2.2 Markov model

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

## 2.2.1 Dividing states

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 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>.
