Errata

p. 20 (2019-03-28): Caption of Figure 2.3 should say “…is proportional to the number of observed birds…”

p. 71 (2019-09-19): Penultimate line should say “…of size 80km”

p. 54 (2019-10-31): Second paragraph, last line should start with “precipitation,…”

Explanatory note for 2020-07-22 errata: In Ch. 1 – 3, the intercept variable “1” is listed along with p covariates. From Ch. 4 onwards, the intercept is absorbed into the covariate vector, x(s; t), which is specified there to be p-dimensional, in line with standard notation for multivariable regression. This leads to a slight abuse of notation and requires the following errata in Ch. 4 – 5.

p. 139 (2020-07-22): At the end of Section 4.1, add the sentence: “Note that in this and subsequent chapters, the covariate vector x(s; t) could include the variable “1,” which models an intercept in the multivariable regression.”

p. 140, line 22 (2020-07-22): Change “(p + 1) matrix given by…” to “p matrix given by…”

p. 152, Technical Note 4.2 (2020-07-22): Change “…column space of the m×(p + 1) design matrix X.” to “…column space of the m×p design matrix X.”

p. 223, line 3 (2020-07-22): Change “…is an n×(p + 1) matrix that could be time-varying…” to “…is an n×p matrix that could be time-varying…”

p. 277 (2020-12-24): On the line directly below (6.23), Z should be Z’, a row vector.

The following errata resulted from questions asked by Nicholas Antoniou; the authors are grateful for his careful reading of the book.

p. 320 (2020-12-24): On the right-hand side of (D.3), the sign in front of “b” should be “+”, not “–“.

p. 320 (2020-12-24): On the fifth line below (D.4), the vector Y_t should be an n-dimensional vector.
. On the same line, the matrix cap-phi should be an n x n_alpha matrix.

p. 320 (2020-12-24): On the sixth line below (D.4), the vector alpha_t contains the associated n_alpha expansion coefficients.

p. 323 (2020-12-24): In equations (E.1) and (E.2), delta_t = 1, and hence “delta_t” should not appear in these two equations.
. On the second line below (E.2), “delta_t” and “time-“ should be removed.

p. 341 (2020-12-24): In the first line, the range of t should be 2, …, T, and the line after (F.8) should read, “where h₁ is a specified initial value, Y_t is the n_y-dimensional response vector… “.
. In equation (F.3), the vector h_t² is defined elementwise, and hence it has the same dimension as the vector h_t; that is, both vectors are n_h-dimensional.
. On the fourth line below (F.9), remove “As in the basic ESN above,” and start the sentence as follows: “The matrix W is the n_h x n_h hidden-process-evolution weight matrix, …”
. On the fifth line below (F.9), the matrix U should be an n_h x n_x-tilde matrix.
. On the fifth and sixth lines below (F.9), the matrices V₁ and V₂ should both be n_y x n_h matrices.

p. 342 (2020-12-24): In the box showing Algorithm F.1, the step “2.” should carry out the calculation (using (F.4)) from t = 2, …, T.