1. Test（S）
• Test(S)
– Test(S) proposed by Okabe-Nakano [26]
• To test whether a given time series is a realization
of a local and weakly stationary process or not.
– A Criterion that multi-dimensional data are a
realization of a local and weakly stationary
process.
0

2. Test（S）: Z(m） μZ RZ
• Time Series Data Z(m）
– Sample mean vector μZ ,
– Sample covariance matrix function RZ
1

3. Test（S） X(n)

4. Test（S） KM2O-Langevin data
• Sample KM2O-Langevin data
– X: random force of data X
– ξ： one-dimensional standardized white noise

5. Test(S) Conditions
• Three Test Values (M) (V) (O)
(M) mean
(V) variance
(O) Co-variance
• Conditions
4

6. Test(S): Shifted data Xi
sample random force of data Xi
Effective number of the sample covariance matrix function Rx
5

7. Test Example with M
N=144，M=（3√146／１）－１≒35
Trials ：N－M＋１ → 144－35+1＝110
Χ(0),X(1), ,X(35) ,X(110) ,X(14３)
Χ0（0）,Χ0（1） ・・・・ Χ0（35） 0
Test
Χ1(0) Test 1
Χ2
Χi Test i
Χ110 Test 110

8. Test(S)
• Test(S) : The Rate of (M) i （V) i and (O)i which
Test(S) is accepted.
Total Passed ／ Trials (N－M＋１)
• (M) i 80%
• （V) i 70%
• (O) i 80%
7

9. 8