
Bayesian Forecasting and Dynamic Models
Mike West and Jeff Harrison
This list includes some points of clarification of text, as well as minor corrections,
for the 2nd Edition, 1st Printing (1997). These have been corrected/clarified in the
1999 2nd printing.
Note that we use some basic TeX notation, e.g., "X_t" is "X" subscripted "t", and so forth
Chapter 2
 p34, line 7
 In " ... is a local linear ..." the word "linear" should read "constant"
 p39, Theorem 2.2 (b) ... X_{t+k} should be X_t(k)
 p44, Theorem 2.3, three lines from the end of the proof.
 ... C_t=A_t/V ... should read
... C_t=A_t V ...
 p49, Section 2.4.1, third displayed equation.
 The lower limit on summation should be j=0 not j=o
and the upper limit should be t2
 the subscript tj+1 on a in the sum should be tj1
Chapter 3
 p74, line 14
 The final v_t should be the greek nu_t
 p91, Section 3.5, line 2
 In { F_t, 1,V_t, W,t } the W,t should of course be W_t
Chapter 4
 p104, l19, part (a)
 in N[0,W] the matrix W should be W_t
 p109, line 3
 In W^*_t the matrix W should be W , i.e., in bold font
 p117, Theorem 4.5 under "Retrospective Recurrence Relations" in the table
 B_v in the first line should be in bold font
 p126, Section 4.9.4, line 3
 Harrison (1996b) should be Harrison (1996)
 p127, Section 4.9.4, last line
 Harrison (1996b) should be Harrison (1996)
 p138, Exercise 2(b)
 D_t should be D_{t1}
 p140, Exercise 11(d)
 reference to "Theorem 4.7" should be "Theorem 4.5"
Chapter 5
 p160, Section 5.5.1, line 5.
 Harrison (1996a) should be Harrison (1997)
 p161162  a typesetting glitch only. The "diamond"
symbol indicating the end of the Proof of Theorem 5.4 should appear after the
proof, at the foot of page 161  it has slipped over onto the top of p162.
 p154160, part (ii) of Definitions 5.7 to 5.11 inclusive
 Definitions of "canonical equivalent models" also require initial priors to
be related as in the basic definition of equivalent models, second displayed equation of
Definition 5.4 (line 11 on p152)
 p160162
 Though based on normal models, the results here do indeed depend only on
the forms of the mean and variance recursions in constant DLMS, as stated at the start of Section 5.5.1.
So they are applicable under traditional least squares,
Kalman filtering and Bayesian least squares assumptions, for example.
 p161, Definition 5.12
The definition requires a condition to hold for all nonzero vectors.
In fact, the condition holds for zero vectors as well, so the definition
should omit the adjective nonzero
 p164, line 1
 the word observable should be omitted
 p172, Exercises 3 and 4
 the state vector elements \theta_{t1} and \theta_{t2} are scalars
and so should not be in bold font
 p173, Exercise 4(c)
 ... the DLM is observable ... should read
... the DLM is unobservable ...
 p174, Exercise 8(b)
 "... final n1 elements" should be "... final n elements"
 p174, Exercise 9(a)
 the second element of F should be 1 (one) not 0 (zero)
Chapter 6
 p205, Question 9(a)
 Theorem 4.7(i) and (ii) should be Theorem 4.5(i) and (ii)
Chapter 8
 p265, Question (7)
 In the definition of the frequency \omega
the term arccos{\sqrt(1+g^2)} should read
arccos{ 1 / \sqrt(1+g^2)}
 p266, Question (11) part (b)
 In the expression for \rho_t the element \omega_{t2} in the
second term should be \omega_{t1,1}
Chapter 9
 p275, line 10 (first line after displayed updating equations)
 In the expression for Q_t the term C_{t1} should, of course, be
R_t
 p302, line 4.
 West (1996a) should be West (1997)
 p304, Section 9.6.1, line 910
 Prado and West (1996) should be Prado and West (1997)
 p306, line 6 and last line
 Prado and West (1996) should be Prado and West (1997)
Chapter 10
 p362, Table 10.4, 2nd line under "Information"
 \delta is missing from the T dof; it should read
 (\theta_tD_{t1}) \sim T_{\delta n_{t1}}[a_t,R_t]
 p362, Table 10.4, 2nd line under "Forecast:"
 In the equation for Q_t the term S_{t1} should be k_t S_{t1}
 p364, in the final equation for n_t(k) the term + \delta n_{tk+1} should be +\delta n_t(k+1)
Chapter 11
 p383, Section 11.3.1, line 1 of para 2
 The firstorder polynomial model ... should be The secondorder polynomial model ...
 p416, l3.
 Add reference to Harrison and Lai (1999)
 p417, Section 11.6.3, line 10
 \mu=E(X_i\eta)=\dot a(\eta) not \dot g(\eta)
Chapter 12
 p469 at the top:
 p_t^*(j_t) should be p_t^*(j_t,j_{t1}) in both its definition in the displayed equation of line 4 and in the summation of line 5
 The summation of line 5 should be over index j_{t1} not j_t
 Similarly, p_t^*(j_{t1}) should be p_t^*(j_t,j_{t1}) in the displayed equation of line 9
Chapter 14
 p529, equation (14.33)
 lines 24 of this equation are missing the divisor /q_t, as
should be clear from equation (14.31).
Chapter 15
 p565, l1.
 Mueller, West and MacEachern (1996) should be 1997
 p569, line 8.
 West (1996d) should be West (1996c)
 p570, line 2
 singulavalue should read singularvalue
 p571, Section 15.3.1, line 4.
 West (1996a,b,d) should be West (1996a,c, 1997)
 p571, Section 15.3.1, line 5.
 West (1995 and 1996c) should be West (1995 and 1996b)
 p578, line 1.
 West (1996c) should be West (1996b)
 p579, line 3.
 West (1995, 1996a,b,c and d) should be West (1995, 1996a,b,c and 1997)
Chapter 16
 p584, line 3
 The Barbosa and Harrison paper should be dated (1992) not (1989)
Chapter 17
 p637, Bivariate Normal section
 The factor Q(.) in the exponent of the density function
should be divided by 1\rho_{ij}^2 and the
arguments Q(x_1, x_2) should be Q(x_i, x_ j ) throughout
 p649651, on Common eigenvalues and Jordan forms
 This section implicitly assumes we are dealing with the system matrix G
of an observable DLM. This should have been explicitly stated.
In such cases, G *must* be similar to the precise Jordan form as stated
(as clarified in Theorem 5.2, p155).
Also add a note on the more general Jordan forms for
G matrices of nonobservable models that are used in the proof of Theorem 5.2
(based on general theory, such as Theorem 8.5, p 106, of
E D Nerig, Linear Algebra and Matrix Theory, Wiley: New York, 1969).
That is, any system matrix G with one eigenvalue e of multiplicity n can be reduced to
a form diag( J_(r_1)(e),....., J_(r_m)(e))
with r_1+.....+r_m=n and where each J_(r_i)(e) is a standard Jordan block.
This might even be the diagonal case where each r_i=1 when G =e I.
This completes the general theory but is of little practical interest.
BIBLIOGRAPHY
References to be added that were wrongly omitted:
 O'Hagan, A., 1994, , "Kendall's Advanced Theory of Statistics, Volume 2B:
Bayesian Inference", Edward Arnold, London.
Corrections to existing references:
 p656: reference to Harrison, P.J., 1996a. Change to
 Harrison, P.J. , 1997. Convergence and the constant dynamic linear
model. J. Forecasting 16, 287292.
 p656: Harrison, P.J., 1996b should be just 1996
 p660: Prado, R., and West, M., 1996 ... etc .. should be changed to
 Prado, R., and West, M., 1997, Exploratory modelling of multiple nonstationary time series:
Latent process structure and decompositions.
In Modelling Longitudinal and Spatially Correlated Data,
(T. Gregoire, Ed). New York: SpringerVerlag.
 p664: West, M., 1996a. Change to
 West, M., 1997. Time series decomposition. Biometrika, 84, 489494.
 p664: West, M., 1996b becomes 1996a
 p664: West, M., 1996c becomes 1996b
 p664: West, M., 1996d becomes 1996c
New references to be added:
 Aguilar, O., and West, M., 1998a, Analysis of hospital quality monitors using hierarchical
time series models, Case Studies in Bayesian Statistics, Volume 4,
C. Gatsonis, R.E. Kass, B. Carlin, A. Carriquiry, A. Gelman, I. Verdinelli and M.West
(Eds), SpringerVerlag, New York.
 Aguilar, O., and West, M., 1998b, Bayesian dynamic factor models and variance matrix
discounting for portfolio allocation.
ISDS Discussion Paper 9803, Duke University.
 Aguilar, O., Huerta, G., Prado, R., and West, M., 1999, Bayesian
inference on latent structure in time series (with discussion), Bayesian Statistics 6,
J.O. Berger, J.M. Bernardo, A.P. Dawid, and A.F.M. Smith (Eds.), Oxford University Press.
 Cooper, J.D., and Harrison, P.J., 1997, A Bayesian approach to modelling
the observed bovine spongiform encephalopathy epidemic, J. Forecasting, 16, 355374.
 Harrison, P.J., and Lai, I.C.H., 1999, Statistical process control
and model monitoring, J App. Stat. 26, 273292.
 Nerig, E.D., 1969, Linear Algebra and Matrix Theory, New York: Wiley.
 Prado, R., Krystal, A.D., and West, M., 1999, Evaluation and comparison of EEG traces:
Latent structure in nonstationary time series, J. Amer. Statist. Assoc., 94, .
