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2024-012 fix crossrefs
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_articles/RJ-2024-019/RJ-2024-019.Rmd

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@@ -260,9 +260,9 @@ typically acquired discretely at a set of grid points and are
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susceptible to contamination by random noise. This phenomenon can be
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represented as follows:
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$$\label{discr_data}
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Y_{i,k} = y_{i}(t_k) +\varepsilon_{i,k}, \quad k=1,\ldots, K. (\#eq:discr-data)$$
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$$
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Y_{i,k} = y_{i}(t_k) +\varepsilon_{i,k}, \quad k=1,\ldots, K. (\#eq:discr-data)
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$$
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In this expression, $t_k\in\mathcal{T}$, and $K$ denotes the count of
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discrete grid points across all samples. The $\varepsilon_{i,k}$ terms
@@ -279,9 +279,9 @@ $\mathbb{H}$. Each sample function $y_{i}(\cdot)$ in
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\@ref(eq:discr-data) is then considered as a finite linear combination
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of the first $d$ basis functions:
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$$\label{basis_expan}
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y_i(s)= \sum_{j=1}^d c_{ij}\nu_j(s). (\#eq:basis-expan)$$
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$$
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y_i(s)= \sum_{j=1}^d c_{ij}\nu_j(s). (\#eq:basis-expan)
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$$
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Subsequently, the coefficients $c_{ij}$ can be estimated using least
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square techniques. By adopting the linear representation form for the
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The roadmap of the main functions used in the
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[**Rfssa**](https://CRAN.R-project.org/package=Rfssa) package is given
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in Figure \@ref(fig:figroadpap). The inputs and outputs of these
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functions are described in Table \@ref(tab:1). As it can be seen from
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Table \@ref(tab:1), three classes (`funts`, `fssa` and `fforecast`) are
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functions are described in Table [1](#tbl:tab-1). As it can be seen from
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Table [1](#tbl:tab-1), three classes (`funts`, `fssa` and `fforecast`) are
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used to support the return objects of theses functions. The
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`funts(`$\cdot$`)`, `fssa(`$\cdot$`)` and `fforecast(`$\cdot$`)`
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functions are the constructors of the `funts`, `fssa` and `fforecast`
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classes, respectively. In the rest of this section we present these
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classes with illustrative examples, and later we describe the
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reconstruction and forecasting functions in details.
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::: {#tab:1}
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::: {#tbl:tab-1}
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-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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Function Descriptions Returns
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--------------------------- ------------------------------------------------------------------------------------------ --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------
@@ -591,8 +591,7 @@ reconstruction and forecasting functions in details.
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`fforecast(`$\cdot$`)` Performs FSSA R-forecasting or FSSA V-forecasting. An object of class `fssa`, list of numeric vectors includes indices of elementary components of a group used for reconstruction and forecasting and forecast horizon $h$. An object of class `fforecast`.
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-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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: Table 1: A summary of FSSA written functions in the
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[**Rfssa**](https://CRAN.R-project.org/package=Rfssa) package.
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: Table 1: A summary of FSSA written functions in the [**Rfssa**](https://CRAN.R-project.org/package=Rfssa) package.
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:::
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### The `funts` class {#subsec:fts}

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