In binary classification of time series what is the accepted margin for measuring accuracy of classification or prediction that permit us to conclude that time series is not accidental, or vice versa?
Or. for example, if accuracy of classification or prediction of one event was a very near accident, 50/50 for example, 51% classified true and 49% false (or even 50.1% correct and 49.9 wrong), is it random or not (this time series consists of a succession of random steps or vice versa)? And how many times should we repeat that test?
A Time series is an stochastic process and it always considered as random. If it is non-random, there there would be no need to consider stochastic models such as models based on standard Box Jenkins methodology. A random error component is always there.
Dear Arash Moradi - an interesting question.
You do not state what is the nature of your time series data. In Neuron discharge for ewxample, a CUSUM technique was utilised by us (and others) over 30 years ago to establish statistical significance of a time series that you desire
[ QV 1. DATTA, A. K. & STEPHENS, J. A. (1980). Journal of Physiology 308,19-20P.
2. DATTA, A. K. & STEPHENS, J. A. (1983). Journal of Physiology 339. 2IP.
3. Datta et al. Journal of Physiology (1989), 413, pp. 213-231 ( PDF Paper attached)
4. Datta et al. (1990) Journal of Physiology 422, 397–419.
5. Datta et al (1991) Journal of Physiology 432,401–425.]
The technique was devised by Page at the University of Cambridge [ Page, E. S. (June 1954). "Continuous Inspection Scheme". Biometrika 41 (1/2): 100–115]
and used by the Imperial Chemical Industries (ICI) for quality control in paint production. Samples from a process are assigned weights , and summed as follows:
S0 = 0 ; Sn+1 = max ( Sn + x n - w n)
When the value of S exceeds a certain threshold value, a change in value has been found. The above formula only detects changes in the positive direction. When negative changes need to be found as well, the min operation should be used instead of the max operation, and this time a change has been found when the value of S is below the (negative) value of the threshold value. w represents the likelihood function, although this was not described explicitly by Page.
Hope this helps. Best wishes
A Time series is an stochastic process and it always considered as random. If it is non-random, there there would be no need to consider stochastic models such as models based on standard Box Jenkins methodology. A random error component is always there.
thanks for all answer, my research is on financial time series. and of course. at first, we consider it random. however, if for example for binary one we designed model that can classified correctly with accuracy near 50/50 in average for example in 51% of time correct and 49% of time incorrect. what we can conclude is it random or not I know that chaotic system but I want to know I classified as support Efficient market hypothesis or vice versa as predictable one.
again thanks a lot
do a "detrended fluctuation analysis" (available on web) and find the exponent characterizing the correlations
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