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Central Bank Intervention Under Target Zones: the Portuguese Escudo in the ERM

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(14)

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(15)

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(16)

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(17)

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(18)

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(19)

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Table 1: MSEGARCH Estimation Results

ERM S ERM 6 ERM 15

Parameter Estimate Std. Error Estimate Std. Error Estimate Std. Error

Mean 10 α -0.0440 0.0188** 0.0206 0.0171 -0.0083 0.0042** 20 α 0.0210 0.0147* 1.3694 0.2212** 0.0048 0.0064 11 α -0.3480 0.0798**   -0.4052 0.0407** 21 α -0.1727 0.0570**   -0.1589 0.0364** 12 α     -0.1027 0.0358** 22 α     -0.0701 0.0281** I 1 α 0.5672 0.1656** 0.2905 0.1022**   I 2 α       D 1 α -0.0307 0.0129**   -0.0533 0.0080** D 2 α   -0.5325 0.0772** Variance 1 0 β -1.7865 0.8673** -2.1055 0.3182** -2.2358 0.3925** 2 0 β -1.0468 0.2913** -1.7153 0.3972** -2.2631 0.4180** | | 1 e β 0.4158 0.2090** 0.4958 0.1304** | | 2 e β 0.4953 0.1241** 0.9561 0.3209** 0.5988 0.1222** v 1 β 0.5220 0.2660**   0.5107 0.0918** v 2 β 0.7057 0.1062**   0.3216 0.1406** | | 1 D β -0.1270 0.0745**   | | 2 D β TVTP 10 γ 2.3742 0.7286** 2.3259 0.2335** 2.9530 0.3943** 20 γ 2.8603 0.7856** 1.3861 0.4145** 2.8992 0.1963** | | 1 I γ -1.1028 0.5678** -0.0389 0.0249* | | 2 I γ -1.1384 0.5098**     1 d 5.0783 1.7604** 2.8172 0.3066** 2 d 5.1138 0.8600** 3.1712 0.4141** N. Obs. 633 438 1358

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Table 1 (continued): MSEGARCH Estimation Results

ERM S ERM 6 ERM 15

Log-Likelihood -20.3 -142.6 484.5. AIC -36.3 -155.4 467.5 SBC -71.9 -180.4 423.2 Diagnostics LB1 0.1609 (0.6883) 0.0309 (0.8606) 1.6842 (0.1944) LB2 1.6936 (0.4288) 0.4600 (0.7945) 2.5075 (0.2854) LB3 1.8364 (0.6070) 1.3105 (0.7266) 3.6172 (0.3059) LB5 6.5247 (0.2585) 1.5975 (0.9016) 7.3356 (0.1969) LB10 15.5343 (0.1138) 6.6423 (0.7587) 10.0977 (0.4320) LB15 18.9789 (0.2147) 13.6070 (0.5555) 20.0782 (0.1690) LM1 0.0398 (0.8418) 0.0262 (0.8713) 0.0947 (0.7583) LM2 0.3407 (0.8434) 0.0365 (0.9819) 0.1758 (0.9159) LM3 1.0791 (0.7821) 0.0370 (0.9981) 0.2965 (0.9607) LM5 1.7351 (0.8844) 0.1049 (0.9998) 0.2988 (0.9977) LM10 2.9764 (0.9820) 0.2412 (1.0000) 0.5173 (1.0000) LM15 4.6686 (0.9946) 0.4484 (1.0000) 3.9165 (0.9980)

Notes: The variables are defined as in the text. A double (single) asterisk means that the estimated parameter is significantly different from zero at a 5% (10%) level. A degree of freedom di = +∞

denotes a Normal distribution in the i-th regime. LBt denotes the Ljung-Box statistic for serial correlation in the standardised residuals up to lag t. LMt denotes the ARCH-LM statistic for the squared standardised residuals up to lag t. The p-values corresponding to these statistics are in given parenthesis.

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Figure 1: Daily Percentage Deviation of PTE/DEM from Central Parity -6 -5 -3 -2 0 2 3 5 6 8 21/09/1989 21/03/1990 21/09/1990 21/03/1991 21/09/1991 21/03/1992 21/09/1992 21/03/1993 21/09/1993 21/03/1994 21/09/1994 21/03/1995 21/09/1995 21/03/1996 21/09/1996 21/03/1997 21/09/1997 21/03/1998 21/09/1998

ERM S ERM 6 ERM 15

Note: The Portuguese Escudo was realigned on the following dates: November 23, 1992;

May 14, 1993; and March 6, 1995. The first realignment occurred in the wake of the 1992 ERM crisis whilst the others were the result of the PTE following the realignments of the Spanish Peseta.

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Figure 2: Smoothed Probabilities of the High-Volatility Regime ERM S 0.0 0.2 0.4 0.6 0.8 1.0 9/21/89 6/28/90 4/04/91 1/09/92

Figure 3: Smoothed Probabilities of the High-Volatility Regime ERM 6 0.0 0.2 0.4 0.6 0.8 1.0 4/06/92 8/24/92 1/11/93 5/31/93

Figure 4: Smoothed Probabilities of the High-Volatility Regime ERM 15 0.2 0.4 0.6 0.8 1.0

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(30)

Table A.2.1:

Whole Sample Period: January, 7 1987 – December, 31 1998

Model 1 without Intervention or Central Parity k log-lik MSE MAE AIC SBC

Single Regime ARCH – constant variance 3 -1682.94 1432.41 15.99 -1685.94 -1692.59 Single Regime ARCH – arch terms 5 -1601.87 2037.89 18.06 -1606.87 -1617.95 SWARCH (2,2) 8 -1527.11 1599.19 15.96 -1535.11 -1552.84 SWARCH (3,2) 11 -1502.12 1458.20 14.56 -1513.12 -1537.51 SWARCH (4,2) 15 -1491.46 1423.61 14.66 -1506.46 -1539.71 SWARCH (5,1) 18 -1488.53 1298.66 14.08 -1506.53 -1546.42

Model 2 with Intervention and Central Parity k log-lik MSE MAE AIC SBC

Single Regime ARCH – constant variance 9 -1655.49 1284.93 15.01 -1687.20 -1702.71 Single Regime ARCH – 2 arch terms 11 -1579.74 1878.86 17.50 -1590.74 -1675.44 SWARCH (2,2) 14 -1511.74 1361.98 14.55 -1525.74 -1556.77 SWARCH (3,2) 17 -1492.84 1334.20 14.17 -1509.84 -1547.52 SWARCH (4,2) 22 -1487.42 1385.37 14.19 -1509.42 -1558.18 SWARCH (5,1) – no convergence - - - -

Model 3 with Intervention and Central Parity k log-lik MSE MAE AIC SBC

Single Regime ARCH – constant variance 7 -1647.01 1282.93 15.01 -1654.01 -1669.52 Single Regime ARCH – 2 arch terms 9 -1579.75 1879.11 17.50 -1588.75 -1608.70 SWARCH (2,2) 12 -1511.78 1362.25 14.55 -1523.78 -1550.36 SWARCH (3,2) 15 -1494.78 1333.85 14.22 -1509.78 -1543.02 SWARCH (4,2) 20 -1487.46 1391.80 14.20 -1507.46 -1551.77 SWARCH (5,1) – no convergence - - - -

Note: k denotes the number of estimated parameters and log-lik the value of the log-likelihood function. All other

designations have the usual interpretations.

Are the Estimated Parameters Significant?

Model 2 with Intervention and Central Parity Mean Variance

Purchases Sales C. Parity Purchases Sales C. Parity

Single Regime ARCH - constant variance Yes** No Yes** No No Yes** Single Regime ARCH – 2 arch terms No No Yes** No No Yes** SWARCH (2,2) Yes* No No No No Yes** SWARCH (3,2) Yes** No Yes** No No No SWARCH (4,2) No No Yes* No No No SWARCH (5,1) - no convergence - - - -

Model 3 with Intervention and Central Parity Mean Variance

Purchases Sales C. Parity C. Parity

Single Regime ARCH - constant variance Yes** No Yes** Yes** Single Regime ARCH – 2 arch terms No No Yes** Yes** SWARCH (2,2) Yes* No No Yes**

SWARCH (3,2) No Yes** Yes** No SWARCH (4,2) No No Yes* Yes*

(31)

Table A.2.2:

Truncated Sample: September 21, 1989 - December 31, 1998

Model 1 without Intervention or Central Parity k log-lik MSE MAE AIC SBC SWARCH (2,2) 8 -1188.01 2091.81 18.91 -1196.01 -1212.70 SWARCH (3,2) 11 -1167.54 1783.63 16.76 -1178.54 -1201.50 SWARCH (4,2) 16 -1158.17 1789.16 16.14 -1174.17 -1207.56

Model 2 with Intervention and Central Parity k log-lik MSE MAE AIC SBC SWARCH (2,2) 14 -1180.65 1869.10 17.96 -1194.65 -1223.86 SWARCH (3,2) 17 -1166.04 1723.88 16.22 -1183.04 -1218.52 SWARCH (4,2) 22 -1156.46 1743.09 16.17 -1178.46 -1224.37

Model 3 with Intervention and Central Parity k log-lik MSE MAE AIC SBC SWARCH (2,2) 12 -1182.06 1665.75 16.90 -1194.06 -1219.11 SWARCH (3,2) 15 -1166.65 1720.96 16.20 -1181.65 -1212.96 SWARCH (4,2) 20 -1156.56 1743.54 16.19 -1176.56 -1218.30 Note: k denotes the number of estimated parameters and log-lik the value of the log-likelihood function. All other

designations have the usual interpretations.

Are the Estimated Parameters Significant?

Model 2 with Intervention and Central Parity Mean Variance Purchases Sales C. Parity Purchases Sales C. Parity

SWARCH (2,2) No Yes* No No No Yes**

SWARCH (3,2) No No Yes** No No No

SWARCH (4,2) No No Yes** No No No

Model 3 with Intervention and Central Parity Mean Variance Purchases Sales C. Parity C. Parity

SWARCH (2,2) Yes* No No Yes**

SWARCH (3,2) No No Yes** No

SWARCH (4,2) No No Yes** No

(32)

Table A.2.3:

Inconvertible Escudo: September 21, 1989 – December, 9 1992

Model 1 without Intervention or Central Parity k log-lik MSE MAE AIC SBC

SWARCH (2,2) 8 -464.41 1235.12 21.55 -472.41 -484.84

SWARCH (3,1) 10 -459.95 1059.04 20.63 -469.95 -485.48

Model 2 with Intervention and Central Parity k log-lik MSE MAE AIC SBC

SWARCH (2,2) 14 -461.58 1015.89 19.21 -475.58 -497.32

SWARCH (3,1) 16 -457.28 953.60 19.28 -473.28 -498.12

Model 3 with Intervention and Central Parity k log-lik MSE MAE AIC SBC

SWARCH (2,2) 12 -461.56 1014.00 19.23 -473.56 -492.19

SWARCH (3,1) 14 -458.27 985.34 19.80 -472.27 -494.01

Note: k denotes the number of estimated parameters and log-lik the value of the log-likelihood function. All other

designations have the usual interpretations.

Are the Estimated Parameters Significant?

Model 2 with Intervention and Central Parity Mean Variance Purchases Sales C. Parity Purchases Sales C. Parity

SWARCH (2,2) No No No No No No

SWARCH (3,1) No No Yes** No No Yes*

Model 3 with Intervention and Central Parity Mean Variance Purchases Sales C. Parity C. Parity

SWARCH (2,2) No No Yes* No

SWARCH (3,1) No No Yes* No

(33)

Table A.2.4:

Convertible Escudo: December, 16 1992 – December, 31 1998

Model 1 without Intervention or Central Parity k log-lik MSE MAE AIC SBC

SWARCH (2,2) 8 -702.83 3048.91 17.65 -710.83 -725.80

SWARCH (3,2) 12 -690.38 2377.05 15.34 -702.38 -724.84

Model 2 with Intervention and Central Parity k log-lik MSE MAE AIC SBC

SWARCH (2,2) 14 -683.94 2469.30 17.05 -697.94 -724.14

SWARCH (3,2) 18 -681.84 2408.57 15.69 -699.84 -733.52

Model 3 with Intervention and Central Parity k log-lik MSE MAE AIC SBC

SWARCH (2,2) 12 -684.67 2409.46 16.96 -696.67 -719.12

SWARCH (3,2) 16 -681.90 2385.10 15.60 -697.90 -727.85

Note: k denotes the number of estimated parameters and log-lik the value of the log-likelihood function. All other

designations have the usual interpretations.

Are the Estimated Parameters Significant?

Model 2 with Intervention and Central Parity Mean Variance Purchases Sales C. Parity Purchases Sales C. Parity

SWARCH (2,2) No Yes** No No No Yes**

SWARCH (3,2) No No Yes* No No Yes*

Model 3 with Intervention and Central Parity Mean Variance Purchases Sales C. Parity C. Parity

SWARCH (2,2) No Yes** No Yes*

SWARCH (3,2) No No Yes** Yes*

(34)

Figure A.2.1: Inconvertible Escudo– SWARCH (2,2) model Smoothed Probability of the High Volatility State

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 20/09/1989 20/12/1989 20/03/1990 20/06/1990 20/09/1990 20/12/1990 20/03/1991 20/06/1991 20/09/1991 20/12/1991 20/03/1992 20/06/1992 20/09/1992

Note: The SWARCH (2,2) model is chosen using the SBC criterion when considering the top three panels of Table A.2.3.

Figure A.2.2: Convertible Escudo – SWARCH (2,2) model Smoothed Probability of the High Volatility State

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 16/12/1992 16/06/1993 16/12/1993 16/06/1994 16/12/1994 16/06/1995 16/12/1995 16/06/1996 16/12/1996 16/06/1997 16/12/1997 16/06/1998 16/12/1998

Note: The SWARCH (2,2) model is chosen using the SBC criterion when considering the top three panels of Table A.2.4.

(35)

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(36)

Table A.3.1: Descriptive Statistics for the Daily Exchange Rate Returns ERM S

(1989/09/21 – 1992/04/03)

ERM 6

(1992/04/04 – 1993/08/02)

Variable Statistic Value Null Hypothesis p-value

Minimum -1.517 Maximum 1.840 Median 0.005 Mean 0.005 H0: Mean=0 0.652 Std Deviation 0.295 Skewness 0.709 H0: Sk=0 0.000 Kurtosis 8.998 H0: K=0 0.000 Jarque-Bera 1003.691 H0: Normality 0.000 (1) -0.179 Q(20) 41.875 H0: No Autocorrelation 0.003 LM(20) 37.733 H0: No ARCH 0.000

log St ADF -3.145 H0: Unit Root -2.867*

Phillips-Perron -3.438 H0: Unit Root -2.867*

Variable Statistic Value Null Hypothesis p-value

Minimum -2.881 Maximum 4.696 Median 0.012 Mean 0.044 H0: Mean=0 0.182 Std Deviation 0.626 Skewness 1.388 H0: Sk=0 0.000 Kurtosis 24.017 H0: K=0 0.000 Jarque-Bera 6797.496 H0: Normality 0.000 (1) -0.282 Q(20) 40.358 H0: No Autocorrelation 0.003 LM(20) 56.658 H0: No ARCH 0.000

log St ADF 0.559 H0: Unit Root -2.870*

Phillips-Perron 0.402 H0: Unit Root -2.867*

t st s

(37)

Table A.3.1 (continued): ERM 15

(1993/08/03 – 1998/12/31)

Note: St is the PTE/DEM exchange rate while st denotes 100 times the log difference of the

exchange rate. (1)denotes the value of the autocorrelation function at the first lag and Q(20) is

the Ljung-Box Q-statistic with a lag-length of 20 periods. LM(20) denotes the ARCH-LM statistic for the squared standardised residuals with a lag-length of 20 periods. The fourth column gives the null hypotheses of the tests that were conducted. For example, the Jarque-Bera statistic tests for Normality while the ADF/Phillips-Perron procedures test for the presence of unit roots. The last column contains the corresponding p-values, except for the case of the unit root tests where an asterisk denotes the test’s 5% critical value.

Variable Statistic Value Null Hypothesis p-value

Minimum -1.313 Maximum 1.478 Median 0.0008 Mean -0.001 H0: Mean=0 0.849 Std Deviation 0.207 Skewness -0.152 H0: Sk=0 0.027 Kurtosis 10.507 H0: K=0 0.000 Jarque-Bera 2982.689 H0: Normality 0.000 (1) -0.237 Q(20) 106.83 H0: No Autocorrelation 0.000 LM(20) 83.732 H0: No ARCH 0.000

log St ADF -1.871 H0: Unit Root -2.865*

Phillips-Perron -2.489 H0: Unit Root -2.864*

t

s

(38)

Figure A.3.1: Daily Percentage Change in PTE/DEM -4 -3 -2 -1 0 1 2 3 4 21/09/1989 21/03/1990 21/09/1990 21/03/1991 21/09/1991 21/03/1992 21/09/1992 21/03/1993 21/09/1993 21/03/1994 21/09/1994 21/03/1995 21/09/1995 21/03/1996 21/09/1996 21/03/1997 21/09/1997 21/03/1998 21/09/1998

Imagem

Table 1: MSEGARCH Estimation Results
Figure 1: Daily Percentage Deviation of PTE/DEM from Central Parity  -6-5-3-2023568 21/09/1989 21/03/1990 21/09/1990 21/03/1991 21/09/1991 21/03/1992 21/09/1992 21/03/1993 21/09/1993 21/03/1994 21/09/1994 21/03/1995 21/09/1995 21/03/1996 21/09/1996 21/03/1
Figure 2: Smoothed Probabilities of the High-Volatility Regime   ERM S   0.00.20.40.60.81.0 9/21/89 6/28/90 4/04/91 1/09/92
Figure A.2.1: Inconvertible Escudo– SWARCH (2,2) model  Smoothed Probability of the High Volatility State
+4

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