In tsmodels/tsets: Exponential Smoothing Models

knitr::opts_chunk$set(echo = TRUE)

\thispagestyle{fancy} \captionsetup[table]{labelformat=empty} \captionsetup[figure]{labelformat=empty}

library(xts)
options(kableExtra.latex.load_packages = FALSE)
library(kableExtra)
library(tsets)
library(rmarkdown)
x = readRDS(paste0(params$dir,"/tsets_estimate_tmp.rds"))
firstDate = as.character(x$spec$target$index[1])
lastDate = as.character(tail(x$spec$target$index,1))
tab = tsets:::.tables.tsets.estimate(x, digits=4)

Series: r params$name

Estimation Period: r paste0("[",firstDate,"/",lastDate,"]")

Model: r tab$model

X-Regressors: r ifelse(x$spec$model$include.xreg==1, NCOL(x$spec$xreg$xreg),0)

if (tab$n == 2) {
p1 <- kable(tab$params[[1]], format = "latex", caption = "Model Parameter Summary", longtable = T, booktabs = T) %>% kable_styling(position = "float_left", font_size = 6, latex_options = c("striped"))
p2 <- kable(tab$params[[2]], format = "latex",caption = "Model Parameter Summary[x-reg]",longtable = T, booktabs = T) %>% kable_styling(position = "float_left", font_size = 6, latex_options = c("striped"))
p3 <- kable(tab$info,format = "latex", longtable = T, booktabs = FALSE, row.names = FALSE, align = "c") %>% kable_styling(position = "float_left", font_size = 6, latex_options = "hold_position")
p3 <- gsub("\\\\hline", "", p3)
p3 <- gsub("\\|", "", p3)
p4 <- kable(tab$metrics, format = "latex", longtable = T, booktabs = FALSE, row.names = FALSE, align = "c") %>% kable_styling(position = "float_left", font_size = 6, latex_options = "hold_position")
p4 <- gsub("\\\\hline", "", p4)
p4 <- gsub("\\|", "", p4)
cat(c("\\begin{table}[!htb]
    \\begin{minipage}[t]{.6\\linewidth}
      \\raggedleft",
        p1,p3,p4,
    "\\end{minipage}%
    \\begin{minipage}[t]{.5\\linewidth}
      \\raggedright",
        p2,
    "\\end{minipage} 
\\end{table}"
))
} else {
p1 <- kable(tab$params, format = "latex", caption = "Model Parameter Summary", longtable = T, booktabs = T) %>% kable_styling(position = "float_left", font_size = 8, latex_options = c("striped"))
p2 <- kable(tab$info, format = "latex", caption = "Information Criteria", longtable = T, booktabs = T) %>% kable_styling(position = "float_left", font_size = 6)
p3 <- kable(tab$metrics, format = "latex", caption = "Performance Metrics", longtable = T, booktabs = T) %>% kable_styling(position = "float_left", font_size = 6)
cat(c("\\begin{table}[!htb]
  \\begin{minipage}[t]{.6\\linewidth}
    \\raggedleft",
      p1,
  "\\end{minipage}%
  \\begin{minipage}[t]{.4\\linewidth}
    \\raggedright",
      p2,p3,
  "\\end{minipage} 
\\end{table}"
))
}

\clearpage

rETS Decomposition"} plot(x)

\clearpage

Glossary of Key Metrics{-}

MAPE{-}

The MAPE (mean absolute percentage error) is a popular measure for forecast accuracy and is defined as :

$$ MAPE = 100\frac{1}{N}\sum\limits_{i = 1}^N {\left( {\frac{{\left| {{y_t} - {{\hat y}_t}} \right|}}{{\left| {{y_t}} \right|}}} \right)} $$

where $y_t$ denotes an observation and $\hat{y}_t$ denotes its forecast over N time periods. It has an asymmetric bias putting a heavier penalty on negative errors (when $y_t<\hat{y}_t$) than on positive errors.

MASE{-}

The MASE (mean absolute scaled error) scales the abolute error by a naive forecast so that values greater than one indicate that in-sample one-step forecasts from the naive method perform better than the forecast values under consideration.

$$ \frac{{\sum\limits_{i = 1}^N {\left| {{\varepsilon t}} \right|} }}{{\frac{N}{{T - m}}\sum\limits{i = m + 1}^T {\left| {{y_t} - {y_{t - i}}} \right|} }} $$

where $m$ is the seasonal period, and $m=0$ for non seasonal data. It is a symmetric measure of forecast accuracy penalizing positive and negative forecast errors equally, and is scale invariant so can be used to compare forecasts across data sets with different scale.

AIC{-}

Akaike’s Information Criterion (AIC) is a model selection metric penalizing the likelihood by the number of parameters used.

$$ 2k - 2log\left(\hat L\right) $$ where $k$ are the number of parameters and $L$ the maximum value of the likelihood function for the model. A model selected by the AIC after Gaussian MLE will give predictions equal to the conditional mean. It does not require nested models, but does require the same data be used. Asymptotically, minimizing the AIC is equivalent to minimizing the leave-one-out cross-validation mean squared error for cross-sectional data, and equivalent to minimizing the out-of-sample one-step forecast mean squared error for time series models. This property is what makes it such an attractive criterion for use in selecting models for forecasting.

tsmodels/tsets documentation built on Oct. 8, 2022, 9:15 a.m.