A Time Series for the Years 1996-2001 Is Shown Below

question 147

Essay

A time series for the years 1996-2001 is shown below.
$$\begin{array} { | c | c | } \hline \text { Year } & y _ { \mathbf { t } } \\\hline 1996 & 125 \\1997 & 115 \\1998 & 120 \\1999 & 126 \\2000 & 140 \\2001 & 122 \\\hline\end{array}$$ The forecasts for the years 2002-2004 with three smoothing constant values are:
With w = .2,F₂₀₀₂ = F₂₀₀₃ = F₂₀₀₄ = 125.60
With w = .5,F₂₀₀₂ = F₂₀₀₃ = F₂₀₀₄ = 126.75
With w = .6,F₂₀₀₂ = F₂₀₀₃ = F₂₀₀₄ = 126.55
Compare each of the three sets of forecasts with the actual values for 2002-2004 given in the accompanying table,and compute the mean absolute deviation (MAD)for each model.Which model is best?
$$\begin{array} { | c | c | } \hline \text { Year } & y _ { \mathbf { t } } \\\hline 2002 & 130 \\2003 & 125 \\2004 & 135 \\\hline\end{array}$$

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Definitions:

Digestive System

The complex system of organs and glands responsible for the breakdown and absorption of food, extracting nutrients and eliminating waste.

Gallbladder

A small organ situated beneath the liver, responsible for storing and concentrating bile.

Duodenum

The first section of the small intestine in most higher vertebrates, where a significant part of digestion occurs.

Bile

A digestive fluid produced by the liver, stored in the gallbladder, and secreted into the small intestine to aid in the digestion and absorption of fats.