In the time series constituted by stock prices often linear trend curves can be seen. However, different trends are often present on different time scales. For example, can be a long-term trend will be overshadowed by short-term trends.
The Brandes-distribution examined, based on the particle filter method, the different trends and gains from a probability distribution for the probability of the market value.
The starting point is the adaptation of the regression line by the least squares method. For Brandes-distribution regression lines can be calculated for a plurality of time ranges. Each regression line is rated with a figure of merit, the results from the trend length and the standard deviation of the straight line. The process is analogous to the corresponding rating in Monte Carlo methods. So regression lines correspond to a 'particles' for a time range with a probability rating. In the Brandes-distribution of each line is assigned a Gaussian distribution, while the maximum of the weighted Gaussian distribution with the quality factor. The width of the Gaussian distribution corresponds to the standard deviation of the regression line. The superposition of the distributions of all the straight lines constituting the Brandes distribution. By extrapolation of the line with their distributions results in the future probability distribution of market values.
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