# Errata

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

**p. 38 (2021-04-27)**: The right-hand side of equation (2.8) should be divided by 2.

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

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

**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 **h**_{1} is a specified initial value, **Y**_{t} is the n_{y}-dimensional response vector… “.

. In equation (F.3), the vector **h**_{t}^{2} 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 **V**_{1} and **V**_{2} 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.