Handbook of Economic Forecasting part 2 pps
Handbook of Economic Forecasting part 2 pps
... 28 7
Abstract 28 8
Keywords 28 8
1. Introduction and overview 28 9
1.1. Historical notes 29 0
1 .2. Notation, terminology, abbreviations 29 1
2. VARMA processes 29 2
2. 1. Stationary processes 29 2
2. 2. ... misspecified models 25 4
Acknowledgements 27 1
Part IV: Appendices and References 27 1
Appendix A: Assumptions 27 1
Appendix B: Proofs 27 5
References 28 0
PART 2: F...
Handbook of Economic Forecasting part 107 pps
... René M. Stulz
22 . HANDBOOK OF ECONOMIC GROWTH (in 2 volumes)
Edited by Philippe Aghion and Steven N. Durlauf
23 . HANDBOOK OF THE ECONOMICS OF GIVING, ALTRUISM AND
RECIPROCITY (in 2 volumes)
Edited ... Throsby
HANDBOOK OF LAW AND ECONOMICS
Editors A. Mitchell Polinsky and Steven Shavell
HANDBOOK OF THE ECONOMICS OF EDUCATION
Editors Eric Hanushek and Finis Welch...
Handbook of Economic Forecasting part 3 pps
... volatility 9
2. 1.3. The forecasting vector of interest 9
2. 2. Model completion with prior distributions 10
2. 2.1. The role of the prior 10
2. 2 .2. Prior predictive distributions 11
2. 2.3. Hierarchical ... distributions 17
2. 4. Forecasting 19
2. 4.1. Loss functions and the subjective decision maker 20
2. 4 .2. Probability forecasting and remote clients 22
2. 4.3. For...
Handbook of Economic Forecasting part 6 ppsx
... model averaging.
2. 4.4. Conditional forecasting
In some circumstances, selected elements of the vector of future values of y may be
known, making the problem one of conditional forecasting. That ... conventional. This is partially the case in the stochastic volatility model described
in Section 2. 1 .2. If, for example, the prior distribution of φ is truncated Gaussian and
tho...
Handbook of Economic Forecasting part 18 ppsx
... errors:
(14)ω
inv
=
σ
2
2
σ
2
1
+ σ
2
2
, 1 − ω
inv
=
σ
2
1
σ
2
1
+ σ
2
2
.
These weights result in a forecast error variance
(15)σ
2
inv
=
σ
2
1
σ
2
2
(σ
2
1
+ σ
2
2
+ 2
12
σ
1
σ
2
)
(σ
2
1
+ σ
2
2
)
2
.
After ... with the optimal weights:
(13)σ
2
c
(ω
∗
) =
σ
2
1
σ
2
2
(1 − ρ
2
12
)
σ
2
1
+ σ
2
2
− 2
12
σ
1
σ
2
.
It can easily be verified...
Handbook of Economic Forecasting part 20 pps
... is
(68)
¯
ω = ω
0
+
ˆτ
2
ˆσ
2
+ˆτ
2
(
ˆ
ω − ω
0
).
The empirical Bayes combination shrinks
ˆ
ω towards ω
0
and amounts to setting g =
ˆσ
2
/ ˆτ
2
in (67). Notice that if ˆσ
2
/ ˆτ
2
→ 0, the OLS estimator ... σ
−N−v
0
−1
exp
−(v
0
s
2
0
+ (ω −ω
0
)
M(ω − ω
0
))
2
2
.
Under normality of ε the likelihood function for the data is
(65)L(ω,σ|y,
ˆ
y) ∝ σ
−T
exp
−(y...
Handbook of Economic Forecasting part 21 pps
... normal mean:
¯y − 2. 58
σ
T
, ¯y + 1.96
σ
T
,
¯y − 1.96
σ
T
, ¯y + 2. 58
σ
T
.
The average of these confidence intervals, [¯y − 2. 27
σ
T
, ¯y + 2. 27
σ
T
] has a coverage of
97.7%. Combining ... estimation of the full covariance matrix for the
forecast errors.
Aiolfi and Timmermann (20 06) find evidence of persistence in the out -of- sample
performance of linear and nonlin...
Handbook of Economic Forecasting part 22 ppsx
... strategies, categories of economic variables
and forecast horizons (h).
All
TMB25% TMB50% TMB75% Mean Median TK DMSFE PB
h = 1 0.91 0. 92 0. 92 0. 92 0.94 0. 92 0. 92 1.00
h = 2 0.89 0.89 0.89 0.89 ... (h).
h = 1
TMB25% TMB50% TMB75% Mean Median TK DMSFE PB
US 0.88 0.89 0.90 0.90 0.93 0.90 0.91 1.00
UK 0.91 0.91 0. 92 0. 92 0.93 0.91 0. 92 1.00
Germany 0. 92 0.93 0.93 0. 92 0....
Handbook of Economic Forecasting part 24 pps
... use
CS2(i)–(ii) in the study of the limiting behavior of V
1T
and CS2(iii)–(iv) in the study
of V
2T
.
6
For example, if f(Y|X
t
,θ
0
) ∼ N(αX
t
,σ
2
),thenc
0.95
f
(X
t
) = 1.645 + σαX
t
.
20 8 ... − u
2
2
1
|u| 1
.
Also, define
(10)
M(j) =
1
0
1
0
φ(u
1
,u
2
) − 1
2
du
1
du
2
and
(11)
Q(j) =
(n − j)
M(j) −A
0
h
V
1 /2
0
,
with
A
0
h
=
h
−1
− 2...
Handbook of Economic Forecasting part 27 ppsx
... Appendix A.
21
For the case of h = 1, the limit distribution of ENC-T
corresponds with that of ENC-T ,giveninPropo-
sition 4 .2, and the limiting distribution is derived by McCracken (20 00).
23 6 V. ... predictability, a partial list of which includes Berkowitz
and Giorgianni (20 01), Mark (1995), Kilian (1999a), Clarida, Sarno and Taylor (20 03),
Kilian and Taylor (20 03), Ross...
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