TAILIEUCHUNG - Elsevier, Neural Networks In Finance 2005_5

Tham khảo tài liệu 'elsevier, neural networks in finance 2005_5', tài chính - ngân hàng, ngân hàng - tín dụng phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 92 4. Evaluation of Network Estimation TABLE . BDS Test of IID Process Definition Operation Form m-dimensional xm xt . . . xt m t 1 . . . Tm-1 Tm-1 T - m vector xtm Form m-dimensional xs x s . . . xs m s t 1 . . . Tm Tm T m- 1 vector xSm Form indicator function IJ xm xmỊ max 1 xt 1 - xs i e i 0 1 . m-1 Calculate correlation integral C -2. T-1 V I- Cm T e 22 t 1 2 s t 1 Tm Tm-1-1 Calculate correlation integral Form Numerator Sample Standard Dev. of Numerator C. rr 9 V T-1 Y T I xt J C1 T e 2 Xt 1 Z- s t 1 T T-1 T Cm T e - C1 T m ơm T e Form BDS Statistic RD S1 T Cm T i -C1 T i m BDSm T e y T i Distribution BDSm T e - N 0 1 iid processes. This test known as the BDS test is unique in its ability to detect nonlinearities independently of linear dependencies in the data. The test rests on the correlation integral developed to distinguish between chaotic deterministic systems and stochastic systems. The procedure consists of taking a series of m-dimensional vectors from a time series at time t 1 2 . T m where T is the length of the time series. Beginning at time t 1 and s t 1 the pairs xtm xm are evaluated by an indicator function to see if their maximum distance over the horizon m is less than a specified value . The correlation integral measures the fraction of pairs that lie within the tolerance distance for the embedding dimension m. The BDS statistic tests the difference between the correlation integral for embedding dimension m and the integral for embedding dimension 1 raised to the power m. Under the null hypothesis of an iid process the BDS statistic is distributed as a standard normal variate. Table summarizes the steps for the BDS test. Kocenda 2002 points out that the BDS statistic suffers from one major drawback the embedding parameter m and the proximity parameter must be chosen arbitrarily. However Hsieh and LeBaron 1988a b c recommend choosing to be between .5 and standard deviations of the data. The choice of m depends on the lag we wish to .