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Holt-Winters method with general seasonality

Tomáš Hanzák (2012)

Kybernetika

The paper suggests a generalization of widely used Holt-Winters smoothing and forecasting method for seasonal time series. The general concept of seasonality modeling is introduced both for the additive and multiplicative case. Several special cases are discussed, including a linear interpolation of seasonal indices and a usage of trigonometric functions. Both methods are fully applicable for time series with irregularly observed data (just the special case of missing observations was covered up...

How many bins should be put in a regular histogram

Lucien Birgé, Yves Rozenholc (2006)

ESAIM: Probability and Statistics

Given an n-sample from some unknown density f on [0,1], it is easy to construct an histogram of the data based on some given partition of [0,1], but not so much is known about an optimal choice of the partition, especially when the data set is not large, even if one restricts to partitions into intervals of equal length. Existing methods are either rules of thumbs or based on asymptotic considerations and often involve some smoothness properties of f. Our purpose in this paper is to give an automatic,...

How the result of graph clustering methods depends on the construction of the graph

Markus Maier, Ulrike von Luxburg, Matthias Hein (2013)

ESAIM: Probability and Statistics

We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable partition of the graph. Our main question is if and how the construction of the graph (choice of the graph, choice of parameters, choice of weights) influences the outcome of the final clustering result. To this end we study the convergence of cluster quality measures...

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