There is a set of daily measurements. Time and measured values are both discrete. I want to find out whether measured values depend on the day the measurement was taken, or whether measurements are completely random. In other words, I want to find out if it is possible to predict measured values of a certain day or not.
- What subjects of statistics should I study to be able to solve this problem?
Please give me some keywords or direction.
Some more information. Imagine the following situation. A machine chooses each day a letter (simply a byte) and displays it on a screen. The process which is used to choose daily letter is unknown, but it is clearly algorithmic (not measure the wind speed or count people in the room or similar). Someone collected part of daily letter over a period of time and now wants to understand if it is possible to produce the next (or any) daily letter. Some methods possibly employed by the machine are considered "hard" (or random). For example use a secret key to encrypt the current date (predicting the next letter will be equivalent in most cases to braking the encryption). Other are considered "easy", for example xor of all bytes in date's representation. If the method is random, then there is no hope to produce the next daily letter.