A Study On Inflation Forecasting With ECM-MIDAS Model

Based on a mixed-frequency error-correction(ECM-MIDAS) model, this paper uses non-stationary variables sampled at different frequencies that are possibly cointegrated to forecast Chinese inflation, including monthly macroeconomic variables and daily stock price.Inflation, one of the most important macroeconomic indicators, has been received more and more attention by governments,banks and private sector. Many foreign central banks have put increasingly emphasize on the future information rather than historical information about inflation since the last century, then adjust the policy in order to reduce economic shock. As we all know, excessive inflation has a harmful effect on economic and society. It leads to a decline in households' purchasing power, aover-investmentfor investors, a wider gap between rich and poor, a weaker in the comprehensive competitiveness and so on. Therefore, it is important to forecast the inflation accurately for not only governments but also banks and private sector when they make a decision.Traditional inflation forecast is mainly based on Phillips curve and ARIMA model which require same frequency data. However, it will ignore some information when we convert the high frequency data to low frequency data, then reduce accuracy and timeliness. In addition, most variables in the time series are non-stationary, probably leading to spurious regression if there is no cointegration relation among them. This paper builds ECM-MIDAS model by combing mixed data sampling model and cointegration in order to overcome these problems. On one hand, a series of high frequency data but not an aggregate low frequency data means more information, leading to a more accurate result, what's more, its feature of high frequency means updating quickly, leading to a timely result. On the other hand, ECM-MIDAS can deal with non- stationary variables sampled at different frequencies that are possibly cointegrated, avoiding spurious regression.We show that(a)the choice of the timing between the low frequency and high frequency variables to be included in the long-run has an impact on the forecasting performances. We consider the long-run relationship between yt-1 and some observation of x and give three possible cases for the disequilibrium error zt-1,'same-period' case,' x-after-y' case,' x-before-y' case. Then we list twenty-four cointegration equation based on three cases in order to see which case conforms real economy. By using mixed frequency data between 2006 and 2015, we find that the 'x-before-y' case gets a smallest RMSE, that is, a best forecast. Of course, this find agrees the common sense that MPI?M2?HS300 are leading indicators.(b)we compare estimation and forecasting performances in mixed-frequency regressions with low-frequency aggregated model, and find that the former is better at both estimation and forecast. As we known, more information means greater accuracy. MIDAS model include high frequency data which contains fluctuation information and then leads to a better result.(c)Furthermore, same as with same frequency time series, it can improve forecasting performances to introduce error-correction term to the mixed frequency model. Shown as the estimation result, the coefficient of EC is statistically significant, at the same time, RMSE with EC is more smaller then which without EC. They all indicate that error correction mechanism do exist in not only same frequency data model but also MIDAS model.(d)Finally, we explain the influence mechanism of every explanatory variables on China's inflation. The order of lagged variables indicates the length of impact time, the bigger order the longer impact. Shown as estimation result, the previous fluctuation of CPI has no effect on after fluctuation of CPI,M2 has more far-reaching effect on CPI then others, HS300 and PMI have positive impact on CPI, and so on.In short, ECM-MIDAS model has several advantages to forecast China's inflation. Low-frequency data ensures accuracy and high-frequency data ensures timeliness. They make mixed frequency model better than same frequency model together not only in-sample estimate but also out-of-sample forecast. What's more, combine of cointegration theory and mixed frequency model solves the problem of non-stationary when process data. At last, ECM-MIDAS include long-run term and shot-run term which can correct short-term forecast. This study is meaning for governments and central banks, and private when they makers decision.