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Table 3 Continued
Model NL
Model L-I
Model L-II
Model L-IId
Log Price Level
dlog Q
t
=…(x
t
)dt + ¾
0
q
dB
t
?
q
dB
?
t
, …(x
t
)= ‰
0
+‰
0
1
x
t
0
0.0271 ( 0.0035)
0.0280 ( 0.0069)
0.0239 ( 0.0082)
0.0236
(0.0084)
1;1
-0.7843 ( 2.8227)
0.8836 ( 1.4332)
0.0746 ( 0.6436)
0.0729
(0.5890)
1;2
0.0766 ( 0.1062)
0.2563 ( 0.0707)
0.2575 ( 0.1262)
0.2443
(0.1248)
1;3
-0.5094 ( 0.3937)
0.1216 ( 0.1276) -0.0165 ( 0.2079)
-0.0221
(0.2107)
100 £ ¾
q;1
-0.1724 ( 0.0651) -0.1176 ( 0.0720) -0.1050 ( 0.0763)
-0.1076
(0.0757)
100 £ ¾
q;2
-0.0231 ( 0.0803)
0.0597 ( 0.0750)
0.0651 ( 0.0757)
0.0506
(0.0750)
100 £ ¾
q;3
-0.0016 ( 0.0656)
0.0354 ( 0.0594)
0.0306 ( 0.0611)
0.0358
(0.0609)
100 £ ¾
?
q
0.7795 ( 0.0288)
0.7279 ( 0.0241)
0.7144 ( 0.0245)
0.7144
(0.0245)
TIPS Liquidity Premium
l
t
=~°~x
t
0x
t
, d~x
t
=~•(~„ ¡ ~x
t
)dt + ~¾dW
t
,
~
t
=
~
0
+
~
1
~x
t
:
0.6114 ( 0.0411)
0.6152 ( 0.0415)
1.2545
(0.0914)
~•
0.2083 ( 0.2655)
0.2206 ( 0.2630)
0.6037
(0.3973)
~„
0.0218 ( 0.0113)
0.0157 ( 0.0115)
0.0003
(0.0105)
~
0
0.3213 ( 0.6657)
0.2851 ( 0.5090)
-0.0263
(0.3356)
~
1
-0.1091 ( 0.2652) -0.1209 ( 0.2627)
-0.1472
(0.4020)
°
1
-0.6765 ( 1.2459)
-2.9521
(5.7532)
°
2
-0.0179 ( 0.1547)
0.2739
(0.1717)
°
3
-0.0833 ( 0.2509)
-1.0137
(0.3285)
c
1
1.1871
(0.0310)
c
2
0.0014
(0.0001)
c
3
731467.911 ( 25.2593)
48
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Table 3 Continued
Model NL
Model L-I
Model L-II
Model L-IId
Measurement Errors: Nominal Yields
100 £ –
N;3m
0.1005
(0.0026)
0.1012
(0.0027)
0.1012
(0.0027)
0.1013
(0.0027)
100 £ –
N;6m
0.0231
(0.0016)
0.0221
(0.0016) -0.0222
(0.0016) -0.0224
(0.0017)
100 £ –
N;1y
0.0532
(0.0017)
0.0530
(0.0018)
0.0530
(0.0018)
0.0531
(0.0017)
100 £ –
N;2y
0.0000 (140.6008) -0.0000 ( 59.2489) -0.0000 ( 50.6589) -0.0000 ( 27.7162)
100 £ –
N;4y
0.0293
(0.0012)
0.0294
(0.0012)
0.0294
(0.0013)
0.0294
(0.0012)
100 £ –
N;7y
0.0000 (120.1913)
0.0000
(0.9395)
0.0000 ( 44.6608) -0.0000
(0.9058)
100 £ –
N;10y
0.0489
(0.0018)
0.0490
(0.0019)
0.0490
(0.0019)
0.0489
(0.0018)
Measurement Errors: TIPS Yields
100 £ –
T;5y
0.4307
(0.0953)
0.0654
(0.0059)
0.0657
(0.0060) -0.0000
(4.8466)
100 £ –
T;7y
0.3511
(0.0832) -0.0021
(0.0414) -0.0004
(0.2385) -0.0428
(0.0035)
100 £ –
T;10y
0.3578
(0.0802)
0.0647
(0.0060) -0.0643
(0.0059) -0.0520
(0.0038)
Measurement Errors: Survey Forecasts of Nominal Short Rate
100 £ –
f;6m
0.1760
(0.0135)
0.1758
(0.0134)
0.1758
(0.0134)
0.1758
(0.0134)
100 £ –
f;12m
0.2261
(0.0197)
0.2260
(0.0196)
0.2260
(0.0197)
0.2261
(0.0196)
This table reports parameter estimates and standard errors for all four models we estimate. Standard errors
are calculated using the BHHH formula and are reported inparentheses.
49
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Table 4: Specification Tests
Model NL
Model L-I
Model L-II Model L-IId
Panel A: Overall model fit
No. of parameters
42
47
50
53
Log likelihood
53,663.65
55,972.49
55,976.70
56,193.41
AIC
-107,243.30 -111,850.97 -111,853.40
-112,280.81
BIC
-107,041.70 -111,625.37 -111,613.39
-112,026.41
LR p-value
0:00
0.04
0:00
Panel B: Fitting TIPS yields
5-year
CORR (in %)
93.14
99.41
99.42
99.53
RMSE
0.43
0.13
0.13
0.11
R
2
(in %)
83.93
98.61
98.62
99.06
7-year
CORR (in %)
92.99
99.45
99.46
99.50
RMSE
0.36
0.10
0.10
0.10
R2 (in %)
85.96
98.91
98.92
98.93
10-year CORR (in %)
92.52
99.19
99.20
99.42
RMSE
0.37
0.12
0.11
0.10
R
2
(in %)
80.90
98.18
98.21
98.76
Panel C: Fitting TIPS Breakeven Inflation
7-year
CORR (in %)
51.61
97.21
97.24
97.35
RMSE
0.35
0.09
0.09
0.10
R
2
(in %)
23.44
94.47
94.54
94.21
10-year CORR (in %)
32.08
94.76
94.80
95.11
RMSE
0.35
0.11
0.11
0.10
R2 (in %)
-18.12
88.71
88.85
89.74
Panel D: Matching survey inflation forecasts
1-year
CORR (in %)
2.07
62.94
88.65
88.08
RMSE
0.78
0.58
0.33
0.34
R
2
(in %)
-52.21
17.45
72.93
70.71
10-year CORR (in %)
73.34
72.72
83.86
83.92
RMSE
0.51
0.40
0.42
0.42
R
2
(in %)
17.36
49.46
44.35
42.22
This table reports various diagnostic statistics for the four models estimated. Panel A reports the
number of parameters, the log likelihood, the Akaike information criterion (AIC), the Bayesian
information criterion (BIC) values, and the p-value from a Likelihood Ratio test of the current
model against the more general Model to its right, where the p-values reported for Models NL
and L-II are the Davie (1987) upper bounds. Panels B to D report three goodness-of-fit statistics
for the 5-, 7- and 10-year TIPS yields, 7- and 10-year TIPS breakeven inflation and 1- and 10-
year survey inflation forecasts, respetively, including the root mean squared fittederrors (RMSE),
the correlation between the fitted series and the data counterpart (CORR), and the coefficient of
determination (R
2
)as defined in Equation (52).
50
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Table 5: TIPS Bid-Ask Spreads Across Maturities (in ticks)
Less than five years
Five to Ten Years
Above ten years
2003
1to2
2
4to 16
Two-year
Five-year
Ten-Year
Twenty-Year
Thirty-year
2007
1/2 to 1
1
1-2
4-6
6-10
This table reports the TIPS bid-ask spread at various maturities based on two informal survey
conducted by the Federal Reserve Bank of New York in 2003 and 2007, respectively. One tick is
1/32s of a point where a point roughly equals one percent of the security’s par value.
Table 6: What Drives the TIPS Liquidity Premiums
Panel A: Regression Analysis
Coefficients
Adjusted
Maturity
Constant Turnover Imp Vol ASW Spread
R2
5-year
0.3074
-0.4309
0.1196
0.0258
79.52%
(0.0771) (0.0275) (0.0095)
(0.0025)
7-year
0.4139
-0.3752
0.0824
0.0253
80.95%
(0.0641) (0.0229) (0.0079)
(0.0020)
10-year
0.5076
-0.3337
0.0465
0.0251
82.30%
(0.0541) (0.0193) (0.0067)
(0.0017)
Panel B: In-Sample Correlations
Liquidity Premiums
TIPS
10-Year
5-year
7-year
10-year
Turnover Imp Vol
TIPS Turnover
-0.7286 -0.7547 -0.7850
10-year implied volatility
0.5515
0.5098
0.4449
-0.1314
On/off ASW spread
0.7996
0.8189
0.8340
-0.6374
0.4742
Panel A regresses 5, 7- and 10-year TIPS liquidity premium estimates based on Model L-IId
onTIPS turnover, implied volatilityof 10-year nominal Treasuryfuture options andthe difference
betweenthe on-the-run andtheoff-the-run10-year Treasuries par assetswap spreads using weekly
data from either Jan. 6, 1999 to Mar. 14, 2007. Their in-sample pairwise correlations are reported
in Panel B.
51
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Table 7: Variance decomposition of TIPS Yields and TIPS BEI
Panel A: Unconditional Variance Decomposition
TIPS yield
TIPS BEI
Maturity real yield liq prem
inf exp
inf risk prem
liq prem
5-year
1.1717
-0.1717
0.5870
0.1890
0.2240
(0.2836) (0.2836)
(0.3050)
(0.2386)
(0.3170)
7-year
1.1819
-0.1819
0.5659
0.1994
0.2347
(0.2690) (0.2690)
(0.3065)
(0.2616)
(0.3131)
10-year
1.1910
-0.1910
0.5453
0.2090
0.2458
(0.2581) (0.2581)
(0.3192)
(0.2944)
(0.3095)
Panel B: Instantaneous Variance Decomposition
TIPS yield
TIPS BEI
Maturity real yield liq prem
inf exp
inf risk prem
liq prem
5-year
1.1596
-0.1596
0.5447
0.0167
0.4386
(0.2963) (0.2963)
(0.2473)
(0.2064)
(0.2639)
7-year
1.2285
-0.2285
0.5500
0.0239
0.4261
(0.3040) (0.3040)
(0.2710)
(0.2397)
(0.2597)
10-year
1.3024
-0.3024
0.5431
0.0348
0.4221
(0.3073) (0.3073)
(0.2984)
(0.2740)
(0.2556)
Note: This table reports the unconditional and the instantaneous variance decomposi-
tions of TIPS yields into real yields and TIPS liquidity premiums, and of nominal yields
into expected inflation, the inflation risk premiums and the negative of TIPS liquidity pre-
miums, all based on Model L-IId estimates. The variance decompositions of TIPS yields
are calculated according to
1=
cov
¡
yT
t;¿
;yR
t;¿
¢
var
¡
yT
t;¿
¢
+
cov
¡
yT
t;¿
;L
t;¿
¢
var
¡
yT
t;¿
¢
;
while the variancedecompositions of theTIPS breakeveninflationarecalculatedaccording
to
1=
cov
¡
BEI
T
t;¿
;I
t;¿
¢
var
¡
BEI
T
t;¿
¢
+
cov
¡
BEI
T
t;¿
;}
I
t;¿
¢
var
¡
BEI
T
t;¿
¢
+
cov
¡
BEI
T
t;¿
;¡L
t;¿
¢
var
¡
BEI
T
t;¿
¢
;
where the results are based on either the unconditional variance-covariance matrix of the
state variables (Panel A) or the instantaneous variance-covariance matrix of the state vari-
ables, §§
0
(Panel B). Standard errors calculated using the delta method are reported in
parentheses.
52
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Table 8: Variance decomposition of Nominal Yields
Panel A: Unconditional Variance Decomposition
Maturity
real yield
inf exp
inf risk prem
1-quarter
0.5108
0.4156
0.0736
(0.2541) (0.2281)
(0.0927)
1-year
0.5715
0.3497
0.0787
(0.1930) (0.1843)
(0.0924)
5-year
0.6503
0.2609
0.0888
(0.1486) (0.1417)
(0.1146)
10-year
0.6715
0.2347
0.0938
(0.1401) (0.1429)
(0.1362)
Panel B: Instantaneous Variance Decomposition
Maturity
real yield
inf exp
inf risk prem
1-quarter
0.7719
0.2252
0.0029
(0.1090) (0.1009)
(0.0312)
1-year
0.7692
0.2172
0.0137
(0.1082) (0.0915)
(0.0365)
5-year
0.7132
0.2496
0.0372
(0.1231) (0.1154)
(0.0970)
10-year
0.6892
0.2494
0.0614
(0.1331) (0.1438)
(0.1345)
Note: This table reports the unconditional and the instantaneous variance decomposi-
tions of nominal yields into real yields, expected inflation, the inflation risk premiums, all
based on Model L-IId estimates. The variance decomposition is calculated according to
1=
cov
¡
y
N
t;¿
;y
R
t;¿
¢
var
¡
y
N
t;¿
¢
+
cov
¡
y
N
t;¿
;I
t;¿
¢
var
¡
y
N
t;¿
¢
+
cov
¡
y
N
t;¿
;}
I
t;¿
¢
var
¡
y
N
t;¿
¢
;
where the results are based on either the unconditional variance-covariance matrix of the
state variables (Panel A) or the instantaneous variance-covariance matrix of the state vari-
ables, §§
0
(Panel B). Standard errors calculated using the delta method are reported in
parentheses.
53
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1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
0
20
40
60
80
Gross TIPS Issuance (in billions of dollars)
10−year
5−year
20−year
30−year
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
0
100
200
300
400
500
TIPS Outstanding (in billions of dollars)
Less than 2 years
2− to 5−year
5− to 10−year
10− to 20−year
20− to 30−year
Figure 1: TIPS Issuance and Outstanding
The top panel plots gross TIPS issuance broken down by initial maturities of 10, 5, 20 and 30
years. The bottom panel plots TIPS outstanding broken down by remaining maturities, based on
data reported in the Treasury’s Monthly Statement of the Public Debt (MSPD).
54
2000
2001
2002
2003
2004
2005
2006
2007
0
2
4
6
8
10
TIPS Transaction Volumes (in billions of dollars)
2000
2001
2002
2003
2004
2005
2006
2007
0
20
40
60
80
Total Net Assets (in $bil)
−10
5
20
35
50
# of Funds
Number of TIPS Mutual Funds and Assets under Management
Figure 2: TIPS Transaction Volumes and TIPS Mutual Funds
Top top panel plots the weekly TIPS transaction volumes, defined as 13-week moving average of
weekly averages of daily TIPS transaction volumes reported by primary dealers in Government
Securities Dealers Reports (FR-2004). The bottom panels plots number of TIPS mutual funds (left
axis) and the total net assets under management (left axis).)
55
1999
2000
2001
2002
2003
2004
2005
2006
2007
1
1.5
2
2.5
3
3.5
Michigan survey
SPF survey
TIPS breakeven
Figure 3: Survey Inflation Forecasts and TIPS Breakeven Inflation
This chart shows the 10-year TIPS breakeven inflation (red line), long-horizon Michigan inflation
forecast (blue line), and 10-year SPF inflation forecast (black pluses).
56
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
0
2
4
6
8
10
(a) Nominal Yields
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
0
2
4
6
(b) TIPS Yields
5−year
7−year
10−year
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
0
1
2
3
(C) TIPS Breakeven Inflation
7−year
10−year
Figure 4: Nominal and TIPS Yields and TIPS Breakeven Inflation
Top top panel plots the 3- and 6-month, 1-, 2-, 4-, 7- and 10-year nominal yields. The middle
panel plots the 5-, 7- and 10-year TIPS yields. The bottom panels plots the 5- and 7-year TIPS
breakeven inflation.)
57
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