Fig 1.
The structure of the Hidden Markov Model (HMM) that we build as the benchmark.
Fig 2.
The decision process of the Gaussian Mixture Model-Hidden Markov Model (GMM-HMM) that introduces Gaussian Mixture Model (GMM) to transform CPI series into a categorical sequence.
Fig 3.
The whole decision process of Long Short Term Memory Recurrent Neural Network and Hidden Markov Model (LSTM-HMM) with quarterly univariate-input that introduces LSTM to forecast CPI fluctuation states.
Fig 4.
The structure of the LSTM we build to predict CPI fluctuation states using historical CPI series.
Fig 5.
The trend of GDP year-on-year growth rate and CPI year-on-year growth rate.
Table 1.
The linear regression analysis of quarterly GDP growth rate and quarterly year-on-year CPI growth rate.
Table 2.
The result of Granger causality test of quarterly year-on-year GDP growth rate and quarterly year-on-year CPI growth rate.
Table 3.
The result of correlation analysis of quarterly CPI with one phase lag and quarterly GDP.
Fig 6.
The trend of GDP year-on-year growth rate and CPI year-on-year growth rate.
Table 4.
The threshold estimates from two-stage least squares estimation for the threshold model.
Table 5.
Least squares estimates of 2-regime threshold model that we build with CPI and GDP data.
Table 6.
The results of the threshold auto-regression model of the GDP growth rate.
Table 7.
GDP fluctuation states that differ in three types.
Table 8.
A general criteria for CPI fluctuation states with two different types.
Table 9.
Criteria of CPI fluctuation states for HMM with monthly input that vary in four types.
Fig 7.
The predictions of GDP fluctuation states using HMM(q) within 4-year time window.
Fig 8.
Confusion matrixes for prediction results from HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 4-year time window.
Table 10.
The number of observations and predictions of GDP fluctuation states within 4-year, 6-year, 8-year and 10-year time window.
Fig 9.
Confusion matrixes for prediction results from HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 6-year time window.
Fig 10.
Confusion matrixes for prediction results from HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 8-year time window.
Fig 11.
Confusion matrixes for prediction results from HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 10-year time window.
Fig 12.
ROC for HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input within 4-year, 6-year, 8-year and 10-year time windows.
Table 11.
Accuracy, kappa and AUC for HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 4-year time window.
Table 12.
Accuracy, kappa and AUC for HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 6-year time window.
Table 13.
Accuracy, kappa and AUC for HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 8-year time window.
Table 14.
Accuracy, kappa and AUC for HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 10-year time window.
Table 15.
Comparing HMM, GMM-HMM and LSTM-HMM with monthly or quarterly input and 4-year, 6-year, 8-year or10-year time windows based on Accuracy, Kappa and AUC.