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Change iid to IID in heavy_tails.rst and kesten_processes.rst (#788)
- as per style guide
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source/rst/heavy_tails.rst

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@@ -172,7 +172,7 @@ One impact of heavy tails is that sample averages can be poor estimators of
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the underlying mean of the distribution.
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To understand this point better, recall :doc:`our earlier discussion
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<lln_clt>` of the Law of Large Numbers, which considered iid :math:`X_1,
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<lln_clt>` of the Law of Large Numbers, which considered IID :math:`X_1,
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\ldots, X_n` with common distribution :math:`F`
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If :math:`\mathbb E |X_i|` is finite, then

source/rst/kesten_processes.rst

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@@ -63,7 +63,7 @@ A **Kesten process** is a stochastic process of the form
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x_{t+1} = a_{t+1} x_t + \eta_{t+1}
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\quad \text{with } x_0 \text{ given}
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where :math:`\{a_t\}_{t \geq 1}` and :math:`\{\eta_t\}_{t \geq 1}` are iid
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where :math:`\{a_t\}_{t \geq 1}` and :math:`\{\eta_t\}_{t \geq 1}` are IID
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sequences.
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We will focus on the nonnegative scalar case, where :math:`x_t` takes values
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* the initial condition :math:`x_0` is nonnegative,
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* :math:`\{a_t\}_{t \geq 1}` is a nonnegative iid stochastic process and
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* :math:`\{a_t\}_{t \geq 1}` is a nonnegative IID stochastic process and
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* :math:`\{\eta_t\}_{t \geq 1}` is another nonnegative iid stochastic process, independent of the first.
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* :math:`\{\eta_t\}_{t \geq 1}` is another nonnegative IID stochastic process, independent of the first.
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@@ -122,7 +122,7 @@ The GARCH(1, 1) volatility process takes the form
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\sigma_{t+1}^2 = \alpha_0 + \sigma_t^2 (\alpha_1 \xi_{t+1}^2 + \beta)
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where :math:`\{\xi_t\}` is iid with :math:`\mathbb E \xi_t^2 = 1` and all parameters are positive.
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where :math:`\{\xi_t\}` is IID with :math:`\mathbb E \xi_t^2 = 1` and all parameters are positive.
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Returns on a given asset are then modeled as
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@@ -131,7 +131,7 @@ Returns on a given asset are then modeled as
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r_t = \sigma_t \zeta_{t+1}
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where :math:`\{\zeta_t\}` is again iid and independent of :math:`\{\xi_t\}`.
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where :math:`\{\zeta_t\}` is again IID and independent of :math:`\{\xi_t\}`.
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Notice that the volatility sequence :math:`\{\sigma_t\}`, which drives the dynamics, is a Kesten process.
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where :math:`\{R_t\}` is the gross rate of return on assets.
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If :math:`\{R_t\}` and :math:`\{y_t\}` are both iid, then :eq:`wealth_dynam`
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If :math:`\{R_t\}` and :math:`\{y_t\}` are both IID, then :eq:`wealth_dynam`
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is a Kesten process.
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@@ -386,7 +386,7 @@ We can express this idea by stating that a suitably defined measure
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\frac{s_{t+1}}{s_t} = a_{t+1}
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for some positive iid sequence :math:`\{a_t\}`.
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for some positive IID sequence :math:`\{a_t\}`.
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One implication of Gibrat's law is that the growth rate of individual firms
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does not depend on their size.
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s_{t+1} = a_{t+1} s_t + b_{t+1}
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where :math:`\{a_t\}` and :math:`\{b_t\}` are both iid and independent of each
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where :math:`\{a_t\}` and :math:`\{b_t\}` are both IID and independent of each
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other.
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In the exercises you are asked to show that :eq:`firm_dynam` is more

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