PokéBase - Pokémon Q&A
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I'm just wondering. Or is there no such thing as it?

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In Pokémon Colosseum, like in the main series games, there is a 1/8192
chance of a Shadow Pokémon being Shiny; however, when a Shiny Shadow
Pokémon is captured, it is highly improbable that the Pokémon will
retain Shininess. Conversely, when an ordinary Shadow Pokémon is
captured, there is still the 1/8192 chance of that Pokémon becoming
Shiny when it is sent to the player's party or the Pokémon Storage
System. Shininess is retained through purification. However, in
Pokémon XD, this glitch was corrected. When the game calculates a
personality value, it checks against the player's ID numbers and the
opponent's ID numbers. If the game were to generate a Shiny
personality value, it would then recalculate the personality value
until it would not be Shiny with both the player and the opponent's ID
numbers. As a consequence of fixing this glitch from Pokémon Colosseum
in Pokémon XD, the game ensures that all Shadow Pokémon are never
Shiny.

Source: http://bulbapedia.bulbagarden.net/wiki/Shadow_Pokémon

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