3.3 Diagnostic test

together, we can obtain the correlation degree between the original curve and

Time Series Analysis - Data, Methods, and Applications

ri <sup>¼</sup> <sup>1</sup> <sup>n</sup> <sup>∑</sup> n k¼1

GM(1,1). It is critical to divide state and build transition matrix.

which <sup>Q</sup>1<sup>i</sup> <sup>¼</sup> Y k ^ ð Þþ <sup>E</sup>1<sup>i</sup> and <sup>Q</sup>2<sup>i</sup> <sup>¼</sup> Y k ^ ð Þþ <sup>E</sup>2<sup>i</sup>.

can get the <sup>l</sup>th step transition matrix P lðÞ¼ <sup>P</sup>ð Þ<sup>l</sup>

<sup>2</sup> <sup>Q</sup>1<sup>i</sup> <sup>þ</sup> <sup>Q</sup>2<sup>i</sup> ð Þ¼ Y k ^ð Þ¼ <sup>1</sup>

ð Þ¼ k Y<sup>0</sup>

3. Time series model (TSM)

transferring l step from the state Qi to the state Qj

ð Þ1 ; Y<sup>0</sup>

ð Þ2 ; …; Y<sup>0</sup> f g ð Þ m .

Markov chain is proposed by Andrey Markov (1856–1922), and it is a discrete time stochastic process with Markov property in mathematics. Given the current knowledge and information, historical information has no impact on the future. To improve prediction accuracy, Markov model is used to handle the data obtained by

To divide states, four rules are suggested to follow. Firstly, the partition state must have at least one true value in each state. Secondly, elements in a one-step transition matrix cannot be the same. Thirdly, the actual values must fall into one state. Finally, the state must pass Markov test. The numbers vary according to the original data. In this chapter, the overall level of FDI in China is on the rise while fluctuating in detail. Therefore, the level of FDI is a non-stable stochastic process. Taking the curve of Y k ^ð Þ¼ <sup>x</sup>^ð Þ <sup>0</sup> ð Þ <sup>k</sup> <sup>þ</sup> <sup>1</sup> as reference, the sequence can be divided into n states. The intervals can be denoted as Qi ¼ Q1<sup>i</sup>; Q2<sup>i</sup> ½ � and i ¼ 1, 2, …, n, in

Assuming that there are n states denoting as E1, E2, …, En, the transition proba-

The eventual forecast is in the center of the Gray zone, which is denoted as

Burg suggests that recursive algorithm estimated by the AR(P) model is the most practical one [29], while Hannan proposes time series with multidimensional linear stationary RMAð Þ p; q . The times series model mainly includes the autoregressive model and the moving average model [30–32], and generally the modeling steps are

ij 

n�n

.

. Mð Þ<sup>l</sup>

<sup>2</sup> ð Þ E1<sup>i</sup> þ E2<sup>i</sup> . Eventually, the forecasting sequence is

bility amounts to frequency approximately in general, namely, Pij <sup>¼</sup> <sup>M</sup>ð Þ<sup>l</sup>

εið Þk (13)

ij Mi

ij is the data of raw series

. Then, we

the fitting curve:

2.2 Markov model

2.2.1 Dividing states

2.2.2 Transition matrix

2.2.3 The forecasting value

Y0 ð Þ¼ <sup>k</sup> <sup>1</sup>

obtained as Y<sup>0</sup>

as follows.

104

The purpose of diagnostic test is to check and test the rationality of the model, including residual test, autocorrelation function of residual error and partial autocorrelation function test, and the significance test of parameters in the model.
