MI decay is notably smaller than the exponent of ~ -0.4 found in empirical data (Schmidt, 2010). This difference can be explained with that the trading volume of x 0 = 1 is a small shock that yields a EUR/USD return of about 0.05 pips. On the other hand, Schmidt (2010) analyzed MI in the range 1 3 pips. There is no reason to believe that MI is a

linear function of the trading volume. Therefore the CIR estimates obtained with the linear VAR models can be used only for qualitative analysis of MI. The signed trading volume is the major factor that determines MI. The LOB effects have minor contributions to MI within the linear model. Yet one cannot exclude their subtle predictive power. The effects of the LOB push and the LOB pull outlined in this work deserve further analysis. Finally, it is found that the signed inside-market order flow may notably affect MI in currency pairs with wider bid/offer spreads.

Acknowledgments I thank George Li and Olivia Yao for valuable help with compiling and analysis of market data. I am grateful to Alain Chaboud and Clara Vega for their interest to this work and valuable comments. References Almgren, R. and N. Chriss, 2000. Optimal execution of portfolio transactions. J. Risk 3(2), 5 39. Amihud, Y., and H. Mendelson. 1980. Dealership markets: Market making with inventory. Journal of Financial Economics 8: 31 53. Bouchaud, J.-P., J. Kockelkoren, and M. Potters, 2006. Random walks, liquidity molasses and critical response in financial markets. Quantitative Finance, 6, N2, 115-123. Chaboud, A., Chiquoine, B., Hjalmarsson E., and Vega, C. 2009. Rise of the Machines: Algorithmic Trading in the Foreign Exchange Market. Board of Governors of the Federal Reserve System. International Finance Discussion Papers, No 980. Cohen K.J., S.F. Maier, R.A. Schwartz, and D.K. Whitcomb, 1981. Transaction costs, order placement strategy, and bid-ask spread. Journal of Political Economy 89, 287-305. Engle, R.F., and A.J. Patton, 2004. Impact of trades in an error-correction model of quote prices, Journal of Financial Markets 7, 1 25. Hasbrouck, J., 1991. Measuring the information content of stock trades, The Journal of Finance 46, 179 207. Hashimoto Y., T. Ito, M. Ohnishi, H. Takayasu, M. Takayasu and T. Watanabe, Random Walk or A Run: Market Microstructure Analysis of the Foreign Exchange Rate Movements based on Conditional Probability, 2008. NBER Working Paper 14160. Hautsch, N. and R. Huang, 2009. The market impact of a limit order. SFB 649 Discussion Paper 2009-051. Humboldt University, Berlin. Kissell, R. and M. Glantz, 2003. Optimal trading strategies, AMACOM. Parlour C.A., 1998. Price dynamics in limit order markets. Journal of Financial Studies 11, 789 816.

Schmidt, A.B., 2010. Optimal execution in the global FX market, Journal of Trading 5(3), 68-77. Weber, P. and B. Rosenow, 2005. Order book approach to price impact. Quantitative Finance, 5, 357 364.

Notes 1) In the signed trading volume, buy orders and sell orders are assigned positive and negative signs, respectively. Note that in the market microstructure literature, signed trading volume is sometimes called signed order flow. However, order flow equals trading volume only when all orders are market orders that are executed unconditionally. 2) FX prices are usually quoted with five significant digits and two last digits are called pips. Decimal pip pricing implies that FX price is quoted with six significant digits. 3) Similar differences between the realized MI and expected MI were found in equities (Weber & Rosenow, 2005). 4) Base (local) currency in the currency pair is the first (second) currency in its name. 5) The EBS market has separate liquidity pools for trading with the minimal order size of 100000 units of the base currency, which are not considered here. 6) Cohen et al (1981) used the term gravitational pull in the context of LOB. While comparing the LOB top push and the LOB bulk pull, one may find some similarity with physics of fluids since surface tension and bulk pressure act in the opposite directions.

Table 1 Lag x r V 1 +V a d Coefficient Significance Coefficient Significance Coefficient Significance Coefficient Significance 0 4.98E-06 <1.E-7 2.32E-07 <1.E-7 1 1.77E-08 1.34E-01-3.98E-03 8.03E-04 4.41E-07 <1.E-7 3.73E-08 1.54E-02 2-1.59E-08 1.78E-01-0.0104 <1.E-7-1.28E-07 <1.E-7 4.00E-08 9.34E-03 3-6.05E-08 3.30E-07 1.28E-04 9.15E-01-2.70E-08 6.00E-08 2.41E-09 8.76E-01 4-4.93E-08 3.17E-05 5.21E-03 1.21E-05-6.70E-09 1.80E-01-2.20E-09 8.86E-01 5-4.55E-09 7.01E-01 7.63E-04 5.21E-01-2.19E-08 1.19E-05 4.28E-08 5.44E-03 6-3.40E-08 4.09E-03-2.20E-03 6.51E-02-1.04E-08 3.64E-02-4.60E-09 7.65E-01 7-1.44E-08 2.26E-01 1.77E-03 1.36E-01 1.02E-09 8.38E-01-4.37E-09 7.76E-01 8-3.71E-09 7.54E-01-5.47E-03 4.29E-06-6.23E-09 2.12E-01-1.69E-09 9.13E-01 9-1.51E-08 2.03E-01-1.93E-03 1.06E-01-5.87E-09 2.39E-01 5.59E-09 7.17E-01 10 1.30E-08 2.72E-01-6.55E-03 4.00E-08-1.15E-08 2.13E-02-1.44E-08 3.49E-01 11 2.20E-08 6.37E-02-4.25E-03 3.62E-04 7.65E-09 1.25E-01 4.91E-09 7.50E-01 12 1.79E-08 1.32E-01-7.74E-03 <1.E-7 6.12E-10 9.02E-01 4.76E-09 7.57E-01 13 5.00E-09 6.73E-01-7.28E-03 <1.E-7 9.27E-10 8.53E-01 1.05E-08 4.95E-01 14-2.44E-08 3.97E-02-9.51E-04 4.25E-01-2.76E-09 5.81E-01-2.70E-08 7.89E-02 15 3.92E-09 7.40E-01-5.67E-03 1.96E-06-7.58E-09 1.29E-01-3.51E-08 2.24E-02 16-2.34E-08 4.86E-02 7.59E-04 5.24E-01 3.20E-09 5.21E-01 3.26E-09 8.32E-01 17-3.57E-08 2.56E-03-2.47E-03 3.77E-02-5.55E-09 2.66E-01-2.36E-08 1.25E-01 18-1.80E-08 1.29E-01 2.10E-03 7.82E-02-5.52E-09 2.68E-01-2.70E-08 7.98E-02 19 1.19E-08 3.15E-01-4.49E-03 1.65E-04-2.30E-09 6.43E-01-1.38E-08 3.68E-01 20 2.56E-08 2.89E-02-3.52E-03 2.65E-03-8.29E-11 9.85E-01-1.53E-08 3.18E-01 Table 2 Lag x r V 1 +V a d Coefficient Significance Coefficient Significance Coefficient Significance Coefficient Significance 0 4.74E-06 <1.E-7-8.31E-07 <1.E-7 1 9.03E-08 7.38E-03-5.50E-02 <1.E-7 8.50E-07 <1.E-7 2.91E-08 1.52E-01 2-1.44E-08 6.69E-01-2.75E-02 <1.E-7 6.60E-08 5.04E-02 1.92E-08 3.45E-01 3 1.53E-08 6.51E-01-1.96E-02 1.90E-07 2.26E-08 5.05E-01 2.07E-08 3.08E-01 4-8.93E-09 7.91E-01-1.49E-02 7.70E-05 2.09E-08 5.37E-01-2.68E-08 1.88E-01 5-1.52E-07 6.80E-06 1.44E-02 1.37E-04 1.03E-08 7.61E-01 4.80E-08 1.82E-02 6 7.18E-08 3.32E-02-3.75E-02 <1.E-7-4.51E-08 1.83E-01-5.11E-08 1.19E-02 7-1.17E-07 5.35E-04 8.94E-03 1.77E-02 1.07E-07 1.55E-03 1.93E-08 3.42E-01 8 3.40E-08 3.13E-01-9.31E-03 1.35E-02-2.33E-08 4.92E-01-5.57E-08 6.11E-03 9-6.01E-08 7.44E-02-3.70E-03 3.26E-01-1.26E-08 7.11E-01 1.28E-09 9.50E-01 10-2.93E-08 3.84E-01-1.38E-02 2.47E-04 6.67E-09 8.44E-01-5.62E-08 5.71E-03 11 5.11E-08 1.29E-01-8.22E-03 2.92E-02-4.88E-08 1.50E-01-2.02E-08 3.21E-01 12-9.94E-08 3.18E-03 1.23E-02 1.12E-03-8.83E-09 7.95E-01 1.50E-08 4.62E-01 13-1.70E-08 6.15E-01 1.88E-03 6.17E-01-4.41E-08 1.93E-01 2.78E-08 1.71E-01 14-1.19E-07 4.36E-04 6.16E-03 1.02E-01-4.99E-08 1.41E-01-1.96E-08 3.35E-01 15-1.93E-08 5.66E-01 6.70E-03 7.52E-02 1.55E-08 6.48E-01 5.73E-10 9.78E-01 16 1.58E-08 6.39E-01-1.44E-02 1.36E-04 3.31E-08 3.29E-01-1.06E-08 6.03E-01 17-1.12E-07 8.89E-04 3.51E-03 3.51E-01 3.71E-08 2.74E-01-2.09E-08 3.03E-01 18-2.16E-08 5.20E-01-1.01E-03 7.88E-01 1.55E-08 6.48E-01-2.09E-08 3.04E-01 19-6.65E-08 4.76E-02 2.96E-03 4.31E-01-3.20E-08 3.43E-01-2.16E-08 2.86E-01 20 3.72E-08 2.57E-01 1.37E-04 9.71E-01-3.25E-08 3.22E-01-3.13E-09 8.77E-01

Fig.1 5.6E-06 5.5E-06 5.4E-06 Cumulative impulse response, EUR 5.3E-06 5.2E-06 5.1E-06 5.0E-06 4.9E-06 VAR5(r,x,V1,Va), d) VAR3(r,x,d) VAR3(r,x,V1) VAR3(r,x,Va) VAR3(r,x,N1) VAR2(r,x) 4.8E-06 0 2 4 6 8 10 12 14 16 18 20 22 Time, sec

Fig.2 5.60E-06 5.50E-06 5.40E-06 Cumulative impulse response 5.30E-06 5.20E-06 5.10E-06 VAR4(r,x,V1+Va, d) VAR3(r,x,d) VAR3(r,x,V1) VAR2(r,x) VAR3(r,x,Va) 5.00E-06 4.90E-06 0 2 4 6 8 10 12 14 16 18 20 22 Time, sec

Fig.3 2.70E-05 2.50E-05 Cumulative impulse response 2.30E-05 2.10E-05 1.90E-05 1.70E-05 VAR4(r,x,V1+Va,d) VAR3(r,x,V1) VAR3(r,x,Va) VAR3(r,x,d) VAR2(r,x) 1.50E-05 0 2 4 6 8 10 12 14 16 18 20 22 Time, sec

Fig.4a 4.7E-06 4.6E-06 4.5E-06 VAR5(r,x,d,V1,Va) VAR3(r,x,V1) VAR3(r,x,Va) VAR3(r,x,d) VAR2(r,x) 4.4E-06 Cumulative impulse response 4.3E-06 4.2E-06 4.1E-06 4.0E-06 3.9E-06 3.8E-06 3.7E-06 0 20 40 60 80 100 120 140 160 180 Time, sec

Fig.4b 4.6E-06 VAR5 VAR2 Power (VAR5) Power (VAR2) 4.4E-06 y = 5E-06x -0.0422 R 2 = 0.8139 4.2E-06 4.0E-06 y = 4E-06x -0.0576 R 2 = 0.935 3.8E-06 3.6E-06 10 30 50 70 90 110 130 150 170 190

Fig.5a 5.40E-06 5.20E-06 5.00E-06 Cumulative impulse response 4.80E-06 4.60E-06 4.40E-06 VAR4(r,x,V1+Va,d) VAR3(r,x,d) VAR3(r,x,Va) VAR3(r,x,V1) VAR2(r,x) 4.20E-06 0 20 40 60 80 100 120 140 160 180 200 220 Time, sec

Fig.5b 5.4E-06 5.2E-06 5.0E-06 y = 5E-06x -0.0449 R 2 = 0.8933 VAR4 VAR2 Power (VAR4) Power (VAR2) 4.8E-06 4.6E-06 y = 5E-06x -0.0408 R 2 = 0.864 4.4E-06 4.2E-06 10 30 50 70 90 110 130 150 170 190

Fig.6a 2.3E-05 2.2E-05 2.1E-05 VAR4(r,x,V1+Va,d) VAR3(r,x,V1) VAR3(r,x,Va) VAR3(r,x,d) VAR2(r,x) Cumulative impulse response 2.0E-05 1.9E-05 1.8E-05 1.7E-05 1.6E-05 1.5E-05 0 20 40 60 80 100 120 140 160 180 200 220 Time, sec

Fig.6b 2.5E-05 2.3E-05 VAR4 VAR2 Power (VAR4) Power (VAR2) 2.1E-05 y = 5E-06x -0.0422 R 2 = 0.8139 1.9E-05 1.7E-05 y = 4E-06x -0.0576 R 2 = 0.935 1.5E-05 10 30 50 70 90 110 130 150 170 190