Description of the Trend Map methodology

1. In general

Fias Market Signals describes, with this document, the Trend Map methodology and outlines the scientific scope. Fias Market Signals is aware of its breakthrough in calculating future trends using an external variable which correlates. Applying Time series in economical predictions is widely used (Time Series: Economic Forecasting, J.H. Stock, International Encyclopedia of the Social & Behavioral Sciences, Elsevier Science, 2001). The conclusion in the quoted article, begins as follows: ‘It is perhaps overly ambitious to hope for a simple prescription that provides a good forecasting method for all economic time-series’.

2. Input dataset of the methodology

The input of the methodology are historical exchange-rate data of the concerning sufficient liquid market. A history of minimal 35 years leads to the most reliable output.

Table 1: Different prediction methods sorted by type 


3. Type of method

The methodology of Trend Map is a multi-variate, which means that the output of Trend Map depends on the external variable and not only on the historical data, as in the case of uni-variate methods. The output of Trend Map is a non-linear function of the input, which means that the relation between input and output is not in proportion and therefore not constant.

4. External variable

The external variable that Trend Map uses is: time, as a physical quantity, different from the ISQ (International System of Quantities) base unit, seconds. Originally a second is a 60th part of a minute that again is a 60th part of an hour, while an hour is a 24th part of a day. A second is an 86 400th part of a day. Fias Market Signals uses a different quantitative dimension of time as a reference. This is the principle of the external variable.

5. k-nearest-neighbour-methode (kNN) for time series calculations

Trend Map uses the k-nearest-neighbour-method for time series calculations, with the use of the external variable, to get to the Trend Map output. The calculations of Fias Market Signals happen in the frequency (vibration) of the external variable. In the historical exchange-rate data according maps are found to determine the exchange-rate course within the future map (search-map). According maps are determined by the external variable, which determines the classification of the maps. The natural frequency of a market makes the method universally applicable.

Trend Map’s technology comprise of a search function in the time.

Characteristics (to ISQ base quantities).

Width of the search-frame b: 3 years
Length of the prediction h: 1 year
The magnitude of the nearest-neighbour parameter k: 5 or more over a period of 35 years
Direct prediction: in 1 time over the whole prediction period

Example 1: kNN-prediction with k=2 and the rank of the maps

6. Conclusion

The Trend Map methodology is a search-function applied on historical data that, by using an external variable and the nearest-neighbour-method, forms a mathematical formula for time series calculations of financial markets. This way of calculation gives a correlation of more than 80% between the calculation and the realized exchange-rate of the financial markets.